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Mobility management and admission control in heterogeneous wireless networks Stevens-Navarro, Enrique 2008

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M O B I L I T Y M A N A G E M E N T A N D A D M I S S I O N C O N T R O L I N H E T E R O G E N E O U S W I R E L E S S N E T W O R K S by E n r i q u e Stevens-Navarro B.Sc, Un ivers idad A u t o n o m e de San L u i s Po tos i , M e x i c o , 2000 M.Sc, Institute Tecnologico y de Estud ios Superiores de Monterrey , Mex i co , 2002 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Doctor of Ph i losophy in T h e Facu l ty of Graduate Studies (E lec tr i ca l and C o m p u t e r Engineering) T h e Univers i ty O f B r i t i s h C o l u m b i a (Vancouver) Ju ly , 2008 © E n r i q u e Stevens-Navarro 2008 Abstract T h e for thcoming fourth generation (4G) heterogeneous wireless networks are a m i x t u r e of overlapped networks using different wireless access technologies and addressing different needs f rom the users. D u e to mobi l i ty , the users are able to switch connections among networks and hence to per form the so-called hor izontal and vert ica l handoffs. T h e present thesis makes contr ibut ions to the field of mob i l i t y management w i t h focus on handoff management and connection admiss ion control i n heterogeneous wireless networks. T w o different integrated heterogeneous systems are investigated: 1) the interworking of cel lular networks w i t h wireless local area networks ( W L A N s ) based on the I E E E 802.11 s tandard ; 2) the interwork ing of cel lular networks w i t h wireless metropohtan area networks based on the I E E E 802.16e s tandard . To this end, first we develop a novel vert i ca l handoff decision a lgor i thm by model ing the vert i ca l handoff prob lem as a M a r k o v decision process. O u r mode l considers the i m p o r t a n t tradeoff among the qual i ty of service (QoS) of the connection and the s ignal ing cost of performing a vert i ca l handoff. W e also take the connection durat i on into considerat ion for the handoff decision. Second, we propose an ana ly t i ca l model for admission control i n c e l l u l a r / W L A N interworking and investigate the combinat ion of different admiss ion control policies. O u r model considers m o b i h t y of users, capaci ty and coverage of each network, admission policies, and QoS i n terms of b locking and dropp ing probabi l i t ies . W e introduce the concept of po l i cy functions to model the admission control policies a n d formulate two different revenue m a x i m i z a t i o n problems. T h i r d , we extend the v i r t u a l p a r t i t i o n i n g technique w i t h preempt ion for admission control i n cel lular /802.16e interworking . W e propose admission contro l a lgor i thms for each type of connection request. W e also describe the expected m o b i l i t y scenario i n such integrated system. F i n a l l y , to achieve jo int design at the connection-level and packet-level , a joint QoS o p t i m i z a t i o n approach is used. Table of Contents A b s t r a c t i i Table of Contents i i i List of Tables v i List of Figures v i i List of A c r o n y m s x Acknowledgements x i i D e d i c a t i o n x i i i Statement of C o - A u t h o r s h i p x i v 1 Introduct ion 1 1.1 Heterogeneous Wireless Networks Interworking 1 1.2 Handof f Management 2 1.3 A d m i s s i o n C o n t r o l 4 1.4 S u m m a r y of Results and Contr ibut ions 6 1.5 Thesis Organ i za t i on 7 B i b l i o g r a p h y 8 2 M D P - b a s e d V e r t i c a l Handof f A l g o r i t h m for Heterogeneous Networks 14 2.1 R e l a t e d W o r k 16 2.2 M o d e l F o r m u l a t i o n 18 2.3 V e r t i c a l Handof f Decis ion A l g o r i t h m 20 2.3.1 State , R e w a r d Func t i on , and Trans i t i on P r o b a b i l i t y 20 2.3.2 O p t i m a l i t y Equat ions and the Value I terat ion A l g o r i t h m 22 2.4 Ver t i ca l Handof f Implementat ion Issues 22 2.4.1 System Discovery Phase 23 2.4.2 Implementat ion Detai ls 24 2.5 M o d e l Extens ions 25 2.5.1 E x t e n s i o n to A d d i t i o n a l QoS Parameters 25 2.5.2 E x t e n s i o n to User 's Preferences and Hor i zonta l Handof f 26 2.6 N u m e r i c a l Resul ts and Discussions 26 2.6.1 Results for C B R Voice Traffic 28 2.6.2 Results for F T P D a t a Traffic 30 2.6.3 Sens i t iv i ty A n a l y s i s 30 2.6.4 Structure of the O p t i m a l Po l i cy 31 2.6.5 N u m b e r of Iterations 32 2.7 S u m m a r y 32 2.8 Der ivat i on of E x p e c t e d T o t a l R e w a r d 33 B i b l i o g r a p h y 44 3 A d m i s s i o n C o n t r o l for M u l t i - S e r v i c e C e l l u l a r / W L A N System 47 3.1 C e l l u l a r / W L A N System M o d e l 49 3.1.1 Traffic and M o b i l i t y Mode ls 50 3.1.2 M u l t i - D i m e n s i o n a l B i r t h - D e a t h Processes 51 3.2 Connec t i on A d m i s s i o n C o n t r o l 56 3.2.1 P o l i c y Funct ions 56 3.2.2 P o l i c y Combinat i ons and O p t i m i z a t i o n Prob lems 59 3.3 N u m e r i c a l Results and Discussions 62 3.3.1 Results for O p t i m i z a t i o n P r o b l e m 1 64 3.3.2 Results for O p t i m i z a t i o n P r o b l e m 2 65 3.3.3 Results for Handoff Dif ferentiat ion 67 3.4 S u m m a r y 67 3.5 P r o o f of I E E E 802.11 W L A N C a p a c i t y M o d e l 68 3.6 Iterative F i x e d - P o i n t A l g o r i t h m 69 B i b l i o g r a p h y 78 4 V i r t u a l P a r t i t i o n i n g w i t h P r e e m p t i o n in Cei lu lar /802 .16e Interworking 81 4.1 System M o d e l 84 4.1.1 M o b i l i t y Scenario 84 4.1.2 Traffic and M o b i l i t y Mode ls 85 4.2 V i r t u a l P a r t i t i o n i n g w i t h Preempt ion for A d m i s s i o n C o n t r o l 88 4.2.1 A d m i s s i o n C o n t r o l for N e w Requests 89 4.2.2 A d m i s s i o n C o n t r o l for Handoff Requests 91 4.2.3 Connect ion- level M o d e l 92 4.2.4 Packet- level M o d e l 99 4.2.5 Jo int Connect ion and Packet- level QoS O p t i m i z a t i o n 101 4.3 N u m e r i c a l Results and Discussions 102 4.3.1 Effect of Increasing A r r i v a l Rate 103 4.3.2 Effect of Increasing M o b i l i t y 104 4.3.3 Performance C o m p a r i s o n w i t h a F i x e d P o l i c y 105 4.3.4 Jo int Q o S O p t i m i z a t i o n 105 4.4 S u m m a r y 106 B i b l i o g r a p h y 115 5 Conclusions a n d F u t u r e W o r k 119 5.1 S u m m a r y of W o r k Accompl i shed 119 5.2 Re lat ionship A m o n g Chapters and Discussions 121 5.3 Future W o r k 122 B i b l i o g r a p h y 124 Appendices A List of Publ icat ions 126 List of Tables 2.1 Parameters of the wireless networks 34 2.2 Parameters of the reward functions 34 4.1 QoS classif ication among 3 G cellular and I E E E 802.16e networks for admis- sion control 107 List of Figures 2.1 Co - l ocated heterogeneous wireless networks 34 2.2 T i m i n g d iagram of a M a r k o v Decis ion Process ( M D P ) 34 2.3 Funct ions his, a) and /d(s ,a) f rom the l ink reward funct ion 35 2.4 Effect under different swi tch ing cost Ki^a for C B R traffic 37 2.5 Effect under diflî'erent discount factor A for C B R traffic 38 2.6 Effect under different weight factor u for C B R traffic 39 2.7 Effect under different swi tch ing cost Ki^^ for F T P traffic 40 2.8 Effect under different discount factor A for F T P traffic 41 2.9 V a r i a t i o n of the average connection durat i on 42 2.10 St ruc ture of the M D P o p t i m a l po l i cy (^2 = 4 units and the user is current ly connected to network 2) 43 3.1 A n integrated c e l l u l a r / W L A N system 70 3.2 O p e r a t i o n of admission control using po l i cy functions i n the integrated cel- l u l a r / W L A N system 71 3.3 Aggregate network throughput i n a W L A N 72 3.4 Cost of b lock ing connections versus the arr iva l rate of new connection re- quests of service 1 and the arr iva l rate of new connection requests of service 2 for o p t i m i z a t i o n prob lem 1 72 3.5 Cos t of b lock ing connections versus the cost of dropp ing a connection request from a handoff user {an J for a l l s G 5 for o p t i m i z a t i o n prob lem 1 73 3.6 Handof f dropp ing probabi l i t ies i n cell 1 and W L A N 4 for CP"^ — CP"' versus the a r r i v a l rate of new connection requests of service 1 for op t imizat i on prob lem 1 73 3.7 Cost of b lock ing connections versus mob i l i t y in cell i for a l l i e M'^ for o p t i m i z a t i o n problem 1 74 3.8 Cost of b lock ing connections versus mob i l i t y i n W L A N k for a l l A; e W f for op t imizat i on prob lem 1 74 3.9 Cost of b lock ing connections versus ti ie arr iva l rate of new connection re- quests of service 1 and the arr iva l rate of new connection requests of service 2 for op t imiza t i on prob lem 2 75 3.10 Handoff dropp ing probabi l i t ies i n cell 1 and W L A N 4 for CP"^ - CP^ versus the arr iva l rate of new connection requests of service 2 for op t imizat i on problem 2 75 3.11 Cost of b lock ing connections versus mob i l i t y i n cell i for a l l i € M'^ for o p t i m i z a t i o n prob lem 2 76 3.12 Cost of b lock ing connections versus mob i l i t y i n W L A N A; for a l l A; e W f for op t imiza t i on prob lem 2 76 3.13 H o r i z o n t a l and vert i ca l handoff dropping probabi l i t ies i n cell 1 and W L A N 4 for CP'^ — CP"' versus the arr iva l rate of new connection requests of service 1. 77 4.1 Integrated 3 G cel lular /802.16e system 108 4.2 Integrated 3 G cel lular /802.16e system 108 4.3 Hor i zonta l and vert ica l handoff rates w i t h [i,]} G M'^ and {k,l] € A I " . . . 109 4.4 Pr ior i t i es of the different connection requests of service s € SRT i n cell i e M". Case 1 (a^c > Case 2 (a^c < /?=), and Case 3 (a^c = /3f ) 109 4.5 N e w connection b locking probab i l i ty i n cell C I and cel l E l versus the arr iva l rate of connection requests from service 2 110 4.6 H o r i z o n t a l handoff dropp ing probabi l i ty i n cel l C I and cell E l versus the arr iva l rate of connection requests from service 2 I l l 4.7 V e r t i c a l handoff dropp ing probabiUty i n cell C I and cell E l versus the arr iva l rate of connection requests from service 2 112 4.8 Packet loss probab i l i ty i n cell C I and cell E l versus the arr iva l rate of connect ion requests from service 2 112 4.9 H o r i z o n t a l handoff dropping probabi l i ty i n cel l C I and cel l E l versus the level of mob i l i t y 113 4.10 V e r t i c a l handoff dropping probabi l i ty in cell C I and cell E l versus the level of m o b i l i t y 113 4.11 H o r i z o n t a l and Ver t i ca l dropping probabi l i t ies . Performance comparison w i t h a fixed po l i cy 114 4.12 New connection b lock ing probabi l i ty . Compar i son between w i t h and w i t h - out using jo int connect ion and packet-level QoS op t imiza t i on 114 List of Acronyms 3 G T h i r d generation 4 0 F o u r t h generation 3 G P P T h i r d generation partnership project 3 G P P 2 T h i r d generation partnership project 2 A P Access point A S N Access service network B B U Bas i c b a n d w i d t h unit B S Base stat ion C B R Constant bit rate C P Cuto f f pr ior i ty D G F D i s t r i b u t e d coordinat ion funct ion F G Frac t i ona l guard channel F T P F i l e transfer protocol G R A G r e y re lat ional analysis I P Internet protocol M A C M e d i u m access control M D P M a r k o v decision process M I H M e d i a independent handover List of Acronyms N R T Non-rea l - t ime P F C P o i n t coord inat ion funct ion R A N R a d i o access network R S S Received s ignal strength R T R e a l - t i m e S A W S imple addit ive weighting T C P Transmiss ion control protocol T O P S I S Technique for order preference by s i m i l a r i t y to ideal solut ion U D P User da tagram protocol V I A Va lue i terat ion a lgor i thm V P V i r t u a l p a r t i t i o n i n g W i M A X W o r l d w i d e Interoperabi l i ty for Microwave Access W L A N Wireless l oca l area network Acknowledgements I would l ike to express m y deep grat i tude to D r . V i n c e n t W o n g for a l l these years of research work under his supervis ion as graduate student. W i t h o u t his guidance, this thesis would not be possible. F r o m his example, I learned what professional academic life is a l l about. I also want to thank a l l the members of m y supervisory committee for their comments and t ime , D r . V i c t o r L e u n g , D r . L u t z L a m p e , and D r . V i j a y Bhargava . Spec ia l thanks to A m i r - H a m e d M o h s e n i a n - R a d , Y u x i a L i n , C h i S u n , M i n h H a n h Ngo , Jie Zhang , and V i j a y V i v e k a n a n d a n , w h o m I have the great oppor tun i ty to col laborate on w i t h d u r i n g these four years. T h a n k s to m y lov ing wife M a g d a , she encouraged me never to give up. T h a n k s to m y daughter M a r i a Cons tanza , she l ightened m y life since she arr ived to this wor ld . T h a n k s to our coming baby, he gives me hope for a better tomorrow. T h a n k s also to m y brother A d r i a n , to m y parents G u i l l e r m o and L u p i t a , and to my parents- in- law Fe l ix and Cons tanza for a l l their support d u r i n g these years. T h i s work has been supported by B e l l C a n a d a , the N a t u r a l Sciences and Engineer ing Research C o u n c i l ( N S E R C ) of C a n a d a , the Univers idad A u t o n o m a de San L u i s Potos i ( U A S L P ) , and the P r o g r a m a de Mejoramiento del Profesorado ( P R O M E P ) from Mex i co . Dedication With love, to my family. Statement of Co-Authorship I a m the first author and p r i n c i p a l contr ibutor of a l l manuscr ipt chapters. A l l chap- ters are co-authored w i t h D r . V incent W . S . Wong , who supervises the present thesis research. C h a p t e r 2 is also co-authored w i t h Y u x i a L i n , who contr ibuted to the t rans i t i on probabi l i t ies ca l cu lat ion of the W L A N . C h a p t e r 3 is also co-authored w i t h A m i r - H a m e d M o h s e n i a n - R a d , who contr ibuted to the effective capacity of the W L A N as well as the formulated o p t i m i z a t i o n problems. Chapter 1 Introduction Current ly , there are various different wireless networks being deployed. E a c h one aims to address different needs and requirements from the mobi le users. Examples of those net- works include the t h i r d generation (30 ) of cel lular networks, broadband wireless met ropo l i - tan area networks ( W M A N s ) , wireless local area networks ( W L A N s ) , and personal area networks ( P A N s ) . A l l these wireless networks are heterogeneous i n the sense of the different radio access technologies as wel l as the network protocols that they use [1, 2]. T h e t rend is to integrate complementary wireless networks w i t h over lapping coverage. T h e emerging state-of-the-art mobi le devices or mobi le stations w i l l be equipped w i t h mul t ip le network interfaces to access different available wireless networks. These new mo- bile devices w i l l provide the user w i t h great f lexibi l i ty for network access and connectivity. These are new and chal lenging problems on mob i l i ty support among different networks. Users w i l l expect to continue their connections without any d i s rupt i on when they move from one network to another. To deal w i t h these new mobility issues as well as to proper ly l i m i t the number of users that can be accepted into the networks, the present thesis makes contr ibut ions to the field of m o b i l i t y management and admiss ion control i n heterogeneous wireless networks. 1.1 Heterogeneous Wireless Networks Interworking W i t h i n the realm of heterogeneous wireless networks, the in terwork ing of 3 G cel lular net- works w i t h other wireless networks has gained a lot of a t tent ion i n recent years. S t a n - dard izat ion has been conducted w i t h i n the 3 G s tandard izat ion groups, the 3 0 Partnersh ip Pro ject ( 3 G P P ) [3] and the 3 G P P 2 [4], to integrate cel lular networks w i t h W L A N s based on the I E E E 802.11 fami ly of standards. Several levels of integrat ion have been proposed ranging from common b i l l i n g and customer care to seamless m o b i l i t y [5, 6, 7]. W i t h i n the research community , two interworking architectures has been proposed, loosely and tightly coupled architectures [8, 9]. In t ight ly coupled, the W L A N s are d irect ly connected to the ce l lular core network as other access networks. In loosely coupled, the networks are connected through the Internet by a gateway. F r o m the pract i ca l point of v iew, loosely coupled is preferred for short - term deployments [8 . M o r e recently, the interworking of 3 G cel lular networks w i t h mobile broadband W M A N s has become a very relevant case for the coming years. T h e reason is the revision I E E E 802.16e or I E E E 802.16-2005 [10] of the I E E E 802.16 s tandard , which is c ommonly k n o w n as W o r l d w i d e Interoperabi l i ty for Microwave Access ( W i M A X ) . T h e I E E E 802.16e is able to support mobi le terminals , and hence is referred to as mobile WiMAX. W i t h i n the W i M A X forum, the architecture for interworking w i t h 3 G cel lular networks has been s tandard ized i n [11, 12]. T h e proposed network architecture considers the loosely coupled in terwork ing architecture. T h u s , mobi le broadband access networks based on the I E E E 802.16e s tandard are becoming competent and flexible access alternatives to the already deployed ce l lular access networks [13 . 1.2 Handoff Management T h e process of swi t ch ing a connection among networks is referred to as handoff or handover. Trad i t i ona l ly , the handoff process has been studied among wireless networks using the same access technology (e.g., among two base stations (BSs) of a cel lular network) . T h i s handoff process is referred to as horizontal handoff. Such handoff mechanisms m a i n l y use the received s ignal strength (RSS) from the surrounding B S s to trigger the handoff process. For an excellent survey on those handoff a lgor i thms, please refer to [14]. T h e hor izonta l handoff a l g o r i t h m decides to which B S should the connect ion be transferred to, and it is usual ly the one w h i c h provides the highest s ignal level to the mobile device. O n the other h a n d , w i t h the emerging m i x t u r e of overlapped heterogeneous wireless networks, handoff becomes a more compl icated process and some of the previous handoff management techniques cannot be used [15]. T h e new handoff process among networks using different access technologies is referred to as vertical handoff [16] (e.g., f rom a B S to a W L A N access po int ( A P ) ) . To deal w i t h this new vertical mobility problem, novel and improved handoff management techniques are required. T h e handoff decision i n this case requires consider ing add i t i ona l parameters besides the R S S . E x a m p l e s of such parameters, referred to as handoff metrics, are: available b a n d w i d t h , delay, j i t t e r , access cost, t ransmit power, current battery status of the mobi le device, and even the user's preferences. Several vert i ca l handoff decision algorithms have been proposed i n the l i terature. T h e pol icy-enabled system is proposed i n [17]. T h e idea is to separate the decision m a k i n g f rom the handoff mechanism as i n hor izontal handoffs schemes. T h e vert ica l handoff a lgor i thms use handoff metrics to decide which network to use, referred to as the target network. In [18], a generic handoff decision funct ion is presented. It allows users to pr ior i t i ze the different networks characteristics and assigns weights to different network factors. S i m i l a r handoff decision approaches using weighted cos t / r eward functions have been proposed i n 19, 20, 21]. M u l t i p l e a t t r ibute dec is ion-making ( M A D M ) methods have also been proposed to deal w i t h the vert ica l handoff decision. T h e simple addi t ive weighting ( S A W ) and the technique for order preference by s i m i l a r i t y to ideal so lut ion ( T O P S I S ) decision algor i thms were considered i n [22, 23]. T h e gray re lat ional analysis ( G R A ) and the ana ly t i ca l hierarchy process ( A H P ) techniques were appl ied in [24, 25]. In [26], a comparison among several M A D M decision a lgor i thms for vert ica l handoff such as S A W , T O P S I S , G R A , and the mul t ip l i ca t ive exponent weighting ( M E W ) was performed. T h e E L E C T R E a lgor i thm was considered i n [27 . There are also vert i ca l handoff a lgor i thms which follow the approach based on suitable R S S measurements from the available networks [28, 29, 30, 31]. U s u a l l y the decision a l g o r i t h m is different i f the user is mov ing out of the coverage or mov ing i n the coverage of the preferred network. Some algor i thms proper ly trade off several performance parameters as i n [28, 31] (e.g., the number of unnecessary vert i ca l handoffs). O t h e r proposals of vert i ca l handoff a lgor i thms have studied the handoff decision by us ing fuzzy logic [32, 33 and neura l networks [34, 35]. A l t h o u g h there have been various vert i ca l handoff a lgor i thms proposed i n the l i terature , our research work is mot ivated by two part i cu lar aspects. F i r s t , the connection durat i on needs to be taken into account d u r i n g the vert i ca l handoff decision. Second, the process- ing and s ignal ing load d u r i n g the vert i ca l handoff execution also needs to be taken into consideration. O u r work aims to incorporate these two aspects i n the model formulat ion of vert i ca l handoff decision. To deal w i t h the vert i ca l handoff decision prob lem i n heterogeneous wireless networks, we use the M a r k o v decision process ( M D P ) model [36]. T h e M D P theory is a powerful too l to model and to analyze sequential decision problems under uncertainty. To solve our M D P prob lem and determine the o p t i m a l policy, we use the value i terat ion a lgor i thm ( V I A ) [36]. It is wide ly used due to its conceptual s impl i c i ty , and to its ease i n cod ing and implementat i on . A l s o , i n our early research on the vert ica l handoff decision, we also use several M A D M r a n k i n g methods such as S A W , T O P S I S and M E W [37]. Such methods faci l i tate the decision process a n d alternative selection when several and usually confl ict ing cr i ter ia need to be considered. 1.3 Admission Control In order to guarantee the qua l i ty of service (QoS) of the different m u l t i m e d i a applications (e.g., voice, real - t ime video) , i t is necessary to l i m i t the number of connections that can be accepted into a network. A n appropriate connection admission control policy is required i n each network. A n admiss ion control po l i cy cans either accept a connection request and allocate the resources accordingly, or reject the connection request. Tradi t ional ly , i n wireless cel lular networks, higher pr i o r i ty is given to the connect ion requests from the handoff users (as opposed to the new users) since from the users' po int of view, hav ing a connection a b r u p t l y t e rminated is more annoying t h a n being blocked occasionally on new connection attempts. However, in heterogeneous wireless networks, due to the m o b i l i t y of the users, they are able to switch connections among networks and hence to perform hor izonta l and vert ical handoffs. Since now there are two types of handoffs, each one w i t h different execution procedures (e.g., s ignal ing overload, context and authent icat ion transfer) , the t rad i t i ona l approach of g iv ing pr i o r i ty to hor izonta l handoff users over the new users needs to be extended. In fact, as the interwork ing architectures are implemented and the mul t i -mode mobile devices become available, the number of vert i ca l handoffs w i l l increase. T h u s , novel handoff management and admiss ion control techniques are required [15, 38, 39]. Further considerations need to be taken into account and the appropriate mobiUty scenarios should be investigated. Regard ing the case of connection admission control in c e l l u l a r / W L A N interworking, several approaches and models have been proposed i n the l i terature . A d m i s s i o n control schemes considering only single-service class (i.e., i t is assumed that a l l connections request the same amount of b a n d w i d t h resources) have been proposed i n [40, 41 , 42]. Some recent work i n c e l l u l a r / W L A N interworking aims to differentiate service requirements. Thus , admission contro l considering support for multi-service classes has been considered i n [43, 44, 45]. However, most of the previous works have only focused i n the single-cell w i t h s i n g l e - W L A N case. A l t h o u g h there have been various models and admiss ion contro l poUcies proposed i n the hterature for c e l l u l a r / W L A N interworking , our work is mot ivated by three par t i cu lar aspects. F i r s t , the consideration of several W L A N s deployed inside the cell of a wireless cel lular network. Second, the support of mul t ip le service classes w i t h different b a n d w i d t h requirements. T h i r d , the effect of using a combinat ion of different admission control p o l i - cies i n wireless access networks. O u r research work aims to incorporate these impor tant aspects i n an opt imizat ion-based design for connection admission control i n integrated c e l l u l a r / W L A N systems. Regard ing the case of connection admission control i n cel lular /802.16e interworking , few approaches and models have been proposed i n the l i terature . Connect ion admission control i n mobi le broadband wireless networks based on the I E E E 802.16e s tandard has been recently investigated i n [46, 47, 48]. However, none of these previous works consider the interworking and m o b i l i t y issues of I E E E 802.16e systems w i t h 3 G cel lular networks. A c c o r d i n g to [39], the support for multi-class services (e.g., m u l t i m e d i a sessions) and the joint design at the connection and packet-level are impor tant design objectives for admission control and for Q o S provis ioning i n heterogeneous wireless networks. O n the other hand , the V i r t u a l P a r t i t i o n i n g ( V P ) is an efficient, fair and robust resource sharing technique or ig inal ly proposed i n [49]. T h e V P technique has been recently proposed for admission control i n c e l l u l a r / W L A N interworking i n [50, 51 . O u r research work i n cel lular /802.16e interworking is mot ivated by three par t i cu lar aspects. F i r s t , the need of suitable m o b i l i t y scenarios for the case of cel lular networks and 802.16e networks i n terms of the expected hor izontal and vert i ca l handoff. Second, the extension of V P for admission control in heterogeneous wireless networks. T h i r d , the consideration of connection-level and packet-level performance metrics i n the design of admiss ion control and handoff polices. O u r research work aims to incorporate these impor tant aspects for connect ion admission control i n integrated cel lular/802.16e systems. To deal w i t h the admission control prob lem in heterogeneous wireless networks, we use the theory of mult i -service loss systems [52]. In such queuing systems, when a connection request arrives to the system, it can be either admi t ted or blocked and lost. Loss systems have been wide ly used to evaluate the performance of te lecommunicat ion systems at the connection-level (i.e., i n terms of b lock ing probabi l i t ies) . To solve our admission control model , we use the reduced-load approx imat ion and the i terat ive a lgor i thm of repeated subst i tut ions [52]. In our final prob lem, we consider the jo int design at the connection and packet (i.e., i n terms of packet loss probabil i t ies) levels [53 . 1.4 Summary of Results and Contributions This thesis covers the problems of handoff management and admission control i n het- erogeneous wireless networks w i t h special focus on c e l l u l a r / W L A N and cel lular /802.16e interworking. T h e results are d iv ided i n 3 chapters. T h e contr ibutions i n each chapter are as follows. • C h a p t e r 2 presents a novel ver t i ca l handoff decision a lgor i thm for heterogeneous wireless networks. T h e objective of this chapter is to determine the condit ions under which vert ica l handoff should be performed. T h e vert i ca l handoff decision prob lem is formulated as an M D P w i t h the objective of m a x i m i z i n g the t o ta l expected reward per connection. T h e network resources ut i l i zed by the connection are captured by a l i n k reward funct ion. A s ignal ing cost is used to mode l the s ignal ing and processing l oad incurred on the network when vert i ca l handoff is performed. T h e value i t e rat i on a lgor i thm is used to compute a s tat ionary determinist i c policy. For the performance evaluat ion , voice and d a t a appl icat ions are considered. T h e numerica l results show that our proposed scheme performs better t h a n other vert i ca l handoff decision algo- r i thms such as S A W [22], T O P S I S [22], and G R A [24]. T h e work i n this chapter has been inc luded i n a publ ished j o u r n a l art ic le [54], and a publ ished conference paper 55 . • C h a p t e r 3 presents an ana ly t i ca l model to faci l i tate the evaluat ion of different admis - sion control policies i n a mult i -service integrated c e l l u l a r / W L A N system. T h e mode l takes into account the mob i l i t y and the rate of connect ion requests of the users, the capac i ty and the coverage area of each network, the admission control policies, and the Q o S requirements i n terms of b lock ing and dropp ing probabi l i t ies . T h e admis - sion control policies are inc luded by der iv ing their corresponding poUcy functions. T w o different revenue m a x i m i z a t i o n problems are formulated. E a c h prob lem takes different Q o S requirements into account. B y so lv ing the equivalent cost m i n i m i z a t i o n problems, we evaluate the system performance when different combinat ions of cutoff p r i o r i ty ( C P ) [56] and fract ional guard channel ( F G ) [57] admiss ion control policies are be ing used. Results show that using the C P po l i cy i n b o t h wireless access net- works can achieve the o p t i m a l so lut ion for the two o p t i m i z a t i o n problems under a wide range of network conditions. T h e work i n this chapter has been inc luded i n an accepted j o u r n a l art ic le [58], and a publ ished conference paper [59 . • C h a p t e r 4 presents our extension of the V P w i t h preemption tecimique for admission control i n ce l lular /802.16e interworking. F i r s t , we describe the mob i l i t y scenario be- tween 3 G cel lular networks and I E E E 802.16e networks i n terms of the hor izontal and vert ical handoffs that can occur and derive the corresponding handoff rate equations. W e then propose admission control a lgorithms for connection requests that consider the class of service (i.e., real - t ime (RT) or non-real - t ime ( N R T ) ) and the type of user (i.e., new or handoff) . For the handoff requests, different pr ior i ty is assigned to each type of handoff. A jo int connection and packet-level op t imizat i on approach is used for QoS provis ioning . T h e performance of the integrated system is evaluated i n terms of new connect ion b lock ing probabihties , handoff dropping probabi l i t ies , and packet loss probabi l i t ies . N u m e r i c a l results show performance improvement when preemp- t i o n and the jo int Q o S opt imizat i on approach are used. T h e work i n this chapter w i l l be s u b m i t t e d for pub l i ca t i on . Some parts have been publ ished i n a conference paper [50 . 1.5 Thesis Organization T h e remainder of the thesis is organized as follows. O u r proposed vert ica l handoff deci- sion a lgor i thm is described i n C h a p t e r 2. W e present our model for admission control i n c e l l u l a r / W L A N interwork ing i n C h a p t e r 3. W e describe the mob i l i t y scenario and extend V P w i t h preemption for admiss ion control i n cel lular /802.16e interworking i n C h a p t e r 4. 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W o n g , "Connec t i on A d m i s - sion C o n t r o l for M u l t i - S e r v i c e Integrated C e l l u l a r / W L A N System, " IEEE Trans. Veh. TechnoL, i n press, 2008. 59] , " O n O p t i m a l A d m i s s i o n C o n t r o l for M u l t i - S e r v i c e C e l l u l a r / W L A N Interwork- i n g , " i n Proc. of IEEE GLOBECOM'07, Washington , D C , November 2007. Chapter 2 A n MDP-based Vertical Handoff Decision Algorithm for Heterogeneous Wireless Networks T h e architecture for the B e y o n d 3rd Generat ion ( B 3 G ) or 4 G wireless networks aims to integrate various heterogeneous wireless access networks over an I P (Internet Protoco l ) backbone. Current ly , there are various s tandard izat ion bodies work ing towards this v is ion. Examples include the 3 G P P [1], 3 G P P 2 [2], and the I E E E 802.21 M e d i a Independent Handover ( M I H ) work ing group [3]. T h e 3 G P P and 3 G P P 2 have standardized the i n - terconnection requirements between 3 G wireless cel lular systems and W L A N s to provide m o b i l i t y support to users roaming between both systems. Several levels of integrat ion have been proposed ranging from simple common b i l l ing and customer care to seamless m o b i l i t y and session cont inu i ty [4, 5]. In order to provide seamless mobi l i ty , one of the design issues is the vertical handoff support . V e r t i c a l handoff occurs when connections switch from one network to another (e.g., f rom W L A N to Code D i v i s i o n M u l t i p l e Access I x R a d i o Transmiss ion Technology ( C D M A I x R T T ) ) . It is different from conventional hor izonta l handoff i n which the mobi le terminals just move from one B S to another w i t h i n the same access network. In the htera- ture , ver t i ca l handoff is also referred to as intersystem handoff, while hor izontal handoff is referred to as intrasystem handoff [6]. In B 3 G / 4 G wireless networks, mobi le terminals are envisioned to be equipped w i t h mul t ip le interfaces to establish connections w i t h different types of wireless access networks. T h u s , seamless vert ica l handoff is an impor tant network operat ion. T h e vert i ca l handoff process involves three m a i n phases [7, 8], namely system discovery, vertical handoff decision, and vertical handoff execution. Different access networks can be version of this chapter has been published. Enrique Stevens-Navarro, Y u x i a L i n , and Vincent W . S . Wong, " A n M D P - b a s e d Vertical Handoff Decision Algor i thm for Heterogeneous Wireless Networks," IEEE Trans, on Vehicular Technology, vol. 57, no. 2, pp. 1243-1254, M a r c h 2008. co-located w i t h i n the same coverage area. D u r i n g the system discovery phase, the mobi le t e rmina l determines which networks can be used and what services are available i n each network. These networks may also advertise the supported d a t a rates and QoS parameters for different services. Since the users are mobi le , the available co-located networks depend on the ac tual l ocat ion of the user w i t h i n the coverage area. T h e traffic load i n each network m a y also change w i t h t ime. T h u s , this phase may be invoked periodical ly . In the vert i ca l handoff decision phase, the mobi le t e rmina l determines whether the connections should continue using the exist ing selected network or be switched to another network. T h e decision may depend on various parameters inc lud ing the type of the a p p l i - cat ion (e.g., conversational , s treaming, etc.), m i n i m u m b a n d w i d t h and delay required by the app l i ca t i on , access cost, t ransmit power, current battery status of the mobi le t e rmina l , and the user's preferences. D u r i n g the vert i ca l handoff execution phase, the connections are re-routed from the exist ing network to another one i n a seamless manner. T h i s phase also includes the au - thent i cat ion , author izat ion , and transfer of context in format ion . Since the mobi le t e rmina l may s t i l l be c ommunica t ing v i a the exist ing network whi le handoff execution takes place, this provides t ime for the network to perform the necessary functions whi le m i n i m i z i n g any service d isrupt ions . In this chapter, the focus of our work is i n the vert ica l handoff decision phase. To this end, we propose a vert ical handoff decision a lgor i thm for heterogeneous wireless networks. T h e prob lem is formulated as an M D P . There is a l ink reward funct ion associated w i t h the QoS received by the mobile connection. There is also a s ignal ing cost funct ion associated w i t h the s ignal ing overhead and processing load incurred when vert i ca l handoff execution is performed. T h e objective is to determine the po l i cy w h i c h maximizes the expected tota l reward per connection. A s tat ionary po l i cy is obtained when the connection terminat ion t ime is geometrical ly d is tr ibuted . T h e contr ibut ions of this chapter are as follows; 1. T h e proposed model is adapt ive and appl icable to a wide range of condit ions. Differ- ent l ink reward functions can be assigned to various appl icat ions and networks w i t h different QoS requirements. Different s ignal ing cost functions can be used based on the complex i ty of the re -rout ing operat ion and the s ignal ing load incurred on the network. 2. We provide guidelines for the implementat ion of our proposed vert ica l handoff algo- r i t h m . A l l the parameters in our proposed a lgor i thm can be obtained v i a the services provided by t l ie i iandoff -enabling functions i n t i ie I E E E 802.21 s tandard . 3. Performance of our proposed a lgor i thm is evaluated under two types of traffic: voice and data . N u m e r i c a l results show good performance improvement of our proposed scheme over several vert ica l handoff decision a lgor i thms, inc lud ing S A W [9], T O P S I S 9], G R A [10], and two other heurist ic policies. T h e rest of the chapter is organized as follows. T h e related work is summarized i n Section 2.1. T h e M D P model formulat ion is presented i n Section 2.2. T h e vert ica l handoff decision a lgor i thm, the o p t i m a l i t y equations, and the value i terat ion a lgor i thm are de- scr ibed i n Sect ion 2.3. Implementat ion issues are discussed i n Section 2.4. Extensions of the vert ica l handoff a lgor i thm to include other Q o S parameters, user's preferences, and hor izonta l handoffs are described i n Sect ion 2.5. N u m e r i c a l results, sensit iv i ty analysis , and the structure of the po l i cy are presented i n Section 2.6. A s u m m a r y of our work is given i n Sect ion 2.7. 2.1 Related Work In this section, we provide an overview of recent work on vert ical handoff decision i n heterogeneous wireless networks. T h e pol icy-enabled vert i ca l handoff model is proposed i n [11]. It considers the pref- erence of the user and the tradeoff between different characteristics of the networks (e.g., b a n d w i d t h , access cost, and power consumption) . In [9], the vert ica l handoff decision is formulated as a fuzzy M A D M problem. F u z z y logic is used to represent the imprecise in format ion of some attr ibutes of the networks and the preferences of the user. T h e fuzzy M A D M method consists of two steps. T h e first step converts the fuzzy d a t a into a real number. T h e second step uses classical M A D M methods [12] to determine the r a n k i n g of the candidate networks. T w o M A D M r a n k i n g methods are proposed i n [9]: S A W and T O P S I S . In [10], the network selection for vert ica l handoff is modeled by the ana ly t i c hierarchy process ( A H P ) and the G R A . A H P decomposes the network selection prob lem into several sub-problems and assigns a weight value to each sub-problem. T h e n , the G R A is used to rank the networks and selects the one w i t h the highest rank ing . T h e A H P and G R A are also used for network selection i n [13], where a mobi le -control led vert i ca l handoff predict ion a lgor i thm is proposed. In [14], we investigate the performance among S A W , T O P S I S and G R A regarding the vert i ca l handoff decision. A n o t h e r M A D M rank ing a lgor i thm called the M E W is also studied. T h e performance comparison considers the different types of traffic and network parameters such as b a n d w i d t h , packet delay, j i t ter and bit error rate. In [15], the handoff decision mechanism is formulated as an op t imiza t i on problem. E a c h candidate network is associated w i t h a cost funct ion , which depends on the b a n d w i d t h , delay, and power consumpt ion . A n appropriate weight factor is assigned to each parameter to account for its importance on the vert i ca l handoff decision. A n appl icat ion-or iented vert i ca l handoff decision mechanism is proposed i n [16]. E a c h candidate network is associated w i t h a u t i l i t y funct ion. T h e selected network is the one that provides the highest u t i l i t y value calculated from a weighted s u m of the QoS parameters. Such parameters are provided by a l ocat ion service server. In [17], a framework is proposed to compare different vert i ca l handoff algorithms. T h e framework includes a p a t h loss channel model between the mobi le t e rmina l and the access point , a n d a M a r k o v cha in that models the user's movement between different access networks. A mul t i - layer framework for vert i ca l handoff is proposed i n [18]. A rules engine, combined w i t h several threshold parameters, is used to moni tor the decision parameters while the handoff policies are stored i n a database. T h e framework allows the trigger of the ver t i ca l handoff by either changes i n appl icat ions , variat ions of network's condit ions, or preferences of the users. In [19], a proact ive end-to-end mob i l i t y management system is proposed for I E E E 802.11 W L A N s and wireless wide area networks. T h e system relies on various components to support transparent m o b i l i t y management and cont inu i ty of the connection among ac- cess networks. In [20], a ut ihty -based strategy for network selection is proposed. Several u t i l i t y functions are evaluated based on the economic concepts of consumer surplus and risk. In [21], the vert i ca l handoff decision is evaluated v i a a handoff cost funct ion and a handoff threshold funct ion which can be adapted to changes i n the network environment dynamica l ly . In [22], a vert ica l handoff decision a lgor i thm based on d y n a m i c programming is introduced . It considers the movement and locat ion in fo rmat ion , w h i c h is also provided by a locat ion service server. 2.2 Model Formulation E a c h mobi le connection may experience a number of vert ica l handoffs d u r i n g its connec- t i o n Ufetime. T h e envisioned heterogeneous wireless environment considered is shown i n F i g . 2.1, where W L A N s are co-located inside the coverage of a wireless cel lular system. These specific areas are referred to as the co-located coverage areas. T h e mobi le t e r m i - n a l is assumed to receive in format ion from the co-located networks w i t h i n its receiving range periodical ly . T h e advertised in format ion from each network may include, among other parameters , the available b a n d w i d t h and the average delay. Detai ls about how the in format ion is obta ined , and the system discovery phase w i l l be discussed i n Section 2.4. In each t ime per iod , the mobi le t e rmina l decides whether the connection should use the current selected network or be re-routed to another network, which can provide better performance (e.g., lower cost, higher throughput ) . T h e re -rout ing of the connection d u r i n g the vert i ca l handoff execution phase is a complex process. It increases the processing and s ignal ing load of the network. T h u s , there is an impor tant tradeoff between the QoS of the mobi le connection, a n d the processing and s ignahng load incurred on the network. W e now describe how to formulate the above vertical handoff decision problem as an M D P . T h e notations that we use follow those described i n [23]. A n M D P model consists of five elements; 1) decision epochs; 2) states; 3) actions; 4) transition probabilities; and 5) rewards. T h e mobi le t e rmina l has to make a decision whenever a certain t ime per iod has elapsed. Referr ing to F i g . 2.2, the sequence T = {1,2,... ,N} represents the times of successive decision epochs. T h e random variable A'' denotes the t ime that the connection terminates . A t each decision epoch, the mobi le t e rmina l has to decide whether the con- nect ion should use the current chosen network, or be re-routed to another network (i.e., execute a vert i ca l handoff) . Let M denote the to ta l number of co-located networks i n the coverage area of interest. T h e action set is A = {1,2,..., M}, and the random variable Yt denotes the act ion chosen at decision epoch t. T h e mobi le t e r m i n a l chooses an act ion based on its current state in format ion . T h e state space is denoted by S. For each state s e S, the state in format ion includes the address or identi f icat ion number of the network that the mobi le t e r m i n a l is current ly connected to, the available b a n d w i d t h and the average delay provided by a l l the available co-located networks i n the area. T h e random variable Xt denotes the state at decision epoch t. G i v e n that the current state is s and the chosen act ion is a, the state transition probability function for the next state s' is denoted by P[s' | s ,a] . T h i s funct ion is M a r k o v i a n since the state t rans i t i on depends on the current state and act ion but not the previous states. T h e link reward function f{Xt,Yt) reflects the QoS provided by the chosen network to the mobi le connection w i t h i n the t ime interval {t,t + 1). O n the other hand , the signaling cost function g{Xt,Yt) captures the processing and s ignal ing load incurred when the connection switches from one network to another. If the connection remains using the same network d u r i n g the interval (t, t+1), then g(Xt, Yt) is equal to zero. For convenience, we define the reward function as r{Xt, Yt) = f{Xt,Yt) — g{Xt, Yt). A decision rule prescribes a procedure for act ion selection i n each state at a specified decision epoch. Determin is t i c M a r k o v i a n decision rules are functions 5t : S A, which specify the act ion choice when the system occupies state s at decision epoch t. A policy TT = (5-^,02, ••• ,SN) is a sequence of decision rules to be used at a l l decision epochs. L e t f^(s) denote the expected total reward between the first decision epoch u n t i l the connection t e rminat i on , given that the po l i cy TT is used w i t h i n i t i a l state s. W e have. N T,r{Xt,Yt) i=l (2.1) where E^ denotes the expectat ion w i t h respect to the corresponding r a n d o m variables involved when po l i cy TT is used and i n i t i a l state s. Note that different po l i cy TT and i n i t i a l state s w i l l change the chosen act ion a. T h i s w i l l also cause a different state t rans i t ion probab i l i t y funct ion P[s' | s, a] to be used i n the expectat ion E^. T h e r a n d o m variable A'̂ , wh i ch denotes the connection termination time, is assumed to be geometrical ly d is tr ibuted w i t h mean 1/(1 — A). A s shown i n Sect ion 2.8, (2.1) can be w r i t t e n as: z;'^(s) = ^ ; | ^ V - i r ( X „ r , ) | , (2.2) where A can also be interpreted as the discount factor of the mode l , and 0 < A < 1. Because our op t imiza t i on prob lem is to max imize the expected t o t a l discounted reward, we define a po l i cy TT* to be optimal i n 11 if v'^'is) > v^{s) for a l l TT € 11. A po l i cy is said to be stationary iî St = S for a l l t. A s tat ionary po l i cy has the form TT = {5,S,- • •). For convenience we denote TT s i m p l y by 5. O u r objective is to determine an o p t i m a l s tat ionary determinist i c po l i cy 5*, w h i c h maximizes the expected tota l discounted reward given by (2.2). For the rest of the chapter, we refer to (2.2) as the expected total reward, and Ô* as the M D P o p t i m a l policy. Note that 5* is o p t i m a l under the expected to ta l discounted reward o p t i m a l i t y cr i ter ion [23]. 2.3 Vertical Handoff Decision Algorithm In this section, we begin by describing how the M D P model formulated i n Section 2.2 can be used to analyze the vert i ca l handoff decision a lgor i thm. T h e n , the o p t i m a l i t y equations and the value i terat ion a lgor i thm are introduced. 2.3.1 State, Reward Function, and Transition Probability In our proposed vert i ca l handoff decision a lgor i thm, the state space S is defined as: S - {1,2,--- ,M} X xV^ X xV'^ ••• X B'^ xV^, where M denotes the number of available co-located networks, B"" and denote the set of the available b a n d w i d t h and delay from network m (w i th m = 1 , 2 , . . . , M ) , respectively. To reduce the number elements i n the state space, we assume that the b a n d w i d t h in format ion is prov ided i n a multiple of units of b a n d w i d t h . Specifically, we define: H ' " = { 1 , 2 , 3 , . . . , 6 ™ , J , m = l , 2 , . . . , M , where b^^^ denotes the m a x i m u m available b a n d w i d t h provided to a connection by network m. A s an example , each unit of b a n d w i d t h in a W L A N and in a wireless cel lular system can be 500 kbps and 16 kbps , respectively. S imi lar ly , the delay in format ion is also provided i n a multiple of units of delay. T h a t is , P " ^ - { 1 , 2 , 3 , . . . , C a J , m - l , 2 , . . . , M , where d^^^^ denotes the m a x i m u m delay provided to a connection by network m. A s an example, each uni t of delay i n a W L A N and i n a wireless cel lular system can be 50 ms and 20 ms, respectively. G i v e n the current state s and the chosen act ion a, the l ink reward funct ion / (s , a) is: fis, a) = u / i (s , a) -f (1 - a;) /^(s, a), (2.3) where /b(s ,a) denotes the b a n d w i d t h reward funct ion, fd{s,a) denotes the delay reward funct ion , and UJ is the weight (or importance factor) given to the available b a n d w i d t h w i t h 0 < w < 1. Let s = [i,bi,di,..., 6 M , <^M] denote the current state vector where i denotes the current network used by the connection. T h e b a n d w i d t h reward funct ion / i ( s , a ) and the delay reward funct ion /d(s ,a) are defined as follows: Ms, a) = 1, {ba-LB)/{UB-LB), and I 0, 1, K > UB, LB<ba< UB, ba < LB, (2.4) 0 <da< L D , LD <da< UD, da > UD, (2.5) / , ( s , a ) = <̂  iUD-d,)/iUD-LD), . 0, where the constants LB a n d UB in (2.4) denote the m i n i m u m and m a x i m u m b a n d w i d t h required by the connect ion, respectively. O n the other hand , the constants LD and Uo i n (2.5) denote the m i n i m u m and m a x i m u m delay required by the connect ion, respectively. T h e b a n d w i d t h reward funct ion is shown i n F i g . 2.3(a), and the delay reward funct ion is shown i n F i g . 2.3(b). Note that the available b a n d w i d t h is a u t i l i t y parameter , while the delay is a cost parameter . T h e s ignal ing cost funct ion g{s,a) is defined as: gis, a) = 0, i a, i = a, (2.6) where Ki^a is the swi tch ing cost from the current network i to the new network a. Between two successive decision epochs, the reward funct ion r ( s , a) can be defined as: ris,a) = fis,a) - gis, a). (2.7) F i n a l l y , given that the current state s = [i,bi,di,..., b^, d^] and the chosen act ion is a, the probab i l i ty funct ion that the next state s' = [j, b[,d'i,..., l)^^, d^^] is given by: n m = l P[^'m ,d'^\bm,dm], j = a, 0, j ^ a. P[s' I s, a (2.8) In (2.8), we assume that the jo int b a n d w i d t h and delay probab ihty funct ion of each network is independent. T h i s is due to the fact that a l though the networks are co-located, they are managed by different network operators and use different wireless access technologies. 2.3.2 Optimality Equations and the Value Iteration Algorithm L e t v{s) denote the m a x i m u m expected to ta l reward given the i n i t i a l state s. T h a t is. v(s) = max f'^(s). Tren (2.9) F r o m [23], the optimality equations are given by: v{s) = m a x I r(s, a) -h ^ A P[s' | s, a] v{s') (2.10) T h e solutions of the o p t i m a l i t y equations correspond to the m a x i m u m expected t o ta l reward 'i'(s) and the M D P opt ima l pol icy S*{s). Note that the M D P o p t i m a l po l i cy ô*{s) indicates the decision as to which network to choose from, given that the current state is s. There are various a lgor i thms available to solve the o p t i m i z a t i o n prob lem given by (2.10). Examples inc lude the value i terat ion , po l i cy i terat ion , and act ion e l iminat ion algor i thms [23]. T h e V I A shown i n A l g o r i t h m 4 determines a s tat ionary determinist ic o p t i m a l po l i cy and the corresponding expected tota l reward. There are a number of definitions for the n o r m funct ion ||.||. In this chapter, the norm funct ion is defined as ||?;|| = m a x |u(s)| for s E S. Convergence of the V I A is ensured since the operat ion i n step 2 corresponds to a contract ion mapping . T h u s , the funct ion v'^is) converges i n n o r m to v(s). Note that the convergence rate of the V I A is l inear. 2.4 Vertical Handoff Implementation Issues In this section, we first summarize the system discovery phase standardized w i t h i n the I E E E 802.21 M e d i a Independent Handover ( M I H ) work ing group. W e then describe how the in format ion prov ided by the functions of the I E E E 802.21 s tandard can be used to implement our proposed vert ical handoff decision a lgor i thm. 2.4.1 System Discovery Phase In order to estimate t i ie networlc condit ions i n heterogeneous wireless networks, the I E E E 802.21 M I H work ing group [3] is current ly developing standards to enable efficient handofï operations, and to provide inter -operabi l i ty between heterogeneous access networks. T h i s includes bo th 802 and non-802 networks (e.g., 3 G P P and 3 G P P 2 ) . T h e proposed draft for the I E E E 802.21 s tandard [24] relies on a set of handoff -enabling functions w i t h i n the m o b i l i t y management protoco l , and on a new network entity called the M I H F u n c t i o n ( M I H F ) . T h e M I H F provides three services: M e d i a Independent Event Service ( M I E S ) , M e d i a Independent C o m m a n d Service ( M I C S ) , and M e d i a Independent Informat ion Ser- vice ( M H S ) . T h e M I E S provides event classif ication, event filtering and event report ing correspond- ing to d y n a m i c changes i n l ink characterist ics , status and quality . One event m a y indicate changes i n state and transmiss ion behavior of the phys ica l , d a t a l ink and logical l ink lay- ers. T h e M I C S provides a set of commands that enables M I H users to issue commands for handoff control and mobi l i ty . F i n a l l y , the M H S provides the capabi l i ty for obta in ing the necessary in format ion to make effective handoff decisions. Such in format ion includes details on the characteristics and services provided by the serving and co-located networks i n the area. T h e mobi le t e r m i n a l can access the relevant in format ion v i a its current active network interface. Since the other interfaces do not need to be turned on simultaneously, the battery l i fet ime can be preserved. T h e M H S defines a set of in format ion elements ( lEs ) to provide access to s t a t i c / d y n a m i c in format ion and higher layer services supported by the networks. T h e l E s are classified into three specific groups. T h e first group gives an overview of the co-located networks w i t h i n a coverage area. Such in format ion can include the l ist of available networks and operators, roaming agreements, access costs, and security capabi l i t ies . T h e second group provides in format ion about B S s a n d / o r A P s for each co-located network. T h e I E includes addressing in format ion , locat ion of the B S s a n d / o r A P s , supported d a t a rates, and an extended set of l ink and QoS parameters (e.g., d a t a rate, delay, j i t t er ) . It also includes higher layer services offered by the networks (e.g., I P m u l t i m e d i a such as Voice over I P ) . F i n a l l y , the last group includes other relevant in format ion which is vendor specific. 2.4.2 Implementation Details Based on the I E E E 802.21 s tandard [24], a mobile t e rmina l which implements our pro - posed vert ical handoff decision a lgor i thm is able to per iod ica l ly ob ta in in format ion about the co-located networks i n its receiving range by using its current network interface. T h e in format ion provided by the M I I S of the M I H funct ion is used to estimate the parameters of the l ink reward funct ion i n (2.3) and the s ignal ing cost funct ion i n (2.6). T h e in fo rma- t i on about the available b a n d w i d t h and average delay i n the networks can be est imated by fol lowing the s tandardized procedures for performance metrics for Internet services defined by the I E T F I P Performance Metr i c s ( I P P M ) work ing group [25]. These procedures are designed in such a way that they can be implemented by network operators to provide ac- curate and unbiased quant i tat ive measures of such metrics . E x a m p l e s of such s tandardized metrics are: connect ivity , packet delay and loss, packet delay var ia t ion , and l ink b a n d w i d t h capacity. For the l ink reward funct ion i n (2.3), the mobile t e rmina l can map the values of available b a n d w i d t h and delay offered by network m into the b a n d w i d t h and delay units defined by B"^ and V"^, respectively. A d d i t i o n a l l y , the m a x i m u m and m i n i m u m values required by (2.4) and (2.5) as wel l as the value of a; can be defined beforehand for each appl i cat ion . For the s ignal ing cost funct ion i n (2.6), the value of Ki^a is provided by the network operators and can be inc luded w i t h i n one of the I E fields. T h e value of Ki^a ca,n be set according to the agreements between two network operators. Suppose the current network is i and the chosen network a is j, where i 7^ j . A smal l value of Kij w i l l give an incentive to switch from network i to network j, whereas a large value of Kij can indicate that there is no agreement between these two networks. F i n a l l y , the probab ihty funct ion i n (2.8) can be est imated by the network operator based on its own network traffic statistics. G i v e n the values of the reward funct ion and d istr ibut ions of the networks, the V I A can be used to determine the M D P o p t i m a l po l i cy S*{s). T h e V I A operates by ca l cu lat ing successive approx imat i on to the value funct ion :^(s). E a c h i terat ion of the V I A is performed i n (9(|^||>S| )̂, where A is the act ion set and S the state space. Several variants of the V I A have been proposed to enhance the speed of convergence [23]. T h e V I A is widely used due to its conceptual s impl i c i ty , and to its ease i n coding and implementat ion . Once the o p t i m a l po l i cy is ca lculated , i t can be stored in a m a t r i x format. E a c h entry of the m a t r i x specifies the o p t i m a l network to be used given the current state (i.e., b a n d w i d t h , delay) , and swi t ch ing cost of a l l co-located networks. T h e ca l cu lat ion of the o p t i m a l pohcy is performed by t i ie operator offline, and is updated per iodica l ly whenever spare processing capac i ty is available at the network access control ler. 2.5 Model Extensions In this section, we extend the M D P model to include add i t i ona l Q o S parameters and also exp la in how the proposed vert i ca l handoff scheme can handle user's preferences and be integrated into a complete handoff management framework for heterogeneous wireless networks. 2.5.1 Extension to Additional QoS Parameters Suppose that the j i t t e r in format ion needs to be inc luded as one of the Q o S parameters. F r o m Section 2.3.1, the state space S can be extended as: {l,2,...,M}xU^ x^P•••x M^, where A ' " ' " represents the set of QoS parameters offered from network m for the connection, and AT™ = i?'" X î»"* X J ' " , m = l , 2 , . . . , M , where B"^ and T>"^ are the same as introduced i n Sect ion 2.3.1, and J"^ denotes the set of j i t t e r in format ion from network m i n a mul t ip le of units of j i t ter . T h a t is, J"' = {0,1,2,...,C,J, m = l , 2 , . . . , M , where j^^^ denotes the m a x i m u m j i t t e r provided to a connection by network m. A s an example, each uni t of j i t t e r i n a W L A N and i n a wireless cel lular system can be 10 ms and 5 ms, respectively. G i v e n the current state s and the chosen act ion a, the l ink reward funct ion / (s , a) i n (2.3) can be extended as: / (s , a) = Ub fb{s, a) + uJd /d(s, a) + Uj fj{s, a), where J2k={b,d,j} '^k = 1, and fj(s,a) is the j i t ter reward funct ion. T h e weight of the QoS parameters Uk can be defined beforehand according to the specific requirements of the appHcat ion. In general, J\f"^ can be extended to include other relevant Q o S parameters. 2.5.2 Extension to User's Preferences and Horizontal Handoff Here, we propose a framework to integrate b o t h hor izonta l handoff and vert i ca l handoff w i t h the user's preferences. F i r s t , we classify 5"*, V"^, and J"^ f rom network m as network- based Q o S parameters, whi le parameters such as access cost, power consumption , and security denoted by C"^, and respectively, as user-based QoS parameters. Let us now consider a mobi le t e rmina l , wh i ch is connected to network i. W e assume that hor izonta l handoff has pr i o r i ty over vert ica l handoff. T h e mobi le t e rmina l uses a conventional hor izonta l handoff scheme based on the R S S from network i (e.g., [26]). Hence, if the hor izonta l handoff a lgor i thm detects that the R S S is below a certain threshold , then the hor izonta l handoff is executed. O n the other h a n d , i f the mobi le t e r m i n a l discovers that it is w i t h i n a co- located coverage area because of the in format ion provided by the I E E E 802.21 M I I S , then a screening phase is invoked. T h i s phase is capable of f i l tering networks not suitable for per forming vert ica l handoff based on user-based QoS parameters such as C"*, and T h i s set of values may be specified by the user or stored in a user profile beforehand i n the mobi le t e rmina l . O n l y suitable candidate networks w i l l be considered for the vert i ca l handoff decision. Toward the end, the vert i ca l handoff decision is based on the M D P o p t i m a l po l i cy ô*{s) considering the network-based Q o S parameters B"^, and J"^. F i n a l l y , the handoff management framework can be summar i zed i n A l g o r i t h m 5. 2.6 Numerical Results and Discussions In this section, we compare the performance between our proposed M D P - b a s e d vert ica l handoff decision a lgor i thm, S A W [9], T O P S I S [9], and G R A [10]. W e denote these pohcies as 8*, t̂ "̂ -̂ *̂ , J^*-* -^ , and 8'^^'^, respectively. In add i t i on , two other heurist ic policies are inc luded . For the first heurist ic , the network to be selected i n each decision epoch is the one w h i c h has the highest available bandwidth . We denote this po l i cy as 8^^^. For the second heurist ic , no vert i ca l handoff is performed d u r i n g the connection Ufetime. W e denote this po l i cy as (5^^^. T h e performance metrics are the expected total reward per connection, and the expected number of vertical handoffs per connection. T h e expected t o ta l reward is defined in Section 2.2. B y fol lowing the notat ion introduced in Sections 2.2 and 2.3.1, let the state at t ime t be denoted as Sj = [i{t),bi{t),di{t),... ,bM{t),dM{t)]- T h e expected number of vert ica l handoffs per connect ion given po l i cy 5 w i t h i n i t i a l state s is given by: ç^(s) = E , ^ | ^ A * - i . l [ a , 7 ^ z W ] | , (2.11) where ![•] denotes the indicator funct ion (i.e., l[at ^ i(t)] is equal to 1 i f at is not equal to i{t) at t ime t, and is equal to 0 otherwise). T h e average t ime between successive decision epochs is assumed to be 15 s. W e consider a scenario where there are two co-located networks (i.e., M = 2) as i n the heterogeneous system depicted i n F i g . 2.1. Network 1 is a W L A N and network 2 is a wireless cel lular system. T h e parameters of the networks used i n the numer i ca l results are summarized i n Table 2.1. T h e switching costs i n the s ignal ing cost funct ion i n (2.6) are the same (i.e., f^l,2 = - ^ 2 , l ) - T w o appl icat ions are considered. T h e first one is constant b i t rate ( C B R ) voice traffic using the user datagram protoco l ( U D P ) as the transport protocol . T h e second one is file transfer protoco l ( F T P ) d a t a traffic using the transmiss ion control protoco l ( T C P ) . For these appl icat ions , the parameters of the l ink reward funct ion i n (2.3), as well as the b a n d w i d t h and delay reward functions i n (2.4) and (2.5) are summar ized i n Table 2.2. T h e un i t of b a n d w i d t h is equal to 16 kbps , and the uni t of delay is equal to 60 ms. For the connections w i t h C B R traffic, L B and UB are set to m a t c h voice coders and protocol overheads of I P m u l t i m e d i a services [27], and L D and UD are set to m a t c h the target delay lower t h a n 150 ms. T h e connection is s t i l l acceptable if the delay is between 150 ms and 400 ms. T h e qua l i ty of the connect ion is not acceptable i f the delay exceeds 400 ms. These ranges are defined according to I T U Recommendat ion G.114 [28]. For the connections w i t h F T P traffic, L B , U B , L D and Up are set to m a t c h an elastic app l i ca t i on wi thout stringent delay requirements. Note that the importance factor u i n the l ink reward funct ion i n (2.3) is also set accordingly to each of the appl icat ion 's b a n d w i d t h requirements. Unless stated otherwise, the i n i t i a l state at the beginning of the connections w i t h C B R traffic is assumed to be 48 kbps of b a n d w i d t h and 60 ms of delay, and 160 kbps and 60 ms for the connections w i t h F T P traffic. For the state t rans i t ion probab i l i ty funct ion of the wireless cel lular system (i.e., network 2) i n (2.8), we assume that the values of available b a n d w i d t h and delay are guaranteed for the durat i on of the connection. T h u s , ^ I 4 4 | 6 . , 4 1 = { = = (2,12) I 0, otherwise. For the state t rans i t i on probabi l i ty funct ion of the W L A N , however, we cannot make the same assumpt ion as i n the wireless cel lular system. Instead, we follow a s imulat ion-based approach to est imate such probabi l i t ies . A t y p i c a l I E E E 802.11b W L A N is s imulated by using the network s imulator ns-2 (v2.29) [29], where users arrive and depart from the network according to a Poisson process w i t h an average rate of 0.2 users per second. A l l a r r iv ing users remain w i t h i n the coverage of the W L A N for the d u r a t i o n of their connections. T h e r e are only single-hop transmissions between the mobi le terminals and the W L A N A P . A l l packets are t ransmi t ted through the A P to a s ink. T h e A P and the sink are connected by a direct l ink of 100 M b p s . T h e user's connections are either 64 kbps C B R traffic us ing U D P , or F T P traffic using T C P . T h e basic rate and data rate of the W L A N are 1 M b p s and 11 M b p s , respectively. T h e available b a n d w i d t h is ca lculated from the W L A N ' s capacity, which is approx imated to be the achievable throughput by the W L A N under sa turat i on , minus the aggregated traffic of the users. T h e one-way delay is ca lculated f rom each of the users to the sink. T h e values of the available b a n d w i d t h and delay are rounded according to the units defined i n Section 2.3.1. T h e count ing of transit ions among states is performed to estimate the state t rans i t i on probabi l i t ies . For the V I A , e is chosen to be equal to be 10~^. F r o m the M D P o p t i m a l policy, the V I A is used again to determine the expected number of vert i ca l handoffs by so lv ing (2.11). For the other vert i ca l handoff decision algorithms S A W , T O P S I S and G R A , the rank ing of each network is used to determine the policies 5^^^, (5™^, and S^^^. G i v e n the reward functions and the state t rans i t ion probabi l i t ies , the corresponding expected to ta l reward and the expected number of vert ica l handoffs can be determined from (2.2) and (2.11), respectively. For the two heuristics policies 5^^^ and 0^^^, the expected t o ta l reward and number of ver t i ca l handoffs can also be determined using the V I A . 2.6.1 Results for C B R Voice Traffic F i g . 2.4 shows the expected to ta l reward and the expected number of vert ica l handoffs versus the switching cost Ki^a for connections w i t h C B R traffic. T h e average connection durat i on is 10 m i n (i.e., A = 0.975). F i g . 2.4(a) shows that when I^i^a increases, the pol icy S* obtained from M D P a lgor i thm gives the highest expected t o t a l reward per connection compared to the other a lgor i thms. F i g . 2.4(b) shows that when Ki^a increases, there is less incentive to perform vert i ca l handoff and the M D P a lgor i thm chooses not to switch more often. O n the other hand , 5^"^^, 5^^^ and 0'^^^ select the network based on the current available b a n d w i d t h and delay, and do not take the switching cost into consideration, ô^'^^ only considers the available b a n d w i d t h and S^^^ by def init ion never performs a vert ica l handoff. T h u s , the expected number of vert i ca l handoffs is constant for those algorithms. Reca l l that an increase i n the number of vert i ca l handoffs is d i rec t ly related to an increase in the s ignal ing load incurred i n the networks to re-route the connections from one network to another. T h e swi tch ing costs Ki^a i n the s ignahng cost funct ion i n (2.6) provide flexibility for the network operators. T h e values of Ki^a can be selected to reflect the complex i ty of the re -rout ing operations, and the s ignal ing load incurred on the network when vert ical handoffs are performed at the network layer and above. A s examples of such flexibility, smal l values of Ki^a can be set among networks w i t h r oaming or in terwork ing agreements that may faci l i tate or s impl i fy the vert ica l handoffs, such as i n the 3 G P P / 3 G P P 2 - W L A N standardized architectures [4, 5]. Large values of Ki^a can be t emporar i l y set for overloaded networks as a load-balanc ing technique i n order to deter users to connect to t h e m and decrease the traffic load i n the network. T h e impact of the swi t ch ing costs Ki^a i n the M D P po l i cy 5* is further analyzed i n Section 2.6.4. F i g . 2.5 shows the expected to ta l reward and the expected number of ver t i ca l handoffs versus the discount factor A. R e c a l l that i n the discrete-t ime M D P mode l , we assume that the time unit (i.e., the t ime between successive decision epochs) is 1/4 m i n . T h e average connection durat i on is equal to 1/(1 — A) t ime uni t . W h e n A is varied from 0.9 to 0.983, it corresponds to the var iat ion of the average connect ion d u r a t i o n from 2.5 m i n to 15 m i n . F i g . 2.5(a) shows that the po l i cy 5* f rom M D P gives the highest expected to ta l reward per connection for a l l values of A. A s an example , when the average connection durat i on is 15 m i n , the M D P a lgor i thm gives 4.4% more to ta l expected reward than policies 5^^^, and 5^^^, 4 .7% more t h a n 5^^^ and 5% more than ë^^"^. F i n a l l y , when the average connection d u r a t i o n increases, the number of decision epochs and the difference i n the tota l expected reward also increase. T h u s , the expected number of vert ica l handoffs increases for a l l a lgorithms. F i g . 2.6 shows the expected to ta l reward and the expected number of vert ica l handoffs versus the weight factor uj for connections w i t h C B R traffic. T h e po l i cy 5* f rom M D P gives the highest expected t o t a l reward per connection for a l l different values of to. F r o m (2.3), when u increases, the b a n d w i d t h reward funct ion (2.4) becomes more important than the delay reward funct ion (2.5). A s we can see, when u> > 0.25, the t o ta l expected reward and the expected number of vert i ca l handoffs of 5^^^, 5'^°^, and 5^^"^ converge to (5^^^. T h i s is because more t h a n 2 5 % of the importance is placed on the available bandwidth . 2.6.2 Results for F T P Data Traffic F i g . 2.7 shows the expected to ta l reward and the expected number of vert i ca l handoffs versus the swi tch ing cost Ki^a for connections w i t h F T P traffic. F i g . 2.7(a) shows that when Ki^a increases, the pohcy 5* obtained from the M D P a lgor i thm gives the highest expected to ta l reward per connection compared to the other a lgor i thms. Note that i n this case, the po l i cy 6* coincides w i t h the heurist ic po l i cy 5^^^. Reca l l that we set the parameters of the reward functions to m a t c h an elastic appl i cat ion , and this k i n d of appl i cat ion is suitable for the heurist ic po l i cy of selecting the network which offers the highest available b a n d w i d t h . A s imi lar behavior of 5* and 5^^^ is shown i n F i g . 2.7(b) when Ki^a increases. F i g . 2.8 shows the expected to ta l reward and the expected number of vert ica l handoffs versus the discount factor A. F i g . 2.8(a) shows that the M D P pol i cy 5* gives the highest expected t o ta l reward per connection when the average connection durat i on is increased from from 2.5 m i n to 15 m i n , and also coincides w i t h the heurist ic po l i cy ë^^^. F i n a l l y , when the average connection durat i on increases, the number of decision epochs and the difference i n the to ta l expected reward increase as wel l . Note that the expected number of vert i ca l handoffs increases s lowly for a l l a lgorithms compared to the connections w i t h C B R traffic. T h e reason is that the connections w i t h F T P traffic tend to remain connected to network 1 whenever i t is possible. 2.6.3 Sensitivity Analysis In order to calculate the m a x i m u m expected tota l reward of a connect ion, the M D P o p t i m a l po l i cy 5* needs to be determined. T h e o p t i m a l po l i cy depends on different parameters. A l t h o u g h the parameters such as Ki^a can be determined by the network, and parameters such as u), IJB) f^DiUB,UD can be assigned by the user or set beforehand according to the appl icat ion 's requirements, the value of A (i.e., the average connection duration) m a y not always be est imated correct ly by the mobi le terminal d u r i n g the connection setup. In that case, the po l i cy may not indeed be the o p t i m a l one. In this section, we determine the percentage change of the expected t o ta l reward to the var iat ion of the average connection durat ion . T h e procedures for the sensi t iv i ty analysis are given i n the fol lowing steps. 1. G i v e n the ac tua l average connect ion durat i on c = (1 — A)~^ t ime units and other pa - rameters, we first determine the m a x i m u m expected t o ta l reward, denoted as Reward (optimal). 2. L e t c denote the est imated average connection d u r a t i o n a n d A c denote the percentage change of the average connection durat ion . These parameters are related by c = (1-1- Ac )c . Based on the est imated average connection d u r a t i o n c and other parameters, the s u b o p t i m a l po l i cy is determined. T h e s u b o p t i m a l expected t o ta l reward, denoted as Reward (suboptimal), is calculated. 3. T h e change i n the expected t o ta l reward w i t h respect to the var iat ion of the average connect ion durat i on is characterized by the reward rat io , whi ch is defined as Reward (suboptimal) / Reward (optimal). T h e results for different A are shown i n F i g . 2.9 for C B R and F T P traflfic. Note that w i t h i n the (—95, —40) percentage range, there is a smal l decrease i n the reward rat io for bo th appl icat ions , being more noticeable for the connections w i t h F T P traffic w i t h short durat i on . T o overcome this decrease, the results i m p l y that i f there is uncerta inty i n the est imat ion of the average connection durat i on , i t m a y be better to overestimate the connection durat i on i n order to m a i n t a i n the reward rat io to be close to one. 2.6.4 Structure of the Optimal Policy T h e M D P o p t i m a l po l i cy 5*{s) is numer ica l ly computed by implement ing the V I A . Here, we provide relevant examples of the impact of the swi tch ing costs Ki^a of the s ignal ing cost funct ion i n (2.6) on the structure of the pohcy. W e focus on the M D P pol i cy 5*{s) for con- nections w i t h C B R traflflc because the impact of the Ki^a is more noticeable. F igs . 2.10(a) and (b) show the structure of the M D P o p t i m a l po l i cy 5*(&) for the subset of states s = = 2,bi,di,b2,d2 = 4] w i t h switching costs Ki^a = 1 and Ki^a = 0, respectively. Note that in this numer i ca l example, the state space is 5 D . In order to plot the M D P policy, two parameters are fixed to a specific value. W e choose the current network in use (i) to be network 2 and the current delay i n network 2 (^2) to be 4 units . T h e average connection d u r a t i o n is 10 m i n (e.g., A = 0.975), and the t ime between successive decision epoch is 15 s. T h e cubes (bars) represent act ion a = 1 (i.e., perform vert ical handoff to network 1) whi le the absence of cubes (bars) represents act ion a = 2 (i.e., remain us ing network 2). Note that when the switching costs Ki^a change from 0 to 1, there are fewer states i n w h i c h the act ion is to perform the vert ica l handoff. T h i s decrease in the number of states is expected since, as shown i n F i g . 2.4(b), the expected number of vert i ca l handoffs is reduced from 2.75 to 0.5 when the swi tch ing cost Ki^a increases from 0 to 1. 2.6.5 Number of Iterations T h e performance metrics , w h i c h are the expected t o ta l reward and the expected number of vert i ca l handoffs per connect ion, and the M D P pohcy 6* presented i n previous subsections were computed by using the V I A . T h e V I A proves to be a very efficient and stable i t e rat i on a lgor i thm. T h e number of i terations required to converge from point to point is predictable . In general, the number of i terations neither depends on the switching costs Ki^a of the s ignal ing cost funct ion (2.6), nor on the weight factor UJ i n the l ink reward funct ion (2.3), but depends on the value of the discount factor A (e.g., the average connection durat ion) . A s an example , i n F i g . 2.5(a), the V I A requires 45 i terations to converge when the average connection d u r a t i o n is 2.5 m i n (e.g., A = 0.9), but i t requires 183 iterations when the average connect ion d u r a t i o n is 10 m i n (e.g., A = 0.975). Var iants of the V I A have been proposed to enhance convergence [23]. 2.7 Summary In this chapter, we proposed a decision a lgor i thm for the vert i ca l handoff decision phase i n heterogeneous wireless networks. T h e a lgor i thm is based on M D P formulat ion w i t h the objective of m a x i m i z i n g the expected t o ta l reward of a connection. A l ink reward funct ion is used to mode l the QoS of the connection. A s ignahng cost funct ion is used to model the swi t ch ing cost when a vert i ca l handoff occurs. A stat ionary determinist ic pol icy is obta ined when the connection t e rminat i on t ime is geometrical ly d is tr ibuted . For performance evaluat ion , we considered C B R voice traffic and F T P data traffic. Results show that our proposed M D P a lgor i thm gives a higher expected tota l reward and lower expected number of vert ica l handoffs per connection than S A W , T O P S I S , G R A , and two heuristic policies under a wide range of condit ions. 2.8 Derivation of Expected Total Reward In this section, we derive the expression v^{s), the expected t o ta l reward of the connection given a pol i cy n and i n i t i a l state s. Assume the random variable A'' follows a geometric d i s t r ibut i on w i t h mean 1/(1 — A ) . T h a t is, P ( 7 V = n) = A " - i ( 1 - A ) , n = 1 , 2 , 3 , . . . In this case, (2.1) can be w r i t t e n as: ^ oo n '̂̂ (s) = E: \'£J2^{X^,Y,) A " - I (1 - A ) . I,n=l i=l J Since J ^ ^ j Ylt=i ~ X ^ S i interchanging the order of the s u m m a t i o n , we have ^ oo oo '\ '̂̂ (s) = E:\'£T.r{XuY,)X-''{l-X)\ [ t=l n=t J - E: !^^^X'-'riX^Y,)^ M T Wireless CeUular System Co-located Coverage- Area M T - Mobile Terminal BS - Base Station A P - Access Point F i g u r e 2.1: Co - l o cated heterogeneous wireless networks. X\,Yi XiyYï X^,Y-i 1 2 3 •* T * ^ X *̂ N-\ N time F i g u r e 2.2: T i m i n g d iagram of a M a r k o v Decis ion Process ( M D P ) . Table 2.1: Parameters of the wireless networks. N o t a t i o n Parameter def init ion Network i = 1 Network i = 2 M a x i m u m available b a n d w i d t h in network i 25 uni ts 10 units M a x i m u m delay in network i 8 units 8 units K,,2 Switch ing cost from network 1 to network 2 1 - K2,l S w i t c h i n g cost from network 2 to network 1 - 1 Table 2.2: Parameters of the reward fu actions. N o t a t i o n Parameter def init ion C B R F T P LB M i n i m u m available b a n d w i d t h required 2 uni ts 2 units UB M a x i m u m available b a n d w i d t h required 4 units 16 units LD M i n i m u m delay required 2 units 7 units UD M a x i m u m delay required 7 units 8 units UJ Weight factor 0.25 0.90 fb(s,a) (a) F i g u r e 2.3: Funct ions /f,(s,a) and fd{s,a} f rom the hnk reward function. A l g o r i t h m 1 - V I A ; 1: Set f ° (s ) = 0 for each state s. Specify e > 0 and set A: = 0. 2: For each .state s, compute t-''̂ '*"̂ (s) by -^\s) = m a x / r ( s , a) + y^ XP s s, a 3: If - v'^W < e ( l - A ) / ( 2 A ) , go to step 4. Otherwise , k = k+l and re turn to step 2. 4: For each s e S, compute the stat ionary o p t i m a l po l i cy S{s) = arg max < r(s, a) + > A Pis' j s, A€A I s'es and stop. A l g o r i t h m 2 - Hor i zonta l and V e r t i c a l Handoff Decis ion A l g o r i t h m : 1: W h i l e connect ing to network i do 2: If R S S of network i is below a certain threshold, 3: Per f o rm horizontal handoff. 4: If the mobi le t e rmina l is w i t h i n the co-located coverage area, 5: Invoke screening phase based on C " , and 6: Determine vert ica l handoff decision pol icy 5*{s) based on B"", P " , J"". 7: If ac t ion a ^ i , 8: Per f o rm vertical handoff to network a, and set i = a. 9: else 10: R e m a i n connected to network i. Switching Cost K.^ (a) Figure 2.4: Effect under different switc l i ing cost K^^a for C B R traffic, (a) E x p e c t e d total reward, (b) Expec ted number of vert ical handoffs. A = 0.975 and ui = 0.25. 0.92 0.93 0.94 0.95 Discount factor X 0.96 0.97 0.98 (b) Figure 2.5: Effect under different discount factor A for C B f i traffic, (a) Expec ted total reward, (b) E x p e c t e d number of vert ical handoffs. A ' j 2 = / i ' 2 1 = 1 and u = 0.25. iîf^^filJî^^^I^^ for Heterogeneous Networks (b) Figure 2.6: Effect und̂ ^̂ ^ dxffere.t we.ght factor . for C B R traffic, (a) E x p e c t e d tota l reward, (b) Expec ted number of vert ical handoffs. K,^^ = K^^i = 1 and Switching Cost K (a) Switcti ing Cost K (b) F i g u r e 2.7: Effect under different swi tc l i ing cost K^^a for F T P traffic, (a) Expected tota l reward, (b) Expec ted number of vertical liaridoffs. A = 0.975 and UJ = 0.9. 0.91 0.92 0.93 0.94 0.95 Discount factor X 0.96 0.97 0.98 (a) 0.91 0.92 0.93 0.94 0.95 Discount factor X 0.96 0.97 0.98 (b) Figure 2.8: Effect under different discount factor A for F T P traffic, (a) Expec ted total reward, (b) Expec ted number of vert ica l handoffs. Ki 2 = A ' 2 1 = 1 and to = 0.9. 1 _ 0.99 I 0.98 "H 0.97 i & 0.96 0.95 0.94 •S 0.93 I 0.92 0.91 • 0.9 - 1 0 0 "Q— FTP with >v=0.975 CBR with X=0.975 -B— CBR with A.=0.95 - A — FTP with ^=0.95 - 5 0 0 50 Percentage Change in Average Connect ion Duration (%) 100 F i g u r e 2.9: V a r i a t i o n of t i ie average connection durat ion w i t l i Ki^2 = -̂ 2,1 ^ I, LU = 0.25 for C B R traffic, and oj = 0.90 for F T P traffic. 1 2 3 action a = 2 d1 (a) (b) Chapter 2. MDP-based Vertical Handoff Algorithm for Heterogeneous Networks Figure 2.10: Structure of the IVIDP optimal policy (d2 4 units and the user is currently connected to network 2). (a) 1(1,2^K2,1^1. (b)^K2,1^0. 43 Bibliography [1] 3rd Genera t i on Par tners i i ip Pro jec t ( 3 G P P ) , l i t t p : / / w w w . 3 g p p . o r g / . 2] 3rd Generat ion Par tners i i ip Pro jec t 2 ( 3 G P P 2 ) , i i t t p : / / w w w . 3 g p p 2 . o r g / . 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Mag., vol . 34, no. 3, pp. 82-90 , M a r c h 1996. 27] G . C a m a r i l l o and M . G a r c i a - M a r t i n , The 3G IP Multimedia Subsystem. J o h n W i l e y and Sons, 2004. 28] I T U - T , "One-way transmis ion t ime , " Recommendat ion G.114, M a y 2003. 29] T h e Network S imulator - ns-2, h t t p : / / w w w . i s i . e d u / n s n a m / n s . Chapter 3 Connection Admission Control for Multi-Service Integrated C e l l u l a r / W L A N System^ Recent studies liave s i iown t i ia t wireless wide area networks, such as 3 G wireless cel lular systems, can be integrated w i t h W L A N s to offer Internet access and I P m u l t i m e d i a services to mobi le users. In an integrated c e l l u l a r / W L A N system, W L A N s are usual ly deployed in densely populated areas, and wireless cel lular networks are used to provide wide area network coverage. Var ious interworking architectures have been proposed in the l i terature 1, 2, 3, 4]. Users carry ing mobi le devices equipped w i t h mul t ip l e interfaces can estab- l ish connections w i t h different available access networks. A s the users move w i t h i n the coverage areas, they are able to switch connections among networks according to roaming agreements. T h e I E E E has also set up the 802.21 media independent handover work ing group to standardize inter -operabi l i ty between 802 and non-802 networks (e.g., 3 0 cel lular systems) [5]. T h e 3 G P P and 3 G P P 2 are also a iming to extend their 3 0 packet da ta and I P m u l t i m e d i a services to the W L A N environments. Different levels of integrat ion have been proposed ranging from common b i l l ing and customer care to seamless mob i l i t y and session cont inu i ty [6, 7 . T h e process of swi tch ing connections among networks is cal led handoff or handover. A handoff is cal led horizontal i f it is between two networks, w h i c h use the same access tech- nology (e.g., between two W L A N s , or between two neighboring cells i n a wireless cel lular network) . O n the other hand , a handoff is called vertical i f it is between two networks, which use different access technologies (e.g., from a cell i n a wireless cel lular network to a W L A N , or vice versa). In order to guarantee the QoS of different I P m u l t i m e d i a ap- phcations (e.g., voice, real - t ime video), it is necessary to l i m i t the number of connections version of this chapter has been accepted for publication. Enrique Stevens-Navarro, A m i r - H a m e d Mohsenian-Rad, and Vincent W . S . Wong, "Connection Admission Contro l for Mult i -Service Integrated C e l l u l a r / W L A N System," IEEE Trans, on Vehicular Technology, in press, 2008. admit ted to a networlc. T h u s , a proper connection admission control policy is required i n each access network. A n admission control po l i cy can either accept the connection request and allocate the resources accordingly, or reject the connection request. In general, h igher pr ior i ty is given to the requests from the handoff users (as opposed to the new users) since from the users' po int of v iew, having a connection a b r u p t l y terminated is more annoy ing t h a n being blocked occasionally on new connection attempts . Some of the admiss ion control policies for wireless cel lular networks include the cutoff priority [8] and the fractional guard channel schemes [9]. T h e C P pol i cy reserves a f ixed number of channels for connection requests from handoff users. T h e connection requests from new users are blocked i f there is no unreserved channel available. O n the other h a n d , the F G po l i cy reserves channels for handoff requests by b locking the connection requests from new users w i t h a probability wh i ch is proport iona l to the current occupancy. B o t h C P and F G policies manage to hmi t the m a x i m u m number of connections i n each network according to the QoS requirements of the exist ing connections. W e now summar ize some of the related work on the integrated c e l l u l a r / W L A N sys- tems. In [10], an admission po l i cy for 3 G cel lular systems w i t h complementary W L A N s is proposed. In [11], three different load sharing schemes for integrated universal mobi le te lecommunicat ions system ( U M T S ) / W L A N systems w i t h buffering capabil it ies are pro - posed. In [12], an integrated c e l l u l a r / W L A N system w i t h resource sharing and admiss ion control capabi l i t ies is proposed. T h e C P admission control po l i cy is used and the net- work performance is evaluated in terms of the b locking probabi l i t ies of new and handoff connections. A H the work i n [10, 11, 12] only consider single-service class. T h a t is, they assume that a l l a r r i v i n g connections request the same amount of b a n d w i d t h . Some recent work i n c e l l u l a r / W L A N interworking aims to differentiate service requirements. In [13], the WLAN-first admiss ion control scheme is proposed where b o t h voice and d a t a connec- t ion requests w i t h i n the overlapped coverage area are transferred to the W L A N . In [14], a randomized guard channel admission control po l i cy is proposed i n w h i c h a random number of channels is reserved for voice handoffs. Some channels are also selected randomly to be exclusively used by new voice connections. T h e remain ing b a n d w i d t h is then shared by a l l da ta connections. In this chapter , we develop an ana ly t i ca l model to faci l i tate the evaluation of different combinations of connect ion admission control policies i n a mult i -service integrated ce l lu- l a r / W L A N system. In our proposed mode l , several W L A N s are deployed w i t h i n the same coverage area of the wireless cel lular network. To accommodate the behavior of different admission control a lgor i thms, we introduce the concept of policy functions. T h e y are de- fined based on the service category (e.g., voice, data ) , the type of the connection request (i.e., new request, or handofi ' request), and the admiss ion control pohcy being used. Di f fer - ent from our previous work i n [15], here we define different pohcy functions for each type of handoff request (i.e., hor i zonta l / ver t i ca l ) . T h e contr ibut ions of our work are as follows: 1. O u r model takes into account various impor tant system parameters i n c l u d i n g the level of m o b i l i t y and the arr iva l rate of connection requests from the users, the ca - pac i ty and the coverage area of each wireless network, the admission control pohcies, and the Q o S requirements i n terms of the b lock ing and dropping probabi l i t ies . 2. F l ex ib l e po l i cy functions are defined for each service category and for each type of connect ion requests. W e use the cutoff pr i o r i ty [8] and the fract ional guard channel [9 admiss ion control policies and determine the corresponding po l i cy functions. These functions also al low us to evaluate different po l i cy combinations. 3. W e formulate two different revenue m a x i m i z a t i o n problems for mult i -service inte - grated c e l l u l a r / W L A N systems. E a c h o p t i m i z a t i o n prob lem takes a d ist inct set of Q o S requirements into consideration. 4. W e evaluate the performance of the c e l l u l a r / W L A N system using different po l i cy combinat ions under various levels of mob i l i t y and arr iva l rates of connection requests. Results show that using cutoff pr i o r i ty po l i cy i n b o t h wireless access networks can achieve the o p t i m a l so lut ion for b o t h op t imiza t i on problems under a wide range of network condit ions. T h e rest of this chapter is organized as follows. T h e ana ly t i ca l model for the integrated c e l l u l a r / W L A N system is described in Section 3.1. T h e opt imizat ion-based admiss ion contro l problems are formulated i n Section 3.2. N u m e r i c a l results are presented i n Section 3.3. A s u m m a r y of the chapter is given i n Sect ion 3.4. 3.1 Ce l lu lar /WLAN System Model Consider a n integrated c e l l u l a r / W L A N system where one or more W L A N s may be deployed inside each cell of the cel lular network as shown i n F i g . 3.1. There are two specific cover- age areas to be considered: the cellular-only coverage area, and the dual cellular/WLAN coverage area. In this context, coverage corresponds to service availabiUty. In general , the d u a l c e l l u l a r / W L A N coverage areas are deployed i n specific areas where the d e m a n d for d a t a service is m u c h higher than the rest of the ce l lu lar -only area [4]. Hor i zonta l and vert ica l handoflPs can occur due to mob i l i t y of the users under different coverage areas. In this section, we present a model for the mult i -service integrated c e l l u l a r / W L A N system. G i v e n the admiss ion contro l policies, we determine the probabi l i t ies of b locking connect ion requests from the new users, and the probabi l i t ies of dropp ing connection requests f rom the handoff users. 3.1.1 Traffic and Mobility Models We first introduce the notat ions. Let M ' ^ denote the set of a l l cells i n a wireless ce l lular network, denote the set of cells adjacent to cell i, W f denote the set of W L A N s inside the coverage area of cel l i, A ^ denote the set of W L A N s adjacent to W L A N k, and denote the set conta in ing the overlaying cell of W L A N k (i.e., a dua l c e l l u l a r / W L A N coverage area). A s an example , from F i g . 3.1, we have: M ' ^ = {1 ,2 ,3 ,4 } , A ^ = {2 ,3 ,4 } , W j — {5,6}, A ^ = {6}, and = {1}. Let <S denote the set of m u l t i m e d i a services available to the mobi le users. E a c h service s e S requires 6̂  basic b a n d w i d t h units ( B B U s ) 16], and B B U s to guarantee its QoS requirements i n the cel lular network and the W L A N , respectively. A s an example, a B B U i n the wireless cel lular network can be 32 kbps, and a B B U i n the W L A N can be 64 kbps. T h e new connection request for service s arrives at cell i and W L A N k according to independent Poisson processes w i t h rates A^̂  a n d A^^, respectively. T h e d u r a t i o n of the connection us ing service s is defined as connection time ts- W e assume that tg is an exponent ia l ly d i s t r ibuted r a n d o m variable w i t h mean l/vg. Since the exponential d i s t r ibut i on is memoryless, the residual (i.e., remaining) connection t ime is also exponent ia l ly d i s t r ibuted w i t h mean l/vg. To model the mobihty , we define the inter-boundary time, s imi lar to [17], as the t ime interval between any two consecutive access network b o u n d a r y crossings by a mobi le user. T h e inter -boundary t ime depends on the size of the cel l and the m o b i l i t y patterns of the users. If an inter -boundary t ime starts at the moment of entering cel l i, then we denote it by ig,. If an inter -boundary t ime starts at the moment of entering W L A N k, then we denote it by f^'^. We assume that bo th tl^ and t^^ are exponent ia l ly d i s t r ibuted random variables w i t h means 1/r/f and 1/ry^, respectively. F i g . 3.1 shows tĝ  between boundary crossing points A and B, and between boundary crossing points B and C. T h e channel holding time i n cell i is defined as the t ime that a connected mobi le user continues to use B B U s of resources i n the network. T h e association holding time i n W L A N k is defined as the t ime that a connected user continues to associate w i t h the access po int . For service type s, the channel ho ld ing t ime i n cell i and the association ho ld ing t i m e i n W L A N k are obta ined as min(^f , ig , ) and m i n ( i f , i ^ J , respect ively Since tf, tg., and t^^ have exponent ia l d i s tr ibut ions for a l l s € 5 , z € M " , and k E W f , the ho ld ing t imes are also exponent ia l ly d i s t r ibuted w i t h parameters fx^^ - Vs + rjf and yÛ ^ = Vs+t]'^, respectively. A mobi le user who is ho ld ing a connection of service type s i n cell i may terminate its connection at the end of its ho ld ing t ime and leave the integrated c e l l u l a r / W L A N system w i t h probab i l i t y q^^ ~ Vs/i^a + r]^). It may also move w i t h i n the system and continue i n an adjacent cell or an under lay ing W L A N w i t h probab i l i ty 1 - q^^. W e have: where g?? denotes the probab i l i ty of a t t empt ing a hor izonta l handoff from cell i to ne igh- bor ing cel l j, and çf^ denotes the probabi l i ty of a t t e m p t i n g a vert i ca l handoff from cel l i to W L A N k w h i c h is inside the coverage area of cell i. S i m i l a r l y a mobi le user who is ho ld ing a connection of service type s i n W L A N k may terminate its connect ion at the end of its association ho ld ing t ime and leave the integrated system w i t h probab i l i t y = Vs/{vs + r/^). It may also move w i t h i n the system and continue i n an adjacent W L A N or an overlaying cell w i t h probab i l i ty I - q"^^. W e have: 1 - c = TTir^ - E ^^^r + E c (3.2) where denotes the probab i l i ty of a t tempt ing a hor izonta l handoff from W L A N k to adjacent W L A N /, and ĝ -̂  denotes the probab i l i ty of a t t e m p t i n g a vert ica l handoff f rom W L A N k to i ts over laying cell i. 3.1.2 Multi-Dimensional Birth-Death Processes E a c h cell i is assumed to have a capaci ty of C f B B U s . L e t > 0 denote the number of connections using m u l t i m e d i a service type s in cell i. T h e capaci ty constraint requires that , Y,<K<C^, ^ieM'=. (3.3) F r o m (3.3), there can be at most [Cf/b'^J connections of service type s i n cell i at any t ime. W e define = {m1^,m1^,... ,m1^) as the occupancy vector i n cell i. For each cell i e M'^, the admiss ion control policies for connection requests from new, hor izontal h a n d - off, and vert ica l handoff users for service type s G <S can be modeled by policy functions Pni.i^i)' Phhi,i''^i)> and /?^/i,^(m?), respectively. T h e po l i cy funct ion /3^.^(m?) determines the probab i l i ty of not accepting a connection request from a new user for service type s i n cell i. S imi lar ly , the po l i cy functions Plf^.^ (m^) and P^^^.^ (m?) determine the prob - ab i l i ty of not accepting a connection request from a hor izonta l handoff user and from a vert i ca l handoff user for service type s i n cell i , respectively. Since handoff requests (i.e., either hor izonta l or vert ical ) have higher pr i o r i ty than new requests, it is necessary that f^kj^i) < f^njrn^i) and /3,%^(m?) < P^^Jm^i) for a l l i G M', and s E S. Note that the probab i l i ty of not accepting connection requests depends on the specific admiss ion control po l i cy being used. In fact, m a n y admission control policies, in c lud ing C P and F G , can be mathemat i ca l l y modeled i n the form of their corresponding po l i cy functions. W e discuss po l i cy functions i n deta i l i n Sect ion 3.2. A n occupancy vector is feasible i f m? > 0 for a l l s 6 <S and the constraint i n (3.3) is satisfied. We denote the set of a l l feasible vectors by 0? . T h e occupancy of cell i evolves according to a mul t i -d imens iona l birth-death process [18]. O n the other h a n d , a birth event happens when a connection request to cell i horn a handoff or a new user is accepted. A death event occurs when a user either terminates its connection or leaves cell i. T h e mul t i -d imens iona l b i r th -death process has \S\ d imensions, where | • | denotes the card ina l i ty of the set. T h e s^^ d imension models the channel occupancy evolvement due to the changes i n the number of connections using service type s. Let Piinii) denote the probab i l i ty of being i n state i n the |5|-dimensional b i r t h - death process corresponding to cell i. We have, = E ^ ^ K ) « ) ' (3-4) BIH., - E Pi^O l^vh.^ K ) ' (3-6) where B^^_^ denotes the probab ihty of bloclcing connection requests for service s i n cell i f r om new users, and B^^^^ and B^^^.^ denote the probabi l i t ies of dropping connection requests for service s i n cell i from hor izonta l handoff and vert i ca l handoff users, respectively. To mode l the capaci ty i n I E E E 802.11 W L A N s , i t is reasonable to assume that there are only packet transmissions between the A P s and the mobile devices, but not a m o n g the devices. For each W L A N k, the med ia access is control led either i n a central ized manner using the point coord inat ion funct ion ( P C F ) , or i n a decentrahzed manner us ing the d i s t r ibuted coord inat ion funct ion ( D C F ) . W e show i n Section 3.5 that i n either case, the capac i ty constraint can be modeled as: E < ^ ^ ^ ^ f c " ' V A ; 6 W ! ^ , V ^ e ^ ^ ^ (3.7) ses where is the effective d a t a rate i n W L A N k i n B B U s , m^^ > 0 is the number of con- nections using service type s i n W L A N k, and = (m^^, m ^ ^ , . . . , m^^) is the occupancy vector i n W L A N k. If P C F is being used, then the effective d a t a rate is close to the nomina l d a t a rate^. O n the other hand , i f D C F is being used (which is wide ly deployed i n current W L A N s ) , the effective d a t a rate is s igni f icantly less t h a n the nomina l rate. There are a few approx imate ana ly t i ca l models that can obta in the capacity of the W L A N under cer ta in assumptions [20, 21]. However, finding an accurate value is not an easy task. Nevertheless, we can use either 802.11-based s imulat i on or test-bed measurements to estimate . In this chapter, we use ns-2 [22] s imulat ions to estimate C ^ . Further detai ls are given i n Sect ion 3.3. Cons ider an a r b i t r a r y cel l i € M'^. For each W L A N k e W ? , the admission control policies for connection requests from new, hor izonta l , and vert i ca l handoff users for service type s e 5 can be modeled by policy functions (3^^^{m)^), Phh^S^k)^ PvhkS''^k)' respectively. A n occupancy vector is feasible i f m^^ > 0 for a l l s G 5 and the constraint i n (3.7) is satisfied. W e denote the set of a l l feasible vectors by 9 ^ . T h e occupancy of W L A N k evolves according to an 15)-dimensional birth-death process independent of other W L A N s . ^ l E E E 802.11a supports 6, 9, 12, 18, 24, 36, 48, and 54 M b p s nominal data rates. I E E E 802.11b also supports 1, 2, 5.5, and 11 M b p s data rates [19]. Let P^{m^) denote the probab ihty of being i n state in the |<S|-dimensional b i r th -death process corresponding to W L A N k. Le t denote the probab ihty of b locking connection requests for service type s i n W L A N k for new users. O n the other hand , B'^^^ and J3^^^ denote the probabi l i t ies of d ropp ing connection requests for service type s i n W L A N k for hor izonta l handoff and vert i ca l handoff users, respectively. W e have, = E ^ ' ^ ( O /3nl « ) , (3.8) BHH,.= E (3.9) - E PkiOPXAO- (3.10) Let 0?̂  denote the birth rate of service type s in the b i r th -death process corresponding to cell i. S imi lar ly , let denote the b i r t h rate of service type s i n the process corresponding to W L A N k. W e have: C = K ( i - f^k « ) ) + E ( i - PL,. « ) ) + E « + f̂ct) ( l - /^k. « ) ) ' (3-11) +E (̂ ^̂ 3 + O ( l - . (3.12) where h'^^ denotes the horizontal handoff rate of service s offered to cell i from its adjacent cell j, f̂ .̂  denotes the vertical handoff rate of service s offered to cell i from its under ly ing W L A N k, r^^ denotes the rate of a l l handoff traffic of service s that is not accepted i n W L A N k and hence is transferred to cell z, hfj^ denotes the horizontal handoff rate of service s offered to W L A N k f rom its adjacent W L A N I, vf^^ denotes the vertical handoff rate of service s offered to W L A N k from its overlaying cell i, and rf̂ '̂  denotes the rate of a l l handoff traffic of service s that is not accepted i n cell i and hence is transferred to W L A N k. W e have: (3.13) hi: UlC lia ^WC „CW r>W 1 \ ^ UWW T3W leAi K ( i - Bi) €: + E ( i - ^ ^ \ . ) c (3.14) (3.15) (3.16) c + E ( c ^ ' ^ + o ( i - ^ x ) c / J^A^ Rik, J (3.17) (3.18) where Rik denotes the coverage factor between W L A N k and cell i (i.e., the rat io between the radio coverage area of W L A N k and the radio coverage area of cell i). Note that 0 < Rik < 1 for a l l i € M"^ and k G W f . New connection arr iva l rates as well as the hor izonta l and vert i ca l handoff rates are shown in F i g . 3.1, where the subscript s is omit ted for the sake of c larity. Let (fl^ denote the death rate of service type s i n the b i r th -death process corresponding to cell i. R e c a l l that a death event occurs when a user either terminates its connect ion or leaves cel l i. S imi lar ly , let 93̂ ^ denote the death rate of service type s i n the process corresponding to W L A N k. W e have: V^.=KfA., (3.19) ^l^mlt^l. (3.20) G i v e n the po l i cy functions P^.^, /?^^.^, f]^,^^ , (3^^ , (Sj^f,^^ , P^^f^^ , and the network parameters nï, VÏ, f^l, 1^1, q£ qnJq^, Q > vjb'i, a n d 6- for a l l i,j e M^, k,l e and s e S, we can solve the global balance equations from the b i r th -death processes and obta in the corresponding b lock ing and dropp ing probabihties B^^ , Bf^f^, , 5^%^, B^^^, B];:^^^, and B^,^^^ for a l l i E M^, k e W f , and s e S. To compute the b i r t h rates i n (3.11)-(3.12), we need to solve the set of fixed-point equations given by the handoff rates (3.13)-(3.18). It can be accomplished by using the i terat ive fixed-point a lgor i thm of repeated subst i tut ions [23]. T h e fixed-point a lgor i thm is described i n Section 3.6. 3.2 Connection Admission Control In this section, we introduce the concept of po l i cy functions and derive the corresponding functions for the admission control policies. W e also define the po l i cy combinations and formulate the o p t i m i z a t i o n problems. In general, the operat ion of admission control using po l i cy functions i n the integrated c e l l u l a r / W L A N system is i l lus trated i n F i g . 3.2(a) if the connect ion request arrives at cell i G M"^, and i n F i g . 3.2(b) when it arrives at W L A N k G W f . For the sake of s impl ic i ty , the subscript s for service type s is omit ted . 3,2.1 Policy Functions For each cell i G M"^, connection admiss ion control includes the po l i cy functions (m^), /3^;j.^(mf), and /3f^^^(mi) for new, hor izonta l , and vert i ca l handoff connection requests, respectively. T h e po l i cy functions are able to model the behavior of the admiss ion control policies. T h e y determine the probab i l i ty of not accepting a connection for each type of request and service, given the occupancy vector and according to a specific policy. T h u s , network designers can use them either to evaluate admission control policies already proposed or to examine new ones. T o determine the corresponding pohcy functions, the designer decides how each type of connection request is being treated (i.e., accept or reject) based on the current number of connections of each service (i.e., the occupancy vector) . A pohcy can be modeled i f i t can be represented as a funct ion of the occupancy vector. A s ment ioned i n Sect ion 3.1, pr ior i ty is usual ly given to handoff connection requests over new connection requests (i.e., /3ft/,.^(m^) < /3^.^(mf) and /S^^im^) < /?^,^(mf)). In the case of an integrated c e l l u l a r / W L A N system, considerations have to be made on how to set I3lf^.^{m1) and I3l}^.^{mf) based on the differences between hor izontal and ver t i ca l handoff connection requests. Note that the vert ica l handoff decision process always occurs before the connect ion request. Such decision process is more elaborate than the one for the hor izonta l handoff, w h i c h is usual ly based on the R S S from the B S . T h e vert i ca l handoff decision, besides R S S , needs to consider add i t i ona l parameters such as access cost, power consumption , and Q o S factors [24]. Interested readers may refer to [25], [26] and the references therein. For the scope of this work, the admiss ion control po l i cy is invoked once the vert i ca l handoff decision has been made. F r o m the network operator 's po int of v iew, we can d iv ide the treatment of the vert i ca l handoff connection requests into two cases: 1. If the connection request is from a user who is a subscriber of the network on w h i c h admission is requested, then the operator may set the po l i cy functions /?̂ ;̂ , (mf) = l^vhiS^i)- T h a t is , the users i n cel lular networks receive the same QoS i n terms of p robab i l i t y of dropp ing connections when v i s i t ing a W L A N . 2. If the connection request is f rom a user who is not a subscriber of the network on w h i c h admission is requested (i.e., a r oaming user), then the operator m a y set the po l i cy functions (3^f^.^{mi) < P^f^,^{mi). T h a t is, the hor izonta l handoff users from neighbor ing cells have pr i o r i ty over the vert i ca l handoff users from W L A N s . B y us ing the po l i cy functions, we can extend C P and F G as two examples of admiss ion control policies from wireless cel lular networks to the integrated c e l l u l a r / W L A N systems. Reca l l that the C P po l i cy reserves a f ixed number of available channels (i.e., B B U s ) for handoff requests. U s i n g the notat ion of po l i cy functions, a connect ion request to cell i for service type s is rejected by the C P pol i cy w i t h the fol lowing probab i l i ty for new users: /?n.. K ) = <( s'es (3.21) 1, otherwise. and the foUowing probabiht ies for i i or izonta l and vert i ca l handoff users: Plk,, K ) = { (3.22) ( 1, ot i ierwise, K ) = \ ^'es (3.23) ( 1, otherwise, where X^yg^ "z?^,?'̂ ' denotes the current occupancy, the integer parameter T^^ i n (3.21) is used to tune the threshold to give pr ior i ty to handoff requests, and the parameter K-^ i n (3.23) is used to tune the threshold to give pr i o r i ty to hor izonta l handoff requests. Note that for a l l i e and s e S, we have 0<Tf^<C^- 6̂  and 0 < Vf^ < Cf - b",. In (3.22) and (3.23), case 2 is considered. Note that by sett ing V^^ = C f - 6 ,̂ case 2 reduces to case l(i .e., /5 ; ; ,Jm^)=/3 ,^,Jm?)). In the F G pol icy, connection requests from either new users or vert i ca l handoff users are rejected w i t h probabi l i t ies which are proport iona l to the current occupancy. A connection request to cell i E for service type s is rejected by the F G pol i cy w i t h the fol lowing probab i l i ty for new users: f 0, iîYjnlbt,<Tl, / 5 ; , K ) = <̂  s'es (3.24) [ m i n {^{T^ ), l ) , otherwise, HTO = — (3.25) Cf-b'i + l - T l and the fol lowing probabi l i t ies for hor izontal and vert ica l handoff users: \ 0, if E</^'^^^-^- 5'65 (3.26) 1, otherwise. 0, i f x ; < / : ' < ^ , : , = <; Tts (3.27) i^min ($(V^j^),l) , otherwise. Note that (3.25) is equal to zero when the occupancy is at its threshold (i.e., J2s'es '^1 ,K' ~ TfJ, and is greater t h a n or equal to one when there is not enough b a n d w i d t h to al locate (i-6-> Yls'es ^ C'f "-6^ + 1). T h e probab i l i ty of not accepting new connection requests increases linearly f rom zero to one as the occupancy increases from T^^ to C f - 6̂  + 1. For W L A N k, connect ion requests from new, hor izonta l , and vert ica l handoff users for service type s are not accepted w i t h probabi l i t ies Pl^^^ (m^), ^̂ /̂ ^ (m^), and ,5̂ ^̂ ^ (mf), respectively. Such po l i cy functions can be defined s i m i l a r l y according to C P or F G policies. W e need to replace the superscript c w i t h w, and the subscript i w i t h k i n (3.21)-(3.27). 3.2.2 Policy Combinations and Optimization Problems G i v e n the C P and F G admission policies, four different po l i cy combinations can be con- sidered: 1. Wire less cel lular systems and W L A N s bo th use C P po l i cy (i.e., CP^-CP""). 2. Wireless ce l lular systems use C P policy, and W L A N s use F G po l i cy (i.e., CP^-FC"). 3. Wireless cel lular systems use F G p o l i c y and W L A N s use C P pohcy (i.e., FC^-CP""). 4. Wire less cel lular systems and W L A N s b o t h use F G po l i cy (i.e., FC-FC"). For any combinat ion , different parameters T^, T^^, V^] and V;^^ for a l l i € M", € W f and s E S can lead to different performance. T h e questions are: Which of the four possible combined policies should be used? How should the corresponding parameters be chosen? To answer these questions, we consider the fo l lowing two o p t i m i z a t i o n problems: Optimization Problem 1 : G i v e n the po l i cy functions and the network parameters, max imize a l inear objective funct ion of the accepted traffic for connection requests from new as wel l as hor izonta l and vert i ca l handoff users: + E < M ( i - ) + -t..r,,,^ ( i - 5 . - . . J + ,w (3.28) where V^h,^ and xp^^f^^^ denote the aggregated rate of hor izonta l handoff traffic of service type s that arrive at cel l i and W L A N k for a l l i € M'^ and k G W f , respect ively and ip'^f^^ denote the aggregated rate of vert ical handoff and transferred traffic of service type s that arrive at cel l i and W L A N k for a l l i e M" and k e W f , respectively. W e have: - E ^ r > fcewf tel?™ (3.29) (3.30) (3.31) (3.32) Note that the b lock ing and dropp ing probabi l i t ies B^.^, Bl^. , B^ , B'!^^ , 5̂ ^̂ ^ , and B^,^^ depend on the po l i cy functions /J^;^^, and whereas the po l i cy functions depend on T^^^, T^^, Vf^, and V^^. In (3.28), the constants a^^,^, a)^^^ ,̂ a^^. , and ajf^^ denote the revenue of accepting a connection request for service type s from a hor izonta l a n d from a vert i ca l handoff user i n cell i and W L A N k, respectively. S imi lar ly , a^^^ and a^^ denote the revenue of accepting a connection request for service type s f rom a new user i n cell i and W L A N k, respectively. In general, it is reasonable to set a^,^ <C a^/j.^ and a^.^ <C a^^.^ for a l H G A I ' ' and s e S to ensure that a higher pr i o r i ty is given to accepting connect ion requests from handoff users of any type rather than new users. W e can also assign different revenues for different services. It is useful when the services are offered w i t h different service fees. B y removing the constant terms, prob lem (3.28) can be reduced to the fol lowing equiv- alent b lock ing cost m i n i m i z a t i o n problem: m i n i m i z e j'C j^w yc yw / 's' ks- is' ks ^^J^c L (3.33) where af^f^.^ can be interpreted as the amount of revenue lost due to dropping a connection request for service type s f rom a hor izonta l handoff user i n cell i. It can also be interpreted as the cost of dropping. T h e rest of the parameters can be interpreted i n a s imi lar way (i.e., cost of b locking) . T h u s , the objective of prob lem (3.33) is to m i n i m i z e a l l penalty costs (i.e.. revenue loss) incurred i n the integrated c e U u l a r / W L A N system when connection requests from new, hor izonta l , a n d vert i ca l handoff users are blocked and dropped, respectively. For the rest of the paper , we refer to this cost as the cost of blocking connections. Optimization Problem 2: G i v e n the po l i cy functions and the network parameters , max imize a l inear funct ion of accepted traffic for connection requests from new users subject to the constraints on dropp ing probabi l i t ies for connection requests from handoff users: maximize Y < K f 1 - ) + K f 1 - 1 s € 5 ieM" (3.34) subject to B^,^^ < r^,^^, V z e 5 G 5 , < r r . , , , \/kew:,seS, where r^;,,^^ and F)̂ ^^^ are the m a x i m u m dropp ing probabi l i t ies tolerated for hor izonta l handoff users of service type s i n cell i and W L A N k, respectively. F J ^ , and F^^^ are the m a x i m u m dropp ing probabi l i t ies tolerated for vert ica l handoff users of service type s i n cell i and W L A N k, respectively. C o m p a r e d to the objective funct ion i n (3.28), we can see that the one i n (3.34) does not include the revenue obtained from handoff users. Instead, new constraints are introduced to guarantee the QoS requirements for those users. B y removing the constant terms, prob lem (3.34) can be reduced to the fol lowing equiv- alent b lock ing cost m i n i m i z a t i o n problem: minimize V V a^. X' + X^ B. is' ks' is' ks . g _ ^ c L ill; kewf (3.35) subject to Blf,^^ < r ^ , , ^ , V 2 e X ^ s e 5 , B:,,^<rx^, y k e w t , s e s . In problem (3.35), the parameter a'^^^ can be interpreted as the cost of b l ock ing a connection request for service type s from a new user i n cel l i. T h u s , the objective of problem (3.35) is to m i n i m i z e a l l penalty costs incurred in the integrated c e l l u l a r / W L A N system when connection requests f rom new users are blociced subject to Q o S constraints for connect ion requests from fiandoff users. In other words, the QoS is guaranteed for connections f rom users already accepted i n the system, while a iming to m i n i m i z e the penalty of reject ing new users. T h e problems i n (3.33) and (3.35) are combinator ia l o p t i m i z a t i o n problems. T h e y can be solved by using either the exhaustive search, or other meta-heurist ic algorithms [27 . Note that the search space of the problem is = x • • • x T̂ '̂ ^ x Vf^ x • • • x V f ^ x x • • • X Tfc-, x V , - X • • • x V,-^^ where j:^^ = V^; = { 0 , 1 , . . . , L Q / 6 ^ J } ' f o r cell i e a n d s € <S and = VI = { 0 , 1 , . . . , [C^/b'^l} for cell G W f and s e S. T h e complex i ty of the exhaustive search a l g o r i t h m depends on the size of the search space \Q\. O n the other hand , meta-heurist ic a lgor i thms perform a guided search only over a subset ft' of the search space fi. T h u s , the complex i ty of such a lgor i thms is lower i n terms of the search since \Q,'\ < Note that the size of f2' of the guided search depends on the meta-heurist ic a lgor i thm being used. 3.3 Numerical Results and Discussions W e evaluate the performance of an integrated c e l l u l a r / W L A N system consist ing of a wire - less cel lular network w i t h [M''] = 3 cells, and j W f | = 2 W L A N s . T h e cells and W L A N s are enumerated as follows: = {1 ,2 ,3} , W f = {4,5}, W | = {6, 7}, and W f = {8,9}. T h u s , inside the coverage of cel l 1, there are two d u a l c e l l u l a r / W L A N coverage areas given by W L A N 4 and W L A N 5, respectively. In each cell i G M'^, the network capacity is 2 M b p s , and the B B U is set to 32 kbps based on the 3 G P P supported m u l t i m e d i a bearer services 28]. T h i s implies that the capac i ty i n (3.3) of each cell is C f = 62 B B U s . We assume that two m u l t i m e d i a services are offered (i.e., S — {1,2}) . T h e first service, i.e., s = 1, is voice connections requir ing 32 kbps. T h e second service, i .e., s = 2, is video connections requir ing 64 kbps . T h e values are set according to the m u l t i m e d i a codecs for 3 G P P [29]. T h u s , the Q o S provis ioning i n cel l i requires that — 1 B B U and b2 = 2 B B U s . In each W L A N k G W f , we need to determine the effective d a t a rate in order to set the network capac i ty C^ in (3.7). In this paper, we use ns-2 [22] s imulat ions to estimate C ^ . T h e I E E E 802.11b [19] is considered, and the nominal d a t a rate is set to 11 M b p s . T w o groups of constant b i t rate ( C B R ) sources are being s imulated : the first group w i t h 64 kbps d a t a rates representing service 1 for voice connections, and the second group w i t h 128 kbps d a t a rates representing service 2 for video connections. Note that the data rates of the services i n W L A N s are reasonably assumed to be larger t h a n the rates i n the wireless cel lular systems i n order to benefit f rom the add i t i ona l capacity. T h e measured aggregate throughput when the number of connections of service 1 increases from 1 to 110 and the number of connections of service 2 increases from 1 to 60 is shown i n F i g . 3.3. T h e aggregate throughput is ca lculated by s u m m i n g the number of a l l correctly t ransmi t t ed bits d iv ided by the s imulat i on t ime . W e can see that when the number of connections is low, the aggregate throughput increases l inear ly w i t h respect to the increase i n the number of service 1 and service 2 connections. However, as the number of users passes certain thresholds, the network becomes saturated and the throughput does not increase further. T h e aggregate throughput at the saturat ion point is indeed the effective capac i ty that the W L A N can support . F r o m the results i n F i g . 3.3, we see that the effective d a t a rate of C]^ is 7.4 M b p s . For the W L A N s , each B B U is equivalent to 64 kbps. T h e QoS provis ioning i n W L A N k requires that 6]f = 1 B B U and = 2 B B U s . T h u s , the capaci ty of each W L A N i n (3.7) is = 116 B B U s . In our proposed mode l , the capacity of the W L A N s i n (3.7) is an approx imat ion . D u e to the contention nature of the D C F , the exact capacity of the W L A N depends, among other factors, on the number of users. To be precise, should be a funct ion of mj^. T h i s is depicted i n F i g . 3.3. However, since we are interested i n the m a x i m u m number of connections that can be supported simultaneously, we approx imate the capac i ty of the W L A N as the sa turat ion throughput (i.e., constant effective capaci ty i n B B U s ) . In our study, we consider different traffic patterns by assigning different values to p a - rameters Af^ and A^^, and assuming that A^̂  < A^^. T h e coverage factor Rjf. is 0.5. T h e connection durat ions have means l/vi — \/v2 = 6 minutes. T h e inter -boundary t ime in cell i has mean l / r ; ^ = 2 minutes, and the inter -boundary t ime i n W L A N k has mean l/if^ = 4 minutes. For a l l i e and a l l k G W f , the previous values of connection durat i on and inter -boundary times i m p l y that qf^ = qf^ = 0.25 and = q^^ = 0.40, which correspond to a m o b i l i t y level of 7 5 % for the users i n the wireless cel lular network, and a lower m o b i l i t y level of 6 0 % for the users i n the W L A N s . For the fixed-point a lgor i thm described i n Section 3.6, we use e = 10~^. W e first consider case 1 from Sect ion 3.2.1 where the operator offers the same QoS i n terms of d ropp ing probabi l i t ies to hor izonta l and vert ica l handoff users. T h u s , /?^^, (m^) = P'^hjf^i)- In add i t i on , Vf^ = Cf - b", and = C]^ - b"^ for a l l i e M^, k e W f , and s e S. Results for case 2 w i l l be presented i n Section 3.3.3. T o solve the op t imizat i on problems (3.33) and (3.35) and to ob ta in the solutions T^^ and T^^ for a l l i G M", k G W f , and s E S, we used the exhaustive search. For each of the m i n i m i z a t i o n problems (3.33) and (3.35), we consider four po l i cy combinations (e.g., CP'^-CP^, FC^-CP^), and obta in the o p t i m a l value for each case. 3.3.1 Results for Optimization Problem 1 F i g . 3.4 shows the o p t i m a l values obtained from each combined po l i cy for the cost m i n i m i z a - t i on version of the first o p t i m i z a t i o n prob lem (i.e., prob lem (3.33)). We assume that , for a l l iEM^,ke and s e S, < ^ = a - ^ = 1, a^,,^ - a^,^^ = 10, and a^^ = 10. In add i t i on , we set = A?̂  and A^^ = aX^^ new connection requests per minute . Since more traffic is generated i n a d u a l c e l l u l a r / W L A N coverage area [4], we assume that cr = 6. W h e n traffic is low (i.e., A i < 0.25 and A2 < 0.25 new connection requests per minute ) , the four pohcy combinat ions operate quite close due to the sufficient network capacity. H o w - ever, as the arr iva l of connection requests from b o t h services increases, the performance of these four combinat ions differs. T h e lowest b locking cost is achieved by CP'^-CP'^. In F i g . 3.5, we investigate the cost of b locking connection requests from handoff users i n prob lem (3.33). In this figure, an, = al^^^ = a^^^^ = a^^^.^ = o^^^^ for a l l i e M", k e W f , and s € 5, and cnh, increases from 1 to 15. T h u s , the penalty cost (i.e., revenue loss) incurred by the network operator increases when a handoff connection request of any type (i.e., hor izonta l or vertical) is dropped. Not i ce that i n this case, we have: (m^) = PlhiS"^^) ^'^^ PhhkS^k) = PvhkS^k)- Results show that the relative rank ing of the four combinations remains the same, and that po l i cy combinat ion CP'^-CP^ provides the lowest b lock ing cost. W h e n ah, = 10, CP^-CP"" provides 24.7%, 35.2%, and 46.6% lower b locking cost t h a n FG^-CP"", CP^-FG"", and FG^-FG"", respectively. F i g . 3.6 shows the dropp ing probabi l i t ies for handoff connection requests i n cell 1 and W L A N 4 for CP'^-CP^. T h e arr iva l rate of new connection requests for service 1 is increased, whi le the arr iva l rate of requests for service 2 is fixed at 0.5 new connection requests per minute . In this scenario, the o p t i m a l values are 7̂ ?* = 54, T^* = 54, T^* = 111, and T^^* = 109 for CP^-CP"" for a l l ieM" andke W f , and correspond to A i = A2 = 0.5 new connections per minute . In Figs . 3.7 and 3.8, the level of mob i l i t y i n the cells of the wireless cel lular network and W L A N s is increased, respectively. T h e traffic is set to A i = A2 = 1 new connection requests per minute . In F i g . 3.7, the level of mob i l i ty i n cell i for a l l i G M'^ and s E S given by (3.1) (i.e., 1 - ) is increased from 0.1 to 0.7, while the m o b i l i t y i n W L A N k for all k e W f and s e S is fixed at ĝ ^ = q^^ = 0.40. T h e mob i l i t y is increased by reduc ing the probab i l i ty of t e rminat ing a connection from service s i n cell i. T h u s , more hor i zonta l and vert ica l handoff' requests arrive at the adjacent cells and W L A N s . D u e to the fixed capacity and traffic, an increase i n connection requests from handoff users translates into more connections being blocked and dropped. T h e increase of the b locking cost can be observed i n F i g . 3.7. In F i g . 3.8, the level of m o b i l i t y i n W L A N k for a l l A; e W f and s G 5 given by (3.2) (i.e., 1 - J is increased from 0.1 to 0.5 since the mob i l i t y i n W L A N s is lower t h a n i n the cells, whi le i n cel l i for a l l i € M'^ and s G 5 the level of m o b i l i t y is fixed at gfi = gfj = 0.25. There is an increase i n the cost of b lock ing connections as the level of m o b i l i t y increases. O n the other h a n d , when the m o b i l i t y decreases, the b lock ing cost decreases because most of the connections terminate inside their current cell or W L A N . In b o t h cases, the use of C P i n bo th networks achieves the lowest b lock ing cost. 3.3.2 Results for Optimization Problem 2 F i g . 3.9 shows the o p t i m a l values obtained from each combined pol icy for the cost m i n i m i z a - t i on version of the second op t imiza t i on prob lem (i.e., prob lem (3.35)) w i t h QoS constraints on the dropp ing probabi l i t ies for connection requests from handoff users: F^^ .̂ = F)^;, = 0.01, r ,̂̂ ^ = r-,^^ = 0.01, r^,^^ = r)^,,^ = 0.05 and r^,.^ = = 0.05. We L u m e that for a l l i G M'^, k G W f , and s E S, a%. = a!", = 1. A s the arr ival of new connection requests from b o t h services increases, the performance of these four combinat ions differs. T h e lowest b lock ing cost is achieved by CP^-CP"", wh i ch is followed closely by CP^-FG"". O n the other h a n d , the minimum b lock ing costs of FG^-CP^ and FC^-FG^ appear to be close. D u e to the constraints i n the handoff dropping probabi l i t ies and lower capaci ty of the cel lular network when compared to W L A N s , the performance of the wireless cel lular network dominates the performance of the integrated c e f i u l a r / W L A N system, causing the po l i cy combinat ions using the same po l i cy in the wireless cel lular network (e.g., CP'^-CP'^ and CP'^-FG^) to have s imi lar b lock ing costs; hence, causing po l i cy combinat ions CP'^- FG^ and FC^-CP^ to have different r a n k i n g t h a n i n the first prob lem. However, the lowest b lock ing cost is achieved by CP^-CP^. F i g . 3.10 shows the probab i l i ty of dropp ing connection requests from handoff users of service 1 and 2 i n cell 1 and W L A N 4 when the arr iva l rate of new connect ion requests from service 2 increases. T h e arr iva l rate of new connect ion requests from service 1 is fixed at 0.5. T h e results correspond to the combinat ion CP'^-CP^, wh i ch provides the best performance i n terms of handoff dropp ing probabi l i t ies . In this scenario, the o p t i m a l values are: T^^; = 6 2 , T,^; = 5 3 , 7 ; ^ = 112 , and T;^* = 101 for a l l i e and k e W f , and correspond to the traffic A i = 1 and A2 = 1 new connection requests per minute . Note that i n b o t h access networks, the dropp ing probabi l i t ies for service 2 are higher due to the fact that each connect ion requests twice more B B U s than service 1. A l s o , for both services, the dropp ing probabi l i t ies are higher i n the cel l t h a n i n the W L A N , due to the lower capac i ty i n the wireless ce l lular network compared to the W L A N , which generates values closely approaching the Q o S constraints . In F igs . 3 .11 and 3 .12 , the level of m o b i l i t y i n the cells of the wireless cel lular network and W L A N s is increased, respect ively T h e traffic is set to A i = A2 = 0.5 new connection requests per minute . In F i g . 3 .11 , the level of mob i l i t y i n cell i for a l l i 6 M'^ and s e S is increased from 0.1 to 0 .7 , whi le the mob i l i t y i n W L A N k for a l l A; G W f and s e S is fixed at = Qk, = 0 .40 . In F i g . 3 .12 , the level of mob i l i t y in W L A N k for a l l A; e W f and s e 5 is increased from 0.1 to 0 .5 , whi le the mob i l i t y i n cell i for a l l i G M'^ and s € <S is fixed at Qii — Q.i2 ~ '̂ •25- In b o t h cases, due to the constraints i n the handoff probabi l i t ies , the cost of b l ock ing of the four combinat ions are close when 1 — gf̂  < 0.4 and 1 — < 0.4. T h a t is, only 4 0 % or less of the users perform handoffs. T h i s behavior is different from the first o p t i m i z a t i o n prob lem. F i n a l l y , i n b o t h mob i l i t y cases, the use of C P i n the two networks achieves the lowest b lock ing cost. Results of CP'^-CF^ are expected since C P is the admiss ion control po l i cy that most favors connect ion requests from handoff users. A l s o , the values of the revenue/cost terms (e.g., Q;^^^ , al^. ) for connect ion requests as wel l as the rest of the parameters are consistent and set based on the design objectives proposed for problems (3 .33) and (3.35) which are to guarantee the Q o S for the mobi le users already a d m i t t e d into the system (i.e., handoff users). It is wor th to ment ion that a l though i n some cases F G is able to provide a b lock ing probab i l i ty lower t h a n C P for connection requests from the new users, i t is at an expense of higher dropp ing probab i l i ty for connection requests from the handoff users. T h u s , the tradeoff between these two probabi l i t ies should be set based on the operator 's expected level of QoS . In handoff management, usual ly the connection requests from the handoff users have a higher p r i o r i t y t h a n the requests from the new users since from the users' point of v iew, hav ing a connect ion abrupt ly terminated is more annoy ing than being blocked occasional ly on new connection attempts . 3.3.3 Results for Handoff Differentiation In this subsection, we consider case 2 from Section 3.2.1, where (mf) 7̂  P^^. (mj ) . F i g . 3.13 shows an example of this case i n which we set (mf) as (3.23) w i t h Vf^ = 58 i n cel l i for a l l ieM^ and se S, and (m^) w i t h V^^ = 112 i n W L A N k for a l l keW^ a n d s e S. F i g . 3.13 shows the probab i l i ty of dropp ing connection requests from hor izonta l and vert i ca l handoff users of service 1 and 2 in ceh 1 and W L A N 4 when the arr iva l rate of new connect ion requests from service 1 is increased. T h e arr iva l rate of new connect ion requests from service 2 is fixed at 0.5. T h e arrows depict the difference i n probab i l i ty of dropp ing connect ion requests between each type of handoff request. A s an example, we can see that i n cell 1, the probab i l i ty of dropping a hor izonta l handoff is 8 1 % and 8 4 % lower t h a n the probab i l i ty of dropp ing a vert ica l handoff for service 1 and 2, respectively. 3.4 Summary In this chapter, we developed an ana ly t i ca l mode l to faci l i tate the performance evaluat ion and parameter adjustment of different admiss ion control policies i n a mult i -service inte- grated c e l l u l a r / W L A N system. O u r mode l takes into account the mob i l i t y and the rate of connection requests of the users, the capaci ty and the coverage area of each network, the admission contro l policies, the cost from b locking connection requests for each service, and the QoS requirements i n terms of b lock ing and dropp ing probabi l i t ies . G i v e n the mode l , we also formulate two different revenue m a x i m i z a t i o n problems to adjust the admission control parameters. W e evaluate four different combinat ions of admission contro l pohcies by extending the C P and the F G policies w i t h po l i cy functions. Results show that , under a wide range of condit ions, using the C P po l i cy i n b o t h access networks achieves the best performance. 3.5 Proof of I E E E 802.11 W L A N Capacity Model T h e I E E E 802.11 s tandard [19] defines two media access methods: the P C F and the D C F . We consider b o t h cases: a) W L A N k is contro l led using P C F . Since the media access control is centralized i n this case, there is no interference among the transmissions of different users. A s a result , the users can fu l ly u t i l i ze the available effective capacity. K n o w i n g that the aggregate required da ta rate to support connections from a l l different services is equal to Ylsçs ''^ks^^^ constraint (3.7) is d i rec t ly resulted. Note that i n this case is almost the same as the W L A N n o m i n a l capacity. b) W L A N k is contro l led us ing D C F w i t h carrier sense mul t ip le access w i t h co l l i s ion avoidance ( C S M A / C A ) . W e assume that the neighboring W L A N s operate on different frequency channels so that they do not interfere w i t h each other. Let Us denote the set of connected users of service s. A l s o let / „ denote the fract ion of t ime that user u is active (i.e., it t ransmits / rece ives d a t a from the access po int ) . Since D C F is distributed, users compete to access the channel and interfere i n each other's transmissions. A c c o r d i n g to the protocol interference model [30], i t is necessary to have, E E ^ 1- (3.36) ses ueUa To serve user u e Us, it is required that : K=-îuCt, (3.37) where fuC"^ denotes the d a t a rate achieved by user u. F r o m (3.37), we have: E E / « = E E § = c ^ E < x , (3.38) ses ueUs ses ueu, ses where we used the fact that \Us\ = m^^. Replac ing (3.38) i n (3.36), inequahty (3.7) is obtained. In pract ice , C^ is s ignif icantly lower than the n o m i n a l capacity when D C F is being used. 3.6 Iterative Fixed-Point Algorithm To compute the b lock ing and dropp ing probabi l i t ies for connection requests from new and handoff users of service s, the fol lowing i terative f ixed-point a lgor i thm is used: A l g o r i t h m 3 - F i x e d - P o i n t A l g o r i t h m . 1: Specify e > 0. 2: Set 5;;^^= Bf,,^= 3^ = 0, and B^^ = B}^,^= Bj^h, = 0, V z G A; e W f , and s £ S. _ _ _ 3: W h i l e E^esiK, - 5^. , I + - I + I X H . , - I + 1^:,^ - B^^^ | + I^T,,^ - 5 r . J + - 5 . \ J ) > e do 4: Solve the system of equations of handoff rates given by (3.13)-(3.18). 5: C o m p u t e the b i r t h rates (pl and ç!»̂ ^ given by (3.11)-(3.12). 6: Ca l cu la te the b lock ing and dropping probabi l i t ies B^. , B^^, , B^^, , B^^ , B^^^ , and Byhk so lv ing the global balance equations and using (3.4)-(3.6) and (3.8)-(3.10). 7: U p d l t e B ^ B ^ , S^,^^ = 5 ^ , B^^ = Bû~, B^^^ = S ^ , B^,^^ = S ^ , and 8: end Convergence of the f ixed-point a lgor i thm is ensured since the operat ion i n step 6 cor- responds to a contract ion mapp ing . Note that the convergence rate of the f ixed-point a lgor i thm is geometric [23 . F i g u r e 3.1: A n integrated c e l l u l a r / W L A N system. Reject new connection Reject new connection Connection arrival \ V to cell I J New - .̂connection? , Yes No Policy Accept new connection in cell / > Connection arrival ̂ to WLAN k j New ĉonnection?, No Yes Policy f Accept nevi \ { connection j V in WLAN k J Policy /^Accept handol ( connection V in cell i (a) Policy Accept handoSX connection 1 in WLAN *: / (b) Dual Coverage? No Yes Connection transferred to WLAN/t Policy /icceprhandoffX ( Reiect\isnàon\ I connection 1 \ connection ) V i n WLAN* y ^ Connection transferred to cell/ Policy /Accept handoâ\ [ connection 1 '\ in cell i / ^ Reject handoff V connection F i g u r e 3.2: Operat i on of admission control using po l i cy functions i n the integrated cel lu- l a r / W L A N system: (a) A connection request arrives to cell i for a l l i e M". (b) A connection request arrives to W L A N k for a l l k e W f . F i g u r e 3.3: Aggregate rietworlî t i i rougl iput i n a W L A N wi ien t i ie number of connections for service type 1 varies from 1 to 110 and t i ie number of connections for service type 2 varies from 1 to 60. Arrival rate service 2 (X.^) Arrival rats service 1 (X.^) 1 0 F i g u r e 3.4: Cost of bloclcing connections versus the arr ival rate of new connection requests of service type 1 (Aj) and the arr iva l rate of new connection requests of service type 2 ( A 2 ) for op t imizat i on problem 1. Cost of dropping a tiandoff request (a^ ) F i g u r e 3 .5 : Cost of bloclcing connections versus the cost of dropp ing a connection request from a handoff user (a/^J for a l l s e S for o p t i m i z a t i o n prob lem 1. 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Arrival rate service 1 (X^ ) Figure 3 .6 : Handoff dropping probabi l i t ies in cell 1 and W L A N 4 for CP' - CP"" versus the arr iva l rate of new connection requests of service type 1 (Ai ) for op t imiza - t ion problem 1. Bl,^^^ = 5̂ ^̂ ^̂  and 5^,,^ = B'^^^ for a l l i e M', k e W f , and s e S. 28 1 I 1 : 1 I ^ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Mobility in cell / ( l - q p F i g u r e 3.7: Cost of l i loclcing connections versus mob i l i ty i n cell i for a l l i G for o p t i m i z a t i o n prob lem 1. 25 Qi 1 , i , , , , 1 0.1 0.15 0.2 0.25 0,3 0.35 0.4 0.45 0.5 Mobility in WLAN/ ( Figure 3.8: Cos t of b lock ing connections versus mob i l i ty i n W L A N k for al l k e W- for o p t i m i z a t i o n problem L Arrival rate service 1 (X^) F i g u r e 3.9: Cost of bloclcing connections versus tl ie arr iva l rate of new connection requests of service type 1 (Ai ) and the arr ival rate of new connection requests of service type 2 ( A 2 ) for o p t i m i z a t i o n problem 2. F i g u r e 3.10: Handoff dropping probabi l i t ies in cell 1 and W L A N 4 for CP" - CF" ver- sus the arr iva l rate of new connection requests of service type 2 ( A 2 ) for op t imiza t i on prob lem 2. 5^^^^ = Bl^^^ and Bf^f^^ = B^;,^ for a l l i e M', k e Wf, and s E S. 1.6 -ji J I , j _ 0.2 0.3 0.4 0.5 0.6 Mobility in cell ; ( l - q p F i g u r e 3.11: Cost of b locking connections versus mob i l i t y i n cell i for a l M G M'' for o p t i m i z a t i o n problem 2. 0.35 0.3 F I 0.25 o Q) c 8 0.2 CD .£ lac: S 0.15 0.051- CF^-FG'^ 0*- 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Mobility in W L A N / ( ( l - q " ; F i g u r e 3.12: Cost of b locking connections versus mob i l i ty in W L A N k for a l l A: e W f for o p t i m i z a t i o n problem 2. Arrival rate service 1 (X,) Figure 3.13: Hor i zonta l and vert i ca l handoff dropping probabi l i t ies i n cel l 1 and W L A N 4 for CP'^ — CP"' versus the arr ival rate of new connection requests of service type 1 (Ai ) . 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R o l l , "Metaheur is t i cs i n C o m b i n a t o r i a l O p t i m i z a t i o n : Overv iew and C o n c e p t u a l C o m p a r i s o n , " ACM Computing Surveys, vo l . 35, no. 3, pp. 268-308, 2003. 28] 3 G P P , " C i r c u i t Bearer Services Supported by a P u b l i c L a n d M o b i l e Network , " T S 22.002 (v7.0.0), June 2007. [29] , "Codecs for C i r c u i t Switched M u l t i m e d i a Telephony Service," T S 26.110 (v7.0.0), June 2006. 30] K . J a i n , J . Padhye , V . P a d m a n a b h a n , and L . Q i u , " Impact of Interference on M u l t i - hop Wireless Network Performance , " i n Proc. of ACM MobiCom'03, San Diego, C A , September 2003. Chapter 4 Handoff Management and Admission Control using Virtual Partitioning with Preemption in 3G Cellular/802.16e Interworking A broad range of wireless access technologies is being deployed worldwide. E x a m p l e s include the 3 G cel lular systems such as U M T S and C D M A 2 0 0 0 , W L A N s , and broadband wireless systems such as W o r l d w i d e Interoperabi l i ty for Microwave Access ( W i M A X ) . T h e integrat ion of a l l these networks is usual ly cal led the 4 0 heterogeneous wireless networks 1], [2]. T h e I E E E 802.16e s tandard (also called mobi le W i M A X ) [3] includes the support for mobi le terminals . T h e benefits such as complementary coverage, lower deployment cost, and QoS support make I E E E 802.16e an impor tant candidate to complement the exist ing 3 0 cel lular networks. T h u s , w i t h i n the 4 0 heterogeneous wireless networks, the interworking of 3 0 cel lular systems w i t h mobi le W i M A X is a specific case that has recently gained a lot of a t tent ion from the research and s tandard izat ion communit ies [4]. Since I E E E 802.16e is connection-oriented, i t can support I P m u l t i m e d i a services. Those services are expected to p lay a major role i n 3 0 cel lular networks. Current ly , s tandard izat ion on the interworking architecture between 3 0 ce l lular net- works and I E E E 802.16e networks is being conducted w i t h i n the Network W o r k i n g G r o u p ( N W G ) of the W i M A X F o r u m [5]. T h e N W G is developing specifications for the architec- ture, protocols and services for the mobi le 802.16e systems. T h e loosely and tightly coupled architectures [6, 7], proposed for the integrat ion of 3 0 cel lular networks w i t h W L A N s are also being considered for cel lular /802.16e interworking . W i t h i n the research community , a loosely coupled architecture for cel lular /802.16e interworking is proposed i n [8] w i t h "^A version of this chapter wi l l be submitted for publication. Enrique Stevens-Navarro and Vincent W . S . Wong, "Handoff Management and Admiss ion Control using V i r t u a l Part i t ioning with Preemption in 3G Cellular/802.16e Interworking." emphasis on the Q o S support . Moreover , an interworlcing architecture at the protoco l and s ignal ing level is proposed i n [9] w i t h i n the context of the 3 G cel lular I P m u l t i m e d i a services. In cel lular /802.16e interworking , due to mobi l i ty , users are able to switch connections among networks. T h i s process is cal led handoff. A handoff is defined as horizontal i f i t occurs between two adjacent cells of the same system. O n the other hand , it is defined as vertical i f it occurs between two cells of different systems. Since there are now two types of handoffs, each one w i t h different execution procedures (e.g., s ignal ing overhead, context and authent i cat ion transfer) , the t r a d i t i o n a l approach of g iv ing pr i o r i ty to hor izonta l h a n d - off users over the new users needs to be extended. In fact, as the interworking architecture is fu l ly deployed and the dual -mode terminals become available, the number of vert i ca l handoffs w i l l increase significantly. T h u s , novel handoff management techniques are re- quired [10, 11]. Fur ther considerations need to be taken into account and the appropriate m o b i l i t y scenarios should be investigated. O t h e r technical chaUenges in 3 0 cel lular/802.16e interworking include locat ion m a n - agement, admission contro l , and QoS provis ioning. T h e support for multi-class services (e.g., m u l t i m e d i a sessions) and the joint design at the connection and packet-level are also i m p o r t a n t design objectives for admission control and QoS provis ioning i n 4 0 het- erogeneous wireless networks [2]. A d m i s s i o n control is required to l imi t the number of connections that can be accepted into the network whi le Q o S provis ioning guarantees that the resources are used efficiently and satisfy the appl i cat ion requirements. W e now summarize the related work on I E E E 802.16. A d m i s s i o n control a lgor i thms for mult i -service fixed b roadband wireless networks have been proposed i n [12, 13, 14]. Those works m a i n l y focus on the or ig inal I E E E 802.16 s tandard (i.e., neither mobi le terminals are considered nor m o b i l i t y issues such as handoffs are addressed). A d m i s s i o n control a lgor i thms for I E E E 802.16e have recently been proposed i n [15, 16, 17, 18]. A n admission control a lgor i thm which supports pr ior i t i zed services and adapt ive m u l t i m e d i a appl icat ions is presented in [15]. A dynamic b a n d w i d t h reservation scheme is proposed i n [16] for the variable b i t rate services. A power reservation scheme is presented i n [17]. It uses the t ransmit power of the base stat ion as the indicator to perform admission control . In t ra - cell m o b i l i t y issues as wel l as l ink adaptat i on are considered for admission control i n [18]. T h e proposed model estimates the average number of users w i t h i n a single cell scenario. None of those previous works in [12, 13, 14, 15, 16, 17, 18] consider the interworking of I E E E 802.16e systems w i t h 3 0 cel lular networks. T h e V P is a n efficient, fair and robust resource shar ing technique. V P w i t h the support for mult i - c lass services is proposed i n [19]. It works under the idea of pre-a l locat ing a nom- mai capacity for each service. In [20], V P is considered for admission control i n cel lular networks. T w o schemes w i t h preemption considering R T and N R T connections are pre- sented. R T connections receive guaranteed access, whi le N R T connections can ut i l i ze any unused capacity. Fo l l owing the joint call and packet-level QoS optimization approach i n [21, 22], QoS constraints are considered at the cal l - level i n terms of the b l o c k i n g / d r o p p i n g probabi l i t ies and at the packet-level i n terms of the packet loss probabi l i t ies . In [23], we s tudy the use of V P for admission control i n an integrated c e l l u l a r / W L A N system. B y fo l lowing the concept of po l i cy functions introduced i n [24] for admission con- t r o l , the corresponding po l i cy functions for V P are derived. However, on ly R T connections are considered for admission control . In [25], V P is considered for resource shar ing i n cel - l u l a r / W L A N systems. Resource management for mult i -c lass services and load balanc ing are also investigated. However, m o b i l i t y issues such as hor izonta l and vert i ca l handoffs are not considered. In this chapter, we propose the use of V P w i t h preempt ion for admission control i n cel - lu lar /802.16e interworking and evaluate its performance. O u r mode l formulat ion considers the jo int design at the connection-level and packet-level . T o this end, we first present the m o b i l i t y scenario between 3 0 cel lular networks and I E E E 802.16e networks. T h e m o b i l i t y scenario specifies the hor izontal and vert i ca l handoffs that can occur i n cel lular /802.16e interworking . T h e corresponding set of handoff rate equations is derived. To the best of our knowledge, this is the first at tempt to model this expected scenario. T h e contr ibut ions of our work are as follows: 1. W e propose admiss ion control a lgor i thms for different types of connection requests. For the handoff users, different priorit ies are assigned to each user according to the m o b i l i t y scenario. B o t h hor izonta l and vert ica l handoffs are considered. Preempt i on rules are defined for the R T and N R T connections when V P w i t h preempt ion is used. 2. We determine the corresponding performance metrics at the connection-level in terms of the b locking and dropp ing probabi l i t ies , and at the packet-level i n terms of the packet loss probabi l i ty . W e formulate a b l o c k i n g / d r o p p i n g cost m i n i m i z a t i o n problem fol lowing a jo int connection and packet-level QoS o p t i m i z a t i o n approach. 3. T h e performance of the integrated cel lular /802.16e system using V P w i t h preempt ion is evaluated. N u m e r i c a l results show significant performance improvement. T h e dropping probabi l i t ies for i iandoff requests can be reduced by 6 3 % when the proposed admission a lgor i thms are used. T h e dropping probab i l i ty of the R T connections can be reduced by 4 3 % when preemption is used. T h e b locking probabi l i t ies for new connection requests can be reduced by 6 9 % when the joint QoS o p t i m i z a t i o n approach is used. T h e rest of the chapter is organized as follows. Section 4.1 presents the m o b i h t y scenario and the system mode l for ce l lular /802.16e interworking. Sect ion 4.2 describes the use of V P w i t h preempt ion as wel l as the proposed admission a lgor i thms and cost m i n i m i z a t i o n problem. Section 4.3 presents the numer ica l results and Sect ion 4.4 summarizes the chapter. 4.1 System Model Consider an integrated cel lular /802.16e system as shown i n F i g . 4.1. A 3 G cel lular radio access network ( R A N ) is deployed covering a l l the service area. In a h igh ly populated area or region w i t h h igh service demand , an I E E E 802.16e access service network ( A S N ) is also deployed to provide add i t i ona l capacity. T h i s w i l l be a common deployment alternative [26 . A s mentioned before, the N W G is developing an end-to-end network architecture for I E E E 802.16e networks. It considers the loosely coupled interworking architecture [5] i n w h i c h the access networks are interconnected through the Internet by a gateway. T h e m e d i u m access control ( M A C ) of the I E E E 802.16e A S N operates i n the point-to-multipoint mode. T h u s , the mobi le terminals are served by a central ized base s tat ion . If the base stations of b o t h systems are co-located [4], then we have an overlapped system. 4.1.1 Mobility Scenario Referr ing to the integrated cel lular /802.16e system in F i g . 4.1, hor izontal handoffs can occur due to m o b i l i t y of users among neighboring base stations of the same network (e.g., between two adjacent cells of the 3 G R A N ) . T h e handoff decision is based on the R S S . O n the other hand , ver t i ca l handoffs can occur i n two cases. F i r s t , i t can happen when a user leaves a cell and the mobi le t e rmina l can select another network to obta in services. T h e handoff decision m a y incorporate other factors such as monetary cost, types of Q o S guarantees, and user's preferences [10, 27]. In this case, the vert i ca l handoff is optional because a l though not required, it may improve the QoS of the connection. A vert ical handoff can also occur when a hor izontal handoff cannot be successfully completed i n the overlapped coverage area. Here, the handoff request is vert i ca l ly transferred to the other network i n order to avo id the connection from being dropped. W e consider b o t h types of vert i ca l handoff i n our m o b i l i t y model . 4.1.2 Traffic and Mobility Models W e first introduce the notat ions. Let M'^ and denote the set of cells i n the 3 G R A N and the 802.16e A S N , respectively. For each cell i e A ^ ^ let Ai denote the set of 3 0 cells adjacent to cell i. For each cell k G A / " , let Al denote the set of 802.16e cells adjacent to cell k. Le t Wf denote the set of overlapping 802.16e cells to cell i G M". Le t W^ denote the set of overlapping 3 0 cells to cell k G M". A s an example. F i g . 4.2 shows an integrated cel lular /802.16e system w i t h = { C I , C 2 , C 3 , . . . , C l l , C 1 2 } and = {El, E2, E3}. T h u s , we have A^c2 = { C I , C 3 , C 4 , C 5 , C 6 , C 7 } , A%2 = {^1 ,^3 } , W"c2 = {E2}, and W%2 = {C2}. In the 3 0 R A N , when a connection is established, a circuit bearer service is created. It has several Q o S attr ibutes that describe how the packets i n that service class should be treated. T h e 3 G P P defined four different classes of Q o S for connections [28]: conver- sat ional , s treaming, interact ive , and background. In the 802.16e A S N , when a connection is established, a service flow is created i n the M A C layer w i t h specific QoS parameters. T h e I E E E 802.16e defined five different classes of QoS for service flows [3]: unsol ic i ted grant service ( U O S ) , real - t ime pohing service ( r t - P S ) , extended r t - P S ( E r t - P S ) , non-real - t ime po l l ing service ( n r t - P S ) , and best effort ( B E ) . For admission control , conversational , s treaming , U O S , r t - P S and E r t - P S classes are grouped into RT connections, while i n - teractive, background, n r t - P S and B E classes are grouped into NRT connections. T h e classif ication is summar ized i n Table 4.1. L e t S denote the set of services available to the mobi le users. T h e services are clas- sified into two groups: R T services as SRT and N R T services as SNRT- T h u s , SRT C S a n d iSjvKT C <S. A service s G «S requires B B U s , and b^ B B U s to guarantee its QoS requirements i n the 3 0 R A N and the 802.16e A S N , respect ive ly For i G M'', k e M" and s G 5 , the new connection requests for service s arrive at cel l i and cell k according to independent Poisson processes w i t h rates  ^ and A^^, respectively. T h e connection duration of service s, tg, is exponent ia l ly d i s t r ibuted w i t h mean l/vs- Since the exponential d i s t r ibut i on is memoryless, the residual (i.e., remaining) connection t ime i f is also exponent ia l ly d i s t r ibuted w i t h mean 1/vg. For i G A^*^ and k G .AA^, we assume that the cell residence times t1 and t% are also exponent ia l ly d i s t r ibuted w i t h means 1/77̂  and l/r?fc, respectively. T h e channel holding time i n cell i is defined as the t ime that a user continues to use the assigned 6̂  B B U s i n the 3 G R A N (i.e., a c i rcuit bearer service), whi le i n cell k i t is the t ime that a user continues to use the assigned B B U s i n the 802.16e A S N (i.e., a service flow i n the M A C layer). For service s eS, the channel ho ld ing t ime i n cell i and cell k are obtained as min(tf ,!^-) and min(<f ,^|) , respectively. Since i f , tl, and tl are exponent ia l ly d i s t r ibuted for a l l s € 5 , i G M", and k G M^, the ho ld ing t imes are also exponent ia l ly d i s t r ibuted w i t h parameters ji'i^ — Vs + r}f and fil^ = + rjl, respectively. A user of service s i n cell i G M'^ may terminate its connection at the end of its channel ho ld ing t ime and leave the integrated system w i t h probab i l i ty gf̂  = Vs/{vs+r]i). Otherwise , i t m a y move w i t h i n the system and continue i n an adjacent cell w i t h probab i l i ty 1 - qf^. W e have: i - c = E c + E (4-1) where q^^ denotes the probab i l i ty of a t t e m p t i n g a hor izonta l handoff from cel l i G M'^ to a ne ighbor ing cell j G A^, and g?f̂  denotes the probab i l i ty of a t t empt ing an opt ional vert ical handoflP from cel l i to a neighboring cel l I Ç Al oî overlapped cell k G >Vf. S imi lar ly , a user of service s i n cell k G may terminate its connection at the end of its channel ho ld ing t ime and leave the integrated system w i t h probab i l i ty q^^ = Vg/(vs+rjl). Otherwise , it m a y move w i t h i n the system and continue i n an adjacent cel l w i t h probab i l i ty ^ ~ Qks- have: = E (4-2) where g£f̂  denotes the probab i l i ty of a t t e m p t i n g a hor izonta l handoff f rom cell k G M"^ to a neighboring cell I e A^, and ĝ ^̂  denotes the probab i l i ty of a t tempt ing an opt ional vert i ca l handoff from cell A; to a neighboring cell j G Al of overlapped cell i G W^ . T h e arrival rates of service s to cel l i and cell k, cpl^ and 0^^, respectively, include a l l the connect ion requests from the new, hor izontal , and vert i ca l handoff users. T h e y are given by: < = K + Y. ^jl + V z G A ^ ^ (4.3) C = + E f'lL + ' V G A ( ^ (4.4) leAl where hf^^ denotes the horizontal handoff rate of service s offered to cel l i from its adjacent ceU j G Ai, and hf^^ denotes the horizontal handoff rate of service s offered to cell k f rom its adjacent cell / e Al. B o t h hor izonta l handoff rates are shown i n F i g . 4.3. O n the other hand , the terms and "iff^ denote the vertical handoff rates offered to cell i and cell k, respectively. F r o m the m o b i l i t y scenario described earlier and m a k i n g reference to F i g . 4.3, the vert ica l handoff rates i n (4.3) and (4.4) are given by: E V ^ G ^ ^ ^ (4.5) * ^ : = E < ^ ^ . + E ^ 1 1 ' v f c e ^ ^ ^ (4.6) where wĵ t denotes the vertical handoff rate of service s offered to cell i from its overlapped cell k e W f , vff^ denotes the vertical handoff rate of service s offered to cell i from neigh- bor ing cel l I G of overlapped cell k G W f , vf^^ denotes the vertical handoff rate of service s offered to cell k from its overlapped cel l i G W^, and v^l^ denotes the vertical handoff rate of service s offered to cel l k f rom neighboring cel l j G Ai ai overlapped cell i G W^. T h e first t e r m i n b o t h (4.5) and (4.6) corresponds to transferred vert ica l handoffs, whi le the last t e rm corresponds to opt ional vert ica l handoffs. W e can state the handoff rate equations as follows: - ^ 5 . ( l - ^ n J C + E ^ S . ( l - ^ ^ . J ^ t (4.7) xeA^ + E - s . ( i - ^ ^ / . J c + E - ^ K ^ - ^ ^ ' ' J ^ ^ ' - ( l - C + E ( l - Dl,,^) 41 (4.8) xeAt + E 'yi ( i - d:,,^) c + E ( i - ^kjs htl = Af̂  ( l - 5 ^ J + E ^ ^ l - ^ ^ / ^ O ' ^ ' t (4.9) ce 'jks (4.10) xeA^j 2J = E KlMk.. + E ^yl^'Hk, ' (4-11) ^ X = E ^ S . ^ k + E ^ ^ t ^ S . . > (4.12) where B^.^ and 5^^^ are the probabihties of b lock ing connection requests from new users of service s i n cell i e M" and ceU k G M", respectively. Dlh^^ and D^^^^ are the probabi l i t ies of dropp ing connection requests from hor izonta l handoff users of service s i n cell i G and cell k £ M^, respectively. D^y^.^ and Dl^^^ are the probabi l i t ies of dropping connection requests from vert i ca l handoff users of service s i n cel l i G M"^ and cell k G M'^, respectively. 4,2 Virtual Partitioning with Preemption for Admission Control E a c h cell i G M'^ has a capaci ty of C f B B U s . R e c a l l from Sect ion 4.1 that the transmiss ion rate of service s i n the 3 0 R A N (i.e., bfj is normal ized w i t h respect to the B B U s . Due to schedul ing and statistical multiplexing, each cell i supports |*S| different services and can admit connections w i t h at most A f B B U s , where Nf > C f . T h e value of is a design parameter [20, 22]. If N[ has a smaU value, then the cel l may experience a low packet loss probab i l i ty and a h igh connect ion b locking probabi l i ty . O n the other hand , i f has a large value, then the cel l m a y experience a low connection b lock ing probab i l i ty and a h igh packet loss probabi l i ty . T h i s happens because A f restricts the number of connections that can be a d m i t t e d , and the capaci ty Cf restricts the number of t r a n s m i t t e d packets from the a d m i t t e d connections. F i n a l l y , i f iVf = Cf, then there is no s tat i s t i ca l mul t ip l ex ing gain. A c c o r d i n g to the QoS classif ication shown i n Table 4.1, services are grouped into two types: R T and N R T . For admission control i n cel lular /802.16e interworking , by extending one of the resource a l locat ion schemes proposed i n [20], we can use V P w i t h preemption for the N R T group. T h u s , the R T group is offered guaranteed access while the N R T group is offered best effort access. In each cell i G M"", V P st ipulates that i f a nominal capacity or nominal allocation has to be assigned for each group, then the parameter Nf of cell i G M"^ is par t i t i oned into Nf^j.. and Nf^j^j... Nfij.. is the n o m i n a l a l locat ion for R T connections and ^NRTi is n o m i n a l a l locat ion for N R T connections, w i t h Nfj^_ + A^^THTJ = ^i- T h e resource a l locat ion i n cell i of the 3 G R A N is defined as: ^mlbl < AT;^ , V Z G M", g G {RT,NRT}, (4.13) where mf^ is the number of service s connections i n cell i. G i v e n the nomina l al locations, V P defines a group as underloaded i f a l l connections from that group are assigned fewer resources t h a n its n o m i n a l a l locat ion , and as overloaded i f a l l connections from that group are assigned more resources t h a n its n o m i n a l a l locat ion. T h e R T connections receive guar- anteed access and better QoS . T h e y can preempt N R T connections when the N R T group is overloaded. In the meantime, the unused capacity is available for the N R T connections. S imi lar ly , each cell k G has a capaci ty of C^ B B U s . D u e to schedul ing a n d stat is t i ca l m u l t i p l e x i n g , each cell k supports |>S| different services and can admit connections w i t h at most A^^ B B U s , where > C^. T h e parameter A^^ of cell k G M'' is also part i t i oned into Nfij,^ and A ^ ^ ^ ^ ^ , w i t h Ny^+N^f^j,^ = N^. T h e resource a l locat ion i n cel l k of the 802.16e A S N is defined as: ^rnlbl<N;^, VkeM\ ge{RT,NRT}, (4.14) S€Sg where m^^ is the number of service s connections i n cell k. 4.2.1 Admission Control for New Requests Besides the pr i o r i ty of R T connections over N R T connections, for admiss ion control , the mob i l i t y of the users also needs to be taken into account. In the case of cel lular/802.16e interworking , we consider connection requests from new, hor izonta l , and vert i ca l handoff users. To this end, we propose admiss ion control a lgor i thms for each type of connection request. T h e admiss ion a lgor i thm for the new requests us ing V P w i t h preemption is shown i n A l g o r i t h m 4. L e t 5? denote the number of B B U s that can be reserved for connection requests from the handoff users of any type i n each n o m i n a l a l locat ion (i.e., Nf^j. and N^j^j,) i n cell i E M ' ^ . Consider the case for a connection request from service s E SRT i n cell i E M ' ^ ( A l g o r i t h m 4, step 1). W e have A^^.. — of B B U s that can be used for connection requests from either new, hor izonta l or vert i ca l handoff users. W h e n the N R T group is underloaded, the new request is accepted i f J2S'€SHT "^V^s' + ~ ( A l g o r i t h m 4, step 6). O n the other hand , i f the N R T group is overloaded, Z^ '̂e^ATflT " ^ t ' ^ * ' ^ ^NRT, ( A l g o r i t h m 4, step 2), then two s i tuat ions can happen. F i r s t , i f the to ta l amount of resources used by the R T users, the overloaded part of the N R T users (i.e., I^yg^^^j, m.̂  - A ^ ^ j , , ) , and the new connection is less t h a n or equal to A^^j j . . - 5f, then the connection is accepted ( A l g o r i t h m 4, step 3). Otherwise , preempt ion is invoked and some connections from the N R T group are removed. To achieve the preempt ion , suitable rules need to be defined. These rules specify whether or not the preempt ion of R T over N R T connections can be appl ied based on the number of users of each service. W e modi f ied and extended the or ig ina l preempt ion rules m 20] to consider connection requests from the vert ica l handoff users and to include our proposed admiss ion control a lgor i thms. T h e preemption rules for the connection requests from the new users are defined as follows: preemption happens when a connection request from a new user of service s E SRT arrives under the condit ions that the N R T group is overloaded, E^'eS^lK, > N[ - of, and Zs'eSnr'^lK' + K< N%r, - ( A l g o r i t h m 4, step 4). R e c a l l that new requests can only use A ^ ^ . — 6f B B U s . T h u s , new connection requests are accepted w i t h preempt ion u n t i l we reach the point where A^^^^ — of B B U s are used by the connections of the R T group. O n the other h a n d , for the case of the connection requests f rom service s E SNRT in cell i E M ' ^ , a n e w request is accepted i^YLs'es''^'i.:K''^K ^ ^i~^ï ( A l g o r i t h m 4, step 8). Note that the parameter A f is used instead of the n o m i n a l a l locat ion N^RT^ to al low the connections from the N R T group to use a l l the available capac i ty i n cell i. If preemption of a connection from service s E SRT happens over services s' E S^RT, t e rminat i on only applies to one service i n SJVRT wh i ch is un i formly selected at r a n d o m (i.e., 1/\SNRT\)- T h e number of terminated users from service s' is given by \b'^/b'^,1. 4.2.2 Admission Control for Handoff Requests We now describe our admiss ion control a lgor i t i ims for the handoff requests as follows. L e t a? and /3f denote the parameters that define the threshold values after which connection requests from handoff users of each type w i l l either be accepted or not i n cell i e M^. O u r proposed admiss ion a lgor i thm assigns the values of a f and Pf based on the reserved B B U s a n d sets the pr i o r i ty for admission control among handoff requests according to the m o b i l i t y scenario described i n Section 4 . L T h u s , we have: V i e A f ' (4.15) Pl^SI-al, yieM'. (4.16) T h e value of parameter is assigned based on the corresponding hor izonta l handoff rates. If the number of connect ion requests from hor izonta l handoff users increases, then more resources are al located and hence higher pr i o r i ty is given to that type of handoff users and vice versa. B o t h parameters a? and /?f have integer values and 0 < < Sf. Note that the denominator i n (4.15) considers a l l types of handoff requests. There are three different cases to consider i n the proposed admission a lgor i thm. In case 1 {a^ > /??), hor izonta l handoffs w i l l have the highest p r i o r i ty for admission control and they w i l l be always accepted as long as there is capaci ty available i n the cell . In case 2 (af < /??), vert ica l handoffs w i l l have the highest pr i o r i ty for admiss ion control . In case 3 [a^ — /5f), b o t h hor izonta l and vert ical handoffs are equally impor tant . In a l l three cases, the connection requests from the new users w i l l have the lowest pr i o r i ty for admission control . These three cases and the corresponding handoff priorit ies for service s e SRT i n cell i e are shown i n F i g . 4.4. O u r proposed admission control a lgor i thms using V P w i t h preempt ion for hor izonta l and vert ical handoff requests are shown i n A l g o r i t h m s 5 and 6, respectively. Cons ider the case of a connection request from service s € SRT i n cell i e M'^. In case 1, Nf^j,^ B B U s in cell i e M'^ can be used as follows: Nf^j^. — ôf B B U s can be used for connection requests from either new, hor izonta l or vert ica l handoff users, /5f B B U s can be used for connect ion requests from either hor izontal or vert ical handoff users, and af B B U s can be used for requests from hor izonta l handoff users. W h e n the N R T group is underloaded, a hor izonta l handoff request is accepted if YIS'&SRT ''^i.^K' + ^l ^ ^RXi ( A l g o r i t h m 5, step 7), and a vert i ca l handoff request is accepted if I^s'es^^ + < Ny.. - a f ( A l g o r i t h m 6, step 7). O n the other h a n d , i n case 2, af B B U s can be used for connection requests from either hor izonta l or vert ica l handoff users, and /?f B B U s can be used for requests from vert i ca l handoff users. W h e n the N R T group is underloaded, a hor izonta l handoff request is accepted if YIS'^SRT ,K' + ^ ^RTi ~ Pi ( A l g o r i t h m 5, step 17), and a vert ica l handoff request is accepted i f Z^^/g^^j, m? ,6^, < N%^. ( A l g o r i t h m 6, step 17). In case 3, a hor izonta l or vert i ca l handoff request is accepted if YIIS'^SKT ''^Ï.,K + ^ ^RTt ( A l g o r i t h m 5, step 7) and ( A l g o r i t h m 6, step 17). O n the other hand , i f the N R T group is overloaded, we need to consider the s imi lar s i tuations as described for the new requests. If the t o ta l amount of resources used by the R T users, the overloaded part of the N R T users (i.e., J2s'eSNRT''^i '^s' " ^NRTI)^ ^^^d the handoff connect ion is less t h a n or equal to A^^^ . . — j3f or N^RX^ ~ , then the connection is accepted ( A l g o r i t h m 5, step 14) or ( A l g o r i t h m 6, step 4), respectively. Otherwise , preempt ion is invoked. W e define preemption rules for the handoff requests according to the assigned pr ior i t ies (see F i g . 4.4) whi ch are given by each case (e.g., af > etc.). For the hor izonta l handoff requests we have rules for af > (3f ( A l g o r i t h m 5, step 5) and ai < /3f ( A l g o r i t h m 5, step 15). For the vert ica l handoff requests we have rules for a? > /3f ( A l g o r i t h m 6, step 5) and af < /3f ( A l g o r i t h m 6, step 15). For the case of the connection requests from service s E SNRT i n cell i E M " ^ , i n case 1, a hor izonta l handoff request is accepted if Yls'es''^ï>K' K ^ ( A l g o r i t h m 5, step 9), and a vert i ca l handoff request is accepted if Yls'es "^iv^s' + ^1 < Nf - af ( A l g o r i t h m 6, step 9). O n the other hand , in case 2, a hor izonta l handoff request is accepted if I^5'e5"^i,/^«' + ^ ~ Pi ( A l g o r i t h m 5, step 19), and a vert i ca l handoff request is accepted i f ^^'es'^t^iK' + bl< A f ( A l g o r i t h m 6, step 19). F i n a l l y , i n case 3, a hor izontal or vert ica l handoff request is accepted i f I3s'65 + - -^f (A lgor i thms 5, step 9) and (A lgor i thms 6, step 19), respectively. T h e admission a lgor i thms i n ceU k E define s imi lar parameters ô^, a^, and (31 as well as preempt ion rules for the connection requests from the new, hor izonta l , and vert ica l handoff users. 4.2.3 Connection-level Model A t the connection-level , for i E and k E M " , the performance metrics of interest using V P w i t h preempt ion are the probab i l i ty of b lock ing connect ion requests from a new user, and the probab i l i ty of dropp ing connection requests from either a hor izonta l or vert ical handoff user. W e model the occupancy of cell i e M " ^ and k G as 151—dimensional M a r k o v chains. L e t = {m1^, m , . . . , m-̂ ^̂  ) and m% = {ml^, ml^,..., ml^^^ ) denote the occupancy vectors i n ceU i G and cell k 6 A^*", respectively. T h e y indicate the number of connections of each service. T h u s , the state space of each ceh is restricted to X^gg^??!? 6̂  < N[ and S s e s ^ ^ L ^ s - ^k- Le t 0i^(mf) and 0|^(m|) denote the to ta l arr iva l rates of connection requests of service s G SHT considering the admission algor i thms to cel l i G M ' ^ and cell k G M ' ^ , respectively. W e have: E + E ^ i t + ' î '^ . 0, i f a f > Ny^ - ôt<Y,mlbl, <Ny-al s'eSRT Hat < PI - 5f<Y^mlX: <Ny-(3t, s'eSRT ii al = Pf, Ny -5t< J2 ml, K, < , S'&SRT i f at > Pf, Ny - at < E</« ' ^ ^RT., S'GSRT iiat<pf,Ny-Pf< Yl^lK'^^RTv s'eSRT otherwise. (4.17) if y2rnlM><Ny^-ôl S'SSRT iial>PlNy^ -^k<)^rnlK'<Ny,-c^l leAi S'€SRT ht + n „ i f (^l<PlNy^ -^k<)_^rnlK'<Ny,'Pl S'eSRT iial^PlNy s'eSRT i f a^> /3 ,^ A ^ ^ ^ - a l < YmlX'<Ny^, s'eSRT i f < PI Ny -Pl< Y,ml,K'<Ny^. s'eSRT 0, otherwise. (4.18) For the to ta l arr iva l rates of connection requests of service s G S^RT to cell i E M ' ^ and to cel l k E M ^ , we s imp ly replace Ny. and Ny^ w i t h A f and i n (4.17) and (4.18), respectively, and SRT w i t h SJVRT- T h e departure rates are defined as /i-̂ (mi) = mf^^f^ for EsesKK < A f , and filiml) = ml^ks T^sesK^l < ^1 respectively. L e t pi{m^) and Ffc(ni|) denote the steady state probabi l i t ies of be ing i n states and m% i n cell i and cel l A;, respectively. W e can state the global-balance equations for the M a r k o v process i n cell i E M ' ^ as: s€S '- <PUmt) + Ki^t) + fourni) = E - '"^^'M - 3̂) + E ^̂ K+e.)<(mf + e,) s e s s e s + E E E mmt+s%-e,,)^l{mt+s"es-e^), SSSNRT s'eSRT X,.., I where is an |5|-dimensional vector of zeros but w i t h 1 i n the s th pos i t ion . T h e term $ f (mf ) is control led by the V P preemption rules and is defined as: ^ f E < s ' e s i ^ E - ^ ^ s ' e s i f E - l s ' e s i f E - ^ t s ' e S i f E - ^ l s ' e s s ' e S f i T s ' e S f t T s ' e S H T (4.19) T h e terms $f̂ (mf) in the global-balance equations incorporate the add i t i ona l state t rans i - tions due to preempt ion of R T connections over N R T connections. Note that in a l l cases i n (4.19), the N R T group shal l be overloaded. For notat ion convenience, we enumerate the services as «S = {1, 2 , . . . ,p,p+ 1 , . . . , |«S|}. T h e R T services correspond to service 1 to service p, and the N R T services correspond to service p + 1 to service \S\. Now, the probab i l i ty of b lock ing connection requests from a new user of service s G SRT i n cei l i E M.'^ fol lowing V P w i t h preempt ion is given by: E — ^ ; r - ^ E m f = 0 •p+i E s ' 6 5 - 1 + E •• ^ E - 1 ^ ^ T T - ^ E •p+1 E m f = 0 E < ^ I K ) ' s ' € 5 (4.20) where the t e r m A? / 0f^,(m?) is the probab i l i ty that the arr iva l is a new request of service s. For service s G S^^RT, the probab i l i ty of b lock ing connection requests from a new user i n cell i is given by: E •• >; E m f ^ = 0 • E i^=(m?)A (4.21) For service s G cS/jr, a l l occupancy vectors need to satisfy the cond i t i on X^^-g^^^ > A^fir^ — of. O n the other h a n d , for service s G S^RT, a l l occupancy vectors need to satisfy the condi t ion that J2s'&s ,K' + > " ^i- For the probab i l i ty of dropp ing requests from a handoff user of service s i n cell i G A l ' ^ , according to the admission a lgor i thms, we need to consider three different cases: In case 1 (a? > /??), the probab i l i ty of dropping connection requests from horizontal handoff users of service s is given by: ^ ^ T . - 1 : 7 = 1 - l / ^ m f = 0 E m? = 0 «P+1 • E (4.22) where the t e r m YljeA^^ ^jt/ S s ' e s ^ '̂̂ ^ probab ihty that the arr iva l is a hor izontal handoff request of service s. For service s E SRT, a l l occupancy vectors mf need to satisfy the condi t ion that I^yeSflT " ^ t ' ^ * ' + ŝ > -^^Tj- O n the other h a n d , for service s E SNRT, a l l occupancy vectors mf need to satisfy the condit ion that X l s ' e s " ^ i «^s' + > ^i- T h e probab ihty of dropp ing connection requests from vert i ca l handoff users of service s E S NRT is given as follows: = 0 5p E ^ î ^ - ^ E (4.23) where the t e r m '^t^/J2s'es^i.ii''^i) is the probab ihty that the arr iva l is a vert i ca l handoff request of service s. O n the other h a n d , i f service s E SRT, the probab i l i ty of dropp ing connection requests from vert i ca l handoff users is given by: E — ^ — E m ? = 0 6̂^ ^ s ' 6 5 E - 1 + E E - 1 m f = 0 E "151 E m f = 0 ' | 5 | E ^ l « ) ' s ' e 5 (4.24) For service s 6 5^^, ah occupancy vectors mf need to satisfy the cond i t i on X^^/g^^^ ,6^-1- > -^RTi ~ O n the other h a n d , for service s G SNRT, a l l occupancy vectors mf need to satisfy the condi t ion that J^s'€s''^t,K' + K> ~ (^t In case 2 (a? < /3f), the probab i l i ty of dropping connection requests from vert ical handoff users of service 5 is given by; m ? = 0 m f = 0 E m f = 0 ' p + l ''151 E m f = 0 ' | 5 | Pf{mt)^1'; s'es (4.25) For service s € 5^^, a l l occupancy vectors mf need to satisfy the cond i t i on Y^^'eSRT ' ^ i + K > -^I^T,- O n the other hand , for service s G S^RT, a l l occupancy vectors mf need to satisfy the cond i t i on that Yls'es '^1,,^' + > ^i- T h e probab i l i ty of dropp ing connection requests from hor izonta l handoff users of service s € SpjRT is given as follows: E E E ^ " m ? = 0 • p + l m f = 0 • |5 | s'65 (4.26) O n the other h a n d , i f service s G SRT, the probab i l i ty of dropp ing connection requests from hor izontal handoff users is given by: DlH,Sm^)= E ' "1 "p E m f = 0 ' p + i • E m f = 0 ^ K ) E ^ i t E C K ) «'es + E - 1 bp E - 1 m f ^ = 0 m f = 0 > ; • E m f = 0 ' p + l m f = 0 X P^m^ p'i^i) E E < ^ l K ) s'es (4.27) For service s G i S ^ r , a l l occupancy vectors m f need to satisfy the condi t ion J2s'eSRT /^s' + K > ^RTi - Pi- O i l the other hand , for service s G SNRT, a l l occupancy vectors m f need to satisfy the condi t ion that Y^^i^s " ^ i ,^s' + K > ^i ~ Pï- In case 3 (a - = /?f), the probabi l i ty of dropp ing connect ion requests from hor izon- ta l handoff users of service s can be calculated as i n (4.22). T h e probab i l i ty of drop- p ing connection requests from vert ica l handoff users of service s can be calculated as i n (4.23). For service s G SRT, a l l occupancy vectors m f need to satisfy the cond i t i on that J2s'eSRT''^is'^s' + ŝ > ^ R T i - O n the other hand , for service s G S^RT, a l l occupancy vectors m f need to satisfy the condit ion that X^^gs ?7if ,6^, + > ^i- S i m i l a r admission po l i cy and preemption rules are appl ied i n the I E E E 802.16e network. Thus , for cell k G M " , the global balance equations, probabi l i t ies for b lock ing new users and dropping hor izonta l and vert i ca l handoff users can be derived s imi lar to (4.18) - (4.27) w i t h the corresponding I E E E 802.16 parameters. G i v e n the networlc parameters A^^, A^^, r]f, ril, nl, fi^, qf^, q^, qH, q^, v^, h% and hi for e M", {k,l} e M'^, and s € 5 , we can solve equations i n the model at the connection-level and ob ta in the b locking and dropping probabi l i t ies 5^, , D^^,. , , , Dl-^^^, and Dlf^^^ for i G M'', k G M^, and s G 5 . Note that to compute the arr ival rates, we need to solve the set of fixed-point equations given by the handoff rate equations. We can use the i terat ive fixed-point a lgor i thm of repeated subst i tut ions [29]. 4.2.4 Packet-level Model A t the packet- level , for i G M."^ and k G M^, the performance metr ic of interest is the probab i l i ty of packet loss. W e consider that packet loss can occur when the t o ta l number of required B B U s from the active connections exceeds the capac i ty of the cell . T h u s , let Lf^ and denote the packet loss probabi l i t ies experienced by connections of service s due to s tat is t i ca l m u l t i p l e x i n g i n cell i and cell k, respectively. To calculate L?^ and L^^, we assume that once a connection is accepted, it behaves as an exponent ia l ly d i s t r ibuted ON - OFF traffic source. T h e ON - OFF traffic model can be used to model voice, bursty data , and video sources [30, 31]. A source from service s requires three parameters to represent i t : the transmiss ion rate h^, the average t ime that the source is i n the ON state (i.e., the burst length) toyv^, and the fract ion of t ime that the source is i n the ON state or the activity factor p^. To model traffic sources as ON — OFF sources, we follow the methodology described i n [31]. Further details are given i n Section 4.3. T h i s model is general enough to capture the behavior where the performance is m a i n l y determined by the hurst-level of the sources. In this case, we are interested i n the s i tuat ion when the aggregated traffic f rom the active connections (i.e., i n the ON state) exceeds the capacity. T h u s , when a connect ion of service s i n cel l i G M'^ [k G M'^) is i n the ON state, it generates packets at a rate that require 6̂  B B U s (6^ B B U s ) to t ransmit the packets. In any network, the fract ion of t ime that a connection spends i n the O A state is given by ps — toNsli^ONs + ioFFs), where tpFFs is the t ime that the connection is i n the OFF state. L e t rfij^ and m^^ denote the number of connections i n the ON state i n cel l i G M'^ and cell k G M^, respectively. T h e n , the probabi l i t ies that there are rnt^ and connections of service s i n the ON state given that there are m^^ and ml connections in each cell are given by: [l-PsT'^-', VieM',0<j<ml, (4.28) ml J [l-Psr^'^'', VkeM', 0<j<ml. (4.29) Paclcet loss can occur i n a cell when the t o ta l number of B B U s required from the connections i n the ON state exceeds the capacity of the ceh (i.e., Ylses'^t^s > Q ) - RecaU that parameters Nf and N^ must not be less than the capacities of the cells. Cons ider ing that the R T connections have pr i o r i ty over the N R T connections, the packet loss probab i l i ty due to s tat i s t i ca l m u l t i p l e x i n g for service s connections i n cel l i G M'^ is given by: wiiere E m f ^ = 0 E ^^K) E - - - E ^ K K ) mf = 0 m f = 0 '1 'is\ (4.30) Is'eSNRT ^ s'eSRT . T + E ^l^^' - .s'eSRT 0, where [a]+ = max[a ,0] , and i f E ^ ^ t ^ ^ ' ^ ^ ^ if ^ '^i^,^s' > C'r and s e SRT, S'eSRT i f 'Y fhlX' < Q and se SRT, s'eSRT (4.31) m f »|S| psfM)-E ••• E ^"^K)E--- E ^Kio---^('^i,.,K.,)E^l^^'- (4.32) m f ^ = 0 m f = 0 In (4.31), i f the n o m i n a l a l locat ion for the R T group is less t h a n or equal to the capacity of the cel l (i.e., iV^j . . < Cf), then the connections from the R T group w i l l not experience packet loss due to s tat i s t i ca l mul t ip l ex ing . F i n a l l y , the same packet loss model considering stat is t i ca l m u l t i p l e x i n g is used for cell k E M^. 4.2.5 Joint Connection and Packet-level QoS Optimization To select the design parameters iVf i n cel l i e M'' and i n cell k e M", a jo int connection-level and packet-level QoS op t imiza t i on approach is used. W e propose the fol lowing blocking/dropping cost m i n i m i z a t i o n prob lem w i t h constraints at the connection- level i n terms of b lock ing and dropp ing probabi l i t ies and at the packet-level i n terms of packet loss probabi l i ty . T h e objective is to m i n i m i z e a l l penal ty costs involved in the b locking and dropp ing of connections. Note that cost m i n i m i z a t i o n is equivalent to revenue m a x i m i z a t i o n . W e define an objective funct ion which is a l inear combinat ion of the b locking and dropp ing probabi l i t ies : subject to B ^ , < "iieM", seS, ykeM^,seS, VzeM', seS, \fkeM^,seS, WieM^, s eS, ykeM',seS, K yieM', seS, LI (4.33) where a;^ and iuf^^ denote the cost of blocking a connection request for service s f rom a new user i n cel l i and cel l k, respectively. S imi lar ly , w^^.^, culf^^^, w^^,^, and cof^^^ denote the costs of dropping a connection request for service s from a hor izontal and vert ica l handoff user i n cell i and cell k, respectively. To ensure that higher pr ior i ty is considered for accepting connection requests from handoff users rather than new users, it is reasonable to set o;̂ . < ^hhi, and < uf^.^ for a l l i e and s e S, and < w^^^^ and < uf^,^ for a l l k e M ' ^ and s E S. A t the connection-level , F^. and F^^ are the m a x i m u m blocking probabi l i t ies al lowed for new connection requests from service s, F^^. and F^^^^ are the m a x i m u m dropp ing probabi l i t ies allowed for hor izonta l handoff requests from service 5, and r^;^.^ and ^1^^^ are the m a x i m u m dropp ing probabi l i t ies allowed for ver t i ca l handoff requests from service s i n cell i and cell fc, respectively. F i n a l l y , at the packet- level , F^, and Fp^^ are the m a x i m u m packet loss probabi l i t ies al lowed for connections from service s i n cell i and cell k, respectively. 4.3 Numerical Results and Discussions W e evaluate the performance of an integrated cel lular /802.16e system consist ing of a 3 0 R A N w i t h \M^\ = 12 cells, and an 802.16e A S N w i t h |A(^| = 3 cells. A s shown i n F i g . 4.2, the cells are labeled as follows: = { C l , C 2 , C 3 , . . . , C 1 2 } and = {El,E2,E2,]. A t the connection-level , we consider different traffic patterns by assigning different values to parameters A^̂  and \% .̂ Three different services are considered. T w o R T m u l t i m e d i a services are offered (i.e., SRT - {1,2}) , and one N R T d a t a service (i.e., S^RT = {3}). T h e connection durat ions have means l/vi — Ijv^ — 6 minutes , and l / t i s = 4 minutes . In the integrated system, cells are of the same size [4]. T h e inter -boundary times i n cell i and in cell k have means I / 7 7 ? = ^l^k — 4 minutes. Different levels of m o b i l i t y of users are also investigated. In each cell i G M . ^ , the network capacity is 2 M b p s , and the B B U is set to 32 kbps based on the 3 G P P supported m u l t i m e d i a bearer services [32], T h i s implies that the capacity of each cell is C f = 62 B B U s . T h e first service, s = 1, is voice connections requir ing 32 kbps. T h e second service, s = 2, is video connections requir ing 64 kbps. These values are set according to the m u l t i m e d i a codecs for 3 G P P [33]. T h e t h i r d service, s = 3, is d a t a connections w i t h H T T P traffic (i.e., web browsing) at 32 kbps. T h u s , the QoS provis ioning in cell i st ipulates that h\=^ \ B B U , 65 = 2 B B U s and h% — \ B B U . In each cell k G M", according to [26], the network capacity is 6 M b p s . In order to benefit from the add i t i ona l capacity, the required d a t a rates of the services are reasonably assumed to be larger in the 802.16e A S N than the rates i n the 3 0 R A N . W e set the B B U to 64 kbps, the voice connections to 64 kbps, video connections to 128 kbps , and d a t a connections to 64 kbps. T h i s implies that the capacity of each cell is C^ = 92 B B U s , and that the QoS provis ioning is 6̂  = 1 B B U , 6̂  = 2 B B U s , and = 1 B B U . Based on t i ie defined Q o S provis ioning (i.e., 6j = 1, 63 = 2, and ^3 = 1) and according to [19], we set t l ie n o m i n a l al locations in cell i as ( A ^ H T J Î - ^ N H T . ) ~ (3,1)^^/4 and Sf = 4. T h e same nomina l al locations app ly to cell k and = 6. To set the integer values of Nf and A^^, we solve the cost m i n i m i z a t i o n problem i n (4.33) by using an exhaustive search a lgor i thm. Note that to have a s tat is t i ca l mul t ip l ex ing gain , the search is restricted to Nf > Cf and > Q . A s i n [24], we set for a l l cell i e M', k e M\ and s e S, ^ni, = ^lus ^' ^hhi, = ^Lf c , = 10. and ufy^^^ = ujff^^^ = 10. T h e QoS constraints are as follows: T^,^^ = 0.05, T^^^ = T^,,^ = 0.01, T^;. = 0.10, and T^,,^^^ = T^,.^^^ = 0.05 for a l l cell i G M''. T h e same values are set i n cel l k € . F i n a l l y , at the packet-level, for service s = 1, the average TQNI - 7.24 sec and T0FF2 = 5.69 sec. T h u s , pi = 0.54 34]. For service s = 2, we assume video frames w i t h an average size F^vg = 300 bytes, w h i c h arrive at per iodic t ime intervals every 1/24 sec. T h u s , p2 = (Favg/b2)/{I/24) = 0.90 31]. For service s = 3, we assume Web pages w i t h an average size of 100 kbytes and an average T0FF3 (i-e., reading t ime) of 30 sec. T h u s , pa = 0.45 [35]. T h e QoS constraints are = F^^ = 10"^ for a l l ceU ieM'',ke A l ^ and s e S. Pis Pks ' 4.3.1 Effect of Increasing Arrival Rate F i g . 4.5 shows the probab i l i t y of b lock ing connection requests from the new users of the three services i n cel l C l and cell E l . T h e arr iva l rate of connection requests from service 2 is increased from 0.2 to 2 connection requests per minute , whi le the arr iva l rates of services 1 and 3 remain constant at 1 connection request per minute . For the fol lowing results, we set Xs = Aj , = A^^ (i.e., the same increase of connection requests occurs i n the 3 G R A N and i n the 802.16e A S N ) . T h e parameters are NQ-^ = 77 and N^i = 116 and correspond to the point A2 = 2. In b o t h networks, the b locking probabihties for new connection requests of service 2 are the highest, since such connections require twice more B B U s t h a n services 1 and 3. O n the other hand , note that the b lock ing probabi l i t ies for new connection requests of service 1 are lower t h a n those for service 3. T h e reason is that the connections from service 1 belong to the R T group (i.e., SNRT = {1)2}) which can preempt the connections from the N R T group (i.e., SNRT = {3}). T h u s , due to the preempt ion , the new requests from service 1 are able to obta in access to the integrated cel lular /802.16e system more often t h a n those from service 3. F i g . 4.5 also shows that the b locking probabi l i t ies i n cell E l of the 802.16e A S N are lower t h a n those i n cell 0 1 due to the higher capacity i n the 802.16e A S N compared to the 3 G R A N . F igs . 4.6 and 4.7 show the probabiht ies of dropp ing connection requests of the three services i n cell C l and cell E l from hor izonta l and vert i ca l handoff users, respectively. In b o t h networks, the highest probabi l i t ies correspond to the connection requests from service 2, followed by those of service 3 and service 1 i n decreasing order. Note also that the dropp ing probabi l i t ies i n ceh C l for hor izonta l handoffs are lower t h a n those for vert ica l handoffs. O n the other hand , the dropp ing probabi l i t ies i n cel l E l for hor izonta l handoffs are higher t h a n those for vert i ca l handoffs. T h e reason is that i n cel l C l , we have case 1 ( a ^ i > Pc^) f rom F i g . 4.4, whi le i n cel l E l , we have case 2 {a%^ < P%^). T h i s is expected since as described i n Section 4.2, each case depends on the handoff rates from the mob ih ty scenario. T h i s can also be seen from F i g . 4.2. C e l l C l of the 3 0 R A N w i t h W ^ i = {£^1} receives hor izonta l handoffs requests from six adjacent cells Aci = { C 2 , C 3 , C7,..., C I O } , but on ly receives opt iona l and transferred vert i ca l handoffs requests from two cells A^i = {E2,E3}. C e l l E l of the 802.16e A S N w i t h W^^ = { C l } receives hor izonta l handoffs requests from on ly two adjacent cells and also receives opt iona l and transferred vert ica l handoffs requests from six cells. F i g . 4.8 shows the probab ihty of packet loss for connections of service 3 i n cell C l and cell E l . In b o t h networks, the nomina l al locations for the connections from the R T group, ^RTci ~ and Nf^TEi ~ ^'^' respectively, are less t h a n the corresponding capacities of their cells, C^i = 62 and C%-^ = 92, respectively. Such connections do not experience packet loss due to s tat is t i ca l mul t ip lex ing . O n the other hand , we can see that as the arr iva l rate of connection request from service 2 increases, service 3 starts to experience a considerable increase on the packet loss probab i l i t y i n b o t h networks. R e c a l l that the connections from the N R T group can only t ransmit when YlseSar — (4.31). 4.3.2 Effect of Increasing Mobility Figs . 4.9 and 4.10 show the probabi l i t ies of dropp ing connection requests i n cell C l and cell E l f rom hor izonta l and vert ica l handoff users, respectively. T h e level of m o b i l i t y i n the networks, whi ch is given by 1 - and 1 - ql^ i n (4.1) and (4.2), respectively, is increased from 0.2 to 0.6. In other words, it corresponds to an increase i n the propor t i on of users that perform handoffs from 2 0 % to 60%. In the figures, qs = qf^ — ql^ (i.e., the increase is un i form i n b o t h networks). T h e arr iva l rate for the three services is set to 1 connection request per minute . Since we are decreasing the number of connections that may terminate inside eacii ce l l , (i.e., by increasing l-Qs), it causes an increase i n t l ie dropp ing probabil i t ies for b o t h types of handoffs. A l t h o u g h connection requests from services 1 and 3 require the same amount of B B U s , note i n Figs . 4.9 and 4.10 that the probabi l i t ies of dropping handoff requests from service 1 i n cel l C l are 4 3 % lower t h a n those from service 3. Due to tl ie preemption rules, lower handoff dropping probabihties can be achieved by the connection requests of the R T group compared to the N R T group. Pr eempt i on can happen in bo th networks whenever service 3 is i n the overloaded state, and hence using more B B U s t h a n its n o m i n a l al locations Nf^nxi and N^f^j-^. 4.3.3 Performance Comparison with a Fixed Policy F i g . 4.11 shows the probab i l i t y of dropping connection requests from hor izonta l and vert ical handoff users of service 1 i n cell C l of the 3 G R A N . We compare the performance of the integrated cel lular /802.16e system operat ing as described i n Sect ion 4.2 versus the system operat ing w i t h a fixed policy. W h e n the fixed po l i cy is used, the system is operat ing as i n case 3 (a^^i = Pci) at a l l t imes and independent from the handoff rates of the mob i l i ty scenario. T h e rest of the parameters are set the same before. In F i g . 4.11, we can see that the hor izonta l handoff dropp ing probabi l i t ies are 170% higher when the fixed po l i cy is used. O n the other hand , the vert i ca l handoff dropping probabi l i t ies are 5 5 % lower when such fixed po l i cy is used. A s expla ined before, since the system is operat ing i n case 2 (a^-j > Pci) (i.e., cell C l receives more requests from hor izonta l handoff users t h a n from vert i ca l handoff users), higher pr i o r i ty is given to connection requests from hor izonta l handoff users and less pr i o r i ty to the requests from vert i ca l handoff users. T h i s translates into lowering the hor izonta l handoff dropp ing probabi l i t ies at the expense of s l ight ly increasing the vert ical handoff dropping probabi l i t ies . T h i s expense is compensated by the fact that fewer vert ical handoff requests w i l l arr ive at cell 0 1 . Nevertheless, we can see that the hor izonta l handoff dropp ing probabi l i t ies are reduced by 6 3 % when the system operates i n case 2 compared to the case when operates w i t h the fixed policy. 4.3.4 Joint QoS Optimization F i g . 4.12 shows the probab i l i t y of b locking connection requests from the new users of services 1 and 2 in cel l E l . W e compare the performance of the integrated cel lular/802.16e system wi thout using the jo int connection and packet-level op t imiza t i on . T h e parameters Nf and are set as the capacities Cf and Q , respectively. In F i g . 4.12, we can see that the b lock ing probabi l i t ies increase faster for service 2. T h e reason is that we are increasing the ar r iva l rate of service 2 whi le the arr iva l rates of service 1 and 3 remain constant. Moreover , connection requests from service 2 require more B B U s . T h e b locking probabi l i t ies of connections from services 1 and 2 are 6 6 % and 6 9 % lower, respectively, when the parameters are set f rom the jo int QoS o p t i m i z a t i o n approach. It is worth ment ion ing that this decrease i n the b lock ing probabi l i t ies at the connection-level should be t raded off against to lerat ing an increase on the packet loss probabi l i t ies . Since for the case Nl = Cl, there is no packet loss due to s tat is t i ca l m u l t i p l e x i n g at the packet-level for neither of the groups (i.e., R T and N R T ) because we always have that Y^^^s ''^EisK ^ ^EV However, the packet loss probabihties can be bounded into a suitable value due to the packet- level constraints i n the jo int QoS op t imiza t i on prob lem i n (4.33). 4.4 Summary In this chapter, we first described the m o b i l i t y scenario for 3 G cel lular /802.16e interwork- ing . T h e scenario specifies the hor izonta l and vert ica l handoffs that can occur i n such integrated system. W e extended the V P w i t h preemption technique to be used for admis- sion contro l i n cel lular /802.16e interworking . W e proposed admiss ion control a lgorithms for each type of connection request. B o t h hor izonta l and vert i ca l handoffs are considered. P r e e m p t i o n rules are defined for the R T and N R T connections. W e formulated a block- i n g / d r o p p i n g cost m i n i m i z a t i o n prob lem fol lowing a jo int connection and packet-level QoS o p t i m i z a t i o n approach. N u m e r i c a l results showed the performance of the integrated system i n terms of the probab i l i ty of b lock ing new connection requests, the probab i l i ty of dropping hor izonta l and vert i ca l handoff connection requests, and the probab i l i ty of packet loss. Table 4.1: Q o S classif ication among 3 G cellular and I E E E 802.16e networks for admission contro l . Class i f i cat ion 3 G cellular I E E E 802.16e R T conversational U G S R T streaming r t - P S R T E r t - P S N R T interactive n r t - P S N R T background B E A l g o r i t h m 4 - A d m i s s i o n control a lgor i thm for new request w i t h b a n d w i d t h requirement b1 i n cell i e M " ^ . 1: if s e SRT 2: if Es'esj^nr < ,^1' > ^NRT, II The N R T group is overloaded 3: if Hs'eSnr + + ( S s ' s S ^ n r ^s' " ^NRT,) < ^RT, " ' t^^ " ^^cept 4: else if (Yis'es mlX' >K— and T.s'eSar K'^s' + ŝ < " ^i)- t^en accept with preemption 5: else reject 6: else if ES'SSRT ^s' + - ^RT, - ^i' a^^^P* / / ^he N R T group is underloaded 7: else reject 8: if .s G S NRT, Y^s'^s '^i,,K' + K< ~ then accept 9: else reject 10: end R A N - Radio access network H H O - Horizontal Iiandoff GW - Gateway A S N - Access service network V H O - Vertical handoff C N - Core network BSC - Base station controller F i g u r e 4 .1: Integrated 3 G cel iular /802.16e system. C7 C6 V C5 > C8 >-•• C2/E2 r C l / E l C4 C9 - C3.^3 CIO \ C12 \ / ( C l l ) F i g u r e 4 .2 : Integrated 3 0 cel lular/802.16e system, 3 0 R A N w i t h \M'\ = 12 and 802.16e A S N w i t h IM'I = 3. F i g u r e 4.3: H o n z o n t a l and vert ica l handoff rates w . th {i,j} e and {k, 1} e M^. Horizontal • Horizontal Vertical Horizontal Vertical New 1 ^ 4 I at f I Pi Vertical « Horizontal • Vertical *• Horizontal Vertical New Pi at N^T-St 2)at<pt Horizontal Vertical *• Horizontal Vertical Horizontal Vertical New \ Pi ^mr-st ^)at-pt F i g u r e 4.4: P r ^ o r ^ e s of the different connection requests of service . e m cell ^ e Case 1 > f3f)^ Case 2 (a . . < 0f), and Case 3 (a,e = (5^^ ' A l g o r i t h m 5 - A d m i s s i o n control for hor izontal handoff request w i t h b a n d w i d t h require- ment 6̂  i n cell i € Ai"^. 1: if a f > f3f, then 2: if s G SRT 3: if Es'€Sf,RT ^•I'^'s' > ^NRT, II The N R T group is overloaded 4: if E y e 5 « , < > ^ ' + + ( E . ' e 5 ; . « , " ^%RT) < ^^^T,- then accept 5: else if YLs'eS ""^ï ,K' + > then accept wi th preemption 6: else reject 7: else if E s ' s s ^ r ' " t ^ ^ ' + - '̂̂ '̂ ^P*^ / / ^^^^ S ^ ^ P underloaded 8: else reject 9: if s G SNRT, E ^ ' e s ^IM' + ^"s < then accept 10: else reject 11; else if < /3f, then 12: if s e SRT 13: if Es'es„nr < .^l' > ^NRT, II The N R T group is overloaded 14: if Es'esnr + ^'s + (Es'eS^nr ^^A' ' ^NRT,) < ~ /if, then accept 15: else if ( E , - e s <,K' > ~ PI and YLs'eSur ^IK' + b's < - / i f ) , then accept with preemption 16: else reject 17: else if E^ 'eS^T ^l, K' + < ^RTt " Pi' then accept / / The N R T group is underloaded 18: else reject 19: if s € SNRT, Es'es + b',<Nf~ 0f, then accept 20: else reject 21: end Arrivai rate service 2 {X^} F i g u r e 4 .5 : N e w connection b locking probabi l i ty in cell C l and cell E l versus the arr ival rate of connection requests from service 2. A l g o r i t h m 6 - A d m i s s i o n control for vert ical handoff request w i t h b a n d w i d t h requirement 6̂  in cel l i € M^. 1: if > (3f, then 2: if 5 e SRT 3- if Es'eSr.rRr "^hK > ^ N R T , II The N R T group is overloaded 4-- if Y.s'eSnr ^ f > ^ ' + + (Ês'es.vnr K ^ ^ s ' " ^NRT/) < ^ /̂ïT. - then accept 5: else if ( E , ' e 5 <,,K' > - < and }Zs'eSnT " ^v^s ' + ŝ < ^  r . ^ < ) , then accept wi th preemption 6: else reject 7: else if E ^ ' e s ^ r "^<v^s' < ^ K T . - " i - then accept / / The N R T group is underloaded 8: else reject 9: if s 6 SNRT, J2s'es + ŝ < - then accept 10: else reject 11: else if af < pf, then 12: if 5 G SRT 13: if Es'es^nr '^l^'s' > ^NRT, II The N R T group is overloaded 14: if Es'eSRT K' + ^1 + iHs'eSr^ar "^h ' ^NRT,) < ^RT, ' then accept 15: else if J2s'es ,K' + K> then accept wi th preemption 16: else reject 17: else if i^s'esnr ™v^s' + < ^RT ' then accept / / The N R T group is underloaded 18: else reject 19: if s G SNRT, ES'esK,,K' + ^1 < iVf, then accept 20: else reject 21: end " 1 1 . 1 ] 1 I 1 : I 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Arrival rate service 2 {X^} F i g u r e 4.6: H o r i z o n t a l handoff dropping probabi l i ty in cell C l and cell E l versus the arr iva l rate of connection requests from service 2. 0-2 0.4 0.6 0.8 1 Arrival rate service 2 (X ) 1-2 1.4 1.6 1.8 F i g u r e 4 .7: Ver t i ca l handoff dropping probab i l i ty in cell C l rate of connection requests from service 2. and cell E l versus the arr ival 10 " 10"^ 3 10" 10 ' o 10 10 ' 10 10 Cl ' E I 0-2 0.4 0.6 0. , . 1-2 1.4 1,6 1.8 2 Arrival rate service 2 F i g u r e 4 .8 : Packet loss probabi l i ty in cell C l and cell E l nection requests from service 2. versus the arr ival rate of con-  F i g u r e 4 . 11 : Hor i zonta l and vert ical dropping probabi l i t ies i n cel l C l versus the arr ival rate of connection requests from service 2. 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Deng , "Traffic Character is t i cs of Packet Voice , " i n Proc. of IEEE ICC'95, Seattle, W A , June 1995. 35] , " E m p i r i c a l M o d e l of W W W Document A r r i v a l s at Access L i n k , " i n Proc. of IEEE ICC'96, D a l l a s , T X , June 1996. Chapter 5 Conclusions and Future Work 5.1 Summary of Work Accomplished In this thesis we have investigated on m o b i l i t y management and admiss ion control i n heterogeneous wireless networks. Specifically, we have considered three different research problems and have archived the fol lowing contr ibut ions to the field: • V e r t i c a l H a n d o f f Decis ion A l g o r i t h m in Heterogeneous Wireless Networks: In C h a p t e r 2 of the thesis, we proposed a novel vert ica l handoff decision a lgor i thm. W e formulated the handoff decision problem as an M D P w i t h the objective of m a x i - m i z i n g the t o ta l expected discounted reward per connection. A l ink reward funct ion models the Q o S of the connection i n terms of the available b a n d w i d t h and delay. A s ignal ing cost funct ion models the switching cost incurred i n the networks when a vert ica l handoff is executed. O u r work aims to make emphasis i n the tradeoff between these two impor tant aspects. B y using the V I A , a s tat ionary determinist ic po l i cy is obtained when the connection terminat ion t ime is assumed to be geometrical ly dis- t r ibuted . Several model extensions as wel l as implementat ion guidelines according to the I E E E 802.21 s tandard are described. W e evaluated our handoff decision scheme by considering connections w i t h C B R voice traflSc and F T P d a t a traffic. W e also d i d a sensi t iv i ty analysis to investigate on the degradation of performance when the aver- age connection durat i on is not correct ly est imated by the mobi le t e r m i n a l dur ing the connection setup. N u m e r i c a l results showed that our handoff a lgor i thm achieves a higher expected reward and a lower number of vert ica l handoffs per connect ion than S A W , T O P S I S , G R A , and two heurist ic policies under a wide range of condit ions. • A d m i s s i o n C o n t r o l in C e l l u l a r / W L A N : In C h a p t e r 3 of the thesis, we devel- oped an ana ly t i ca l model to faci l i tate the performance evaluation a n d parameter adjustment of different admission control policies i n a mult i -service integrated cel- l u l a r / W L A N system. O u r model takes into account the mob i l i t y and the rate of connection requests of t l ie users, the capaci ty and the coverage area of each network, the admiss ion control policies, the cost from b lock ing connection requests for each service, and the Q o S requirements i n terms of b lock ing and dropping probabi l i t ies . O u r work aims to incorporate these impor tant aspects i n an opt imizat ion-based de- sign for connect ion admission control i n integrated c e l l u l a r / W L A N systems. G i v e n the mode l , we also formulated two different revenue m a x i m i z a t i o n problems to adjust the admiss ion contro l parameters. T h e first prob lem aims to max imize the network revenue i n terms of the accepted connection requests from new and handoff users. T h e second prob lem aims to max imize the network revenue i n terms of the accepted connection requests from new users subject to QoS constraints on the handoff drop- p ing probabi l i t ies . W e evaluated four different combinat ions of admission control policies by extending the C P and the F G admiss ion control policies w i t h pol icy func- tions. Resul ts showed that , under a wide range of connection request rates and various users' m o b i l i t y levels, us ing the C P pol i cy i n bo th access networks achieves the best performance for b o t h design objectives. • H a n d o f f M a n a g e m e n t a n d A d m i s s i o n C o n t r o l i n Cel lular /802 .16e : In C h a p - ter 4 of the thesis, we first described the m o b i l i t y scenario for 3 0 cel lular /802.16e interworking . T h e scenario specified the hor izonta l and ver t i ca l handoffs that can occur. W e extended the V P w i t h preemption technique to be used for admission control i n cel lular /802.16e interworking . To this end, we proposed admission con- t r o l a lgor i thms for connection requests that consider the class of service (i.e., R T or N R T ) and the type of user (i.e., new or handoff) . B o t h hor izonta l and vert ical handoffs are considered, and suitable preempt ion rules are defined for the R T and N R T connections. W e formulated a b l o c k i n g / d r o p p i n g cost m i n i m i z a t i o n problem fol lowing a jo int connection and packet-level QoS o p t i m i z a t i o n approach. N u m e r i c a l results showed the performance of the integrated system i n terms of the probabi l i ty of b lock ing new connection requests, the probab i l i ty of d ropp ing hor izontal and ver- t i ca l handoff connection requests, and the probab i l i ty of packet loss. Performance improvement is shown at the connection-level when the proposed admission algo- r i thms are used compared w i t h a fixed po l i cy since they proper ly assign the priorit ies for admission contro l to each type of handoff user based on the described mob i l i t y scenario. Improvement is also shown when preempt ion of R T connections over N R T connections and the joint QoS op t imiza t i on are used. 5.2 Relationship Among Chapters and Discussions In C h a p t e r 2, the focus of our research work was in handoff management w i t h special at tent ion to the vert ica l handoff decision. However, we also extended our decision a lgor i thm into a complete handoff management framework to consider bo th types of handoff. W e explained how our M D P vert ica l handoff scheme can incorporate the user's preferences into the decision as expected by the always best connected ( A B C ) concept [1]. T h e A B C concept allows the users connect iv i ty to appl icat ions us ing the devices and access networks that best suit their needs, thereby combin ing the features of a l l heterogeneous networks. A l t h o u g h the vert i ca l handoff decision is out of the scope of Chapters 3 and 4, because for admission control we are interested on the connection requests to the network once the handoff decision was performed, we can assume, wi thout losing generality, that the handoff framework introduced on C h a p t e r 2 is used. O n the other h a n d , i n Chapters 3 and 4, we focused more on the admission control . In C h a p t e r 3, we introduced the impor tant concept of po l i cy functions. E a c h po l i cy funct ion can be defined based on the service category (e.g., voice, data) , the type of connection request (e.g., new or handoff) , and the admission pohcy being used. O u r framework fa- ci l i tates the incorporat ion of different admission pohcies into the c e l l u l a r / W L A N model . Network designers can use the po l i cy functions either to evaluate the performance i n the network of admiss ion control policies already proposed or to examine new ones. A s an example of the flexibility of our model , in [2], we first derived the corresponding pohcy functions for V P , T h e n we appl ied such functions into our model for c e l l u l a r / W L A N i n - terworking . W e also considered handoff management i n C h a p t e r 3. W e defined different po l i cy functions for each type of handoff request and described the possible relationships between such functions according to the network operator 's policies. In our early research work [3, 4], for s impl i c i ty , we assumed that bo th types of handoff requests were treated equally for admiss ion control . Nevertheless, in C h a p t e r 3, we made our mode l more general by prov id ing handoff diflterentiation. In C h a p t e r 4, we combined b o t h handoff management and admiss ion control i n the same framework. F i r s t , we described i n detai l the m o b i l i t y scenario i n cel lular/802.16e interworking by considering the different hor izontal and vert ical handoff that can occur. Fi-om the scenario, we defined a proper algorithms to be used w i t h V P w i t h preemption for admission control . Since jo int design is expected and required in heterogeneous wireless networks [5], we considered packet-level issues in this model (i.e., the connections should be accepted t a k i n g into account t i ie performance of t i ie network at t i ie packet-level) . To this end, we used the jo int QoS o p t i m i z a t i o n approach. Different to our work i n C h a p t e r 3 on admission control i n c e l l u l a r / W L A N , i n C h a p t e r 4 we considered the mode l formulat ion and performance evaluat ion of the integrated cel lular /802.16e system at the connection- level and at the packet-level . In 4 G heterogeneous wireless networks, the diverse QoS requirements for m u l t i m e d i a appl icat ions , the m o b i h t y of the users, and the presence of different co-located wireless ac- cess networks are significant challenges i n the design of handoff management and admission control schemes. O u r contr ibut ions i n this thesis a imed to proper ly deal w i t h those design challenges. However, we acknowledge that a l l research work can be improved and extended since new challenges w i l l appear i n the forthcoming generations of wireless networks. 5.3 Future Work T h i s thesis can be extended i n several aspects. Here, we present an overview of some current and possible directions for future work. In some cases they are proposed to deal w i t h specific improvements of the current research and i n others to suggest related open research problems. • C o n s t r a i n e d M D P V e r t i c a l HandofF A l g o r i t h m : In [6], we have extended our vert ica l handoff a lgor i thm presented i n C h a p t e r 2. W e have incorporated the locat ion in format ion and the velocity of the user in the vert i ca l handoff decision. It has been formulated as a constrained M D P . T h e objective is to m a x i m i z e the expected to ta l reward of a connection subject to the expected to ta l access cost constraint . Current ly , i n [7], we are work ing on the der ivat ion of some s t ruc tura l results of the o p t i m a l handoff po l i cy by using the concept of supermodular i ty . Such s t r u c t u r a l results may faci l i tate the computat i on and implementat ion of the o p t i m a l vert i ca l handoff pohcy. • M D P Vert ica l HandofF M o d e l i n g : In the discrete-t ime formulat ion of our M D P vert i ca l handoff a lgor i thm i n C h a p t e r 2, the connection durat i on is considered to be geometrical ly d i s t r ibuted . In add i t i on , it also assumed that the vert ica l handoff decision is performed periodical ly . F u r t h e r extensions can consider a continuous-t ime model formulat ion and consider general connection durat i on . Since a more realistic model should allow the decision to be performed whenever there is a state change in the networks. O n the other hand , i n C h a p t e r 2 to deal w i t h the mode l of the t rans i t i on probabi l i t ies of the W L A N , they were est imated from ns-2 s imulat ions . To overcome this issue, other techniques model-free to solve M D P s such as reinforcement learning can also be considered. • M o b i l i t y M o d e l i n g in Heterogeneous Wireless Networks: A l t h o u g h the mo- b i l i t y models i n Chapters 3 and 4 consider the cell residence t ime and the inter- boundary network crossing t ime , such times are assumed to be exponential ly d is - t r ibuted . T h e existence of p a r t i a l l y and to ta l ly overlapped coverage areas i n het- erogeneous wireless networks generates some interrelat ionships between those t imes. Some recent work has a imed to successfully model such issues by using phase-type ( P H ) d is tr ibut ions and mob i l i t y traces [8]. Further extensions can consider to incor- porate such m o b i l i t y models into our proposed framework. • C a p a c i t y of I E E E 802.11 W L A N s : In our model i n C h a p t e r 3, the capacity of the W L A N s is an approx imat ion . D u e to the contention nature of the I E E E 802.11 D C F , the exact capaci ty of the W L A N depends, among other factors, on the number of users. However, since we are interested in the m a x i m u m number of connections that can be supported simultaneously, we approximate the capaci ty of the W L A N as the saturat ion throughput (i.e., constant effective capaci ty) . Moreover , I E E E 802.11 does not guarantee QoS . F u t u r e work should consider instead the revision I E E E 802.11e 9] of the 802.11 s tandard for admission control i n c e l l u l a r / W L A N interworking. • L i n k A d a p t a t i o n in Heterogeneous Wireless Networks : In our model i n C h a p - ter 4, we assume that the cells have a fixed capacity. However, due to l ink adaptat ion i n future evolutions of the 3 G cel lular networks and i n I E E E 802.16e networks, the capacities of the cells are not s t r i c t l y fixed. W e require to incorporate intra-ce l l user mobi l i ty . Based on the posit ion of the user w i t h i n the cel l (i.e., the qual i ty of the wireless channel) , there w i l l be a different capacity. T h i s issue has been recently investigated in [10]. Fur ther extensions can consider adding such mob i l i ty issues into our proposed handoff management and admission control frameworks. • E x t e n s i o n to other Wireless Networks: In the present thesis, we focused only on infrastructure-based and single-hop wireless networks. A n interesting extension of the current work should investigate on mob i l i t y management and admission control i n ad-hoc networks as well as mul t i -hop wireless networks w i t h heterogeneous access technologies. Bibliography fl] E . Gustafsson and A . Jonsson, " A l w a y s Best Connected , " IEEE Wireless Commun. Mag., vo l . 10, no. 1, pp . 49-55 , February 2003. 2] E . Stevens-Navarro and V . W . S. W o n g , " V i r t u a l P a r t i t i o n i n g for Connec t i on A d - mission C o n t r o l i n C e l l u l a r / W L A N Interworking , " i n Proc. of IEEE WCNC'08, Las Vegas, N V , M a r c h 2008. [3] , "Resource Shar ing i n an Integrated Wireless C e l l u l a r / W L A N Sys tem, " i n Proc. of 20th Canadian Conference in Electrical and Computer Engineering (CCECE'07), Vancouver , C a n a d a , A p r i l 2007. 4] E . Stevens-Navarro , A . H . M o h s e n i a n - R a d , and V . W . S. W o n g , " O n O p t n n a l A d - mission C o n t r o l for M u l t i - S e r v i c e C e l l u l a r / W L A N Interworking , " in Proc. of IEEE GLOBECOM'07, Wash ington , D C , November 2007. [5] D . N i y a t o and E . Hossain , " C a l l A d m i s s i o n C o n t r o l for QoS Prov i s i on ing i n 4 0 W i r e - less Networks : Issues and Approaches , " IEEE Network, vo l . 19, no. 5, pp . 5-11, September /Oc tober 2005. [6] C . S u n , E . Stevens-Navarro , and V . W . S. W o n g , " A Cons t ra ined M D P - b a s e d Ver t i ca l Handof f Dec is ion A l g o r i t h m for 4 0 Wireless Networks , " i n Proc. of IEEE ICC'OS, B e i j i n g , C h i n a , M a y 2008. [7] , " A Constra ined M D P - b a s e d Ver t i ca l Handof f Dec is ion A l g o r i t h m for 4 0 Het - erogeneous Wireless Networks , " to be submi t ted to IEEE Trans, on Veh. Technol, 2008. [8] A . H . Z a h r a n and B . L i a n g . , " M o b i l i t y M o d e l i n g and Performance E v a l u a t i o n of Heterogeneous Wireless Networks , " IEEE Trans. Mobile Comput., in press, 2008. 9] I E E E 802.11 W o r k i n g G r o u p , " I E E E S t d 802.11e-2005 A m e n d m e n t to I E E E Std 802.11, 1999 E d i t i o n (Reaff 2003)," 2005. [10] J . L . and SampalH, " C e l l M o b H i t y Based A d m i s s i o n C o n t r o l for W . e l e s s Networks w i t h L m k A d a p t a t i o n , " i n Proc. of IEEE ICC'07, Glasgow, Scot land, June 2007. Appendix A List of Publications J o u r n a l Papers • E n r i q u e Stevens-Navarro , Y u x i a L i n , and V i n c e n t W . S . W o n g , " A n M D P - b a s e d Ver t i ca l Handofï Decis ion A l g o r i t h m for Heterogeneous Wireless Networks , " IEEE Transactions on Vehicular Technology, vo l . 57, no. 2, pp. 1243-1254, M a r c h 2008. • E n r i q u e Stevens-Navarro , A m i r - H a m e d M o h s e n i a n - R a d , and V i n c e n t W . S . W o n g , "Connec t i on A d m i s s i o n C o n t r o l for M u l t i - S e r v i c e Integrated C e l l u l a r / W L A N Sys- t e m , " accepted for pub l i ca t i on in IEEE Transactions on Vehicular Technology, 2008. • E n r i q u e Stevens-Navarro and V incent W . S . W o n g , "Handof f Management and A d - mission C o n t r o l using V i r t u a l P a r t i t i o n i n g w i t h P r e e m p t i o n i n 3 G Cel lu lar /802 .16e Interworking , " to be submit ted to IEEE Transactions on Vehicular Technology. Conference Papers • E n r i q u e Stevens-Navarro and V incent W . S . W o n g , " V i r t u a l P a r t i t i o n i n g for A d m i s - sion C o n t r o l i n C e l l u l a r / W L A N Interworking , " i n Proc. of IEEE Wireless Com- munications and Networking Conference (WCNC'08), L a s Vegas, N E , M a r c h / A p r i l 2008. • E n r i q u e Stevens-Navarro , A m i r - H a m e d M o h s e n i a n - R a d , and V incent W . S . Wong , " O n O p t i m a l A d m i s s i o n C o n t r o l for M u l t i - S e r v i c e C e l l u l a r / W L A N Interworking , " i n Proc. of IEEE Global Telecommunications Conference (Globecom'07), Wash ington , D C , November 2007. • E n r i q u e Stevens-Navarro and Vincent W . S . W o n g , "Resource Shar ing i n an Inte- grated Wireless C e l l u l a r / W L A N System, " i n Proc. of the 20th IEEE Canadian Con- ference on Electrical and Computer Engineering (CCECE'07), Vancouver , C a n a d a , A p r i l 2007. • E n r i q u e Stevens-Navarro , V incent W . S . W o n g , and Y u x i a L i n , " A Ver t i ca l Handoff Decis ion A l g o r i t h m for Heterogeneous Wireless Networks , " i n Proc. of IEEE Wire- less Communications and Networking Conference (WCNC'07), H o n g K o n g , C h i n a , M a r c h 2007. • E n r i q u e Stevens-Navarro a n d V incent W . S . W o n g , " C o m p a r i s o n between Ver t i ca l Handof f Dec is ion A l g o r i t h m s for Heterogeneous Wireless Networks , " in Proc. of IEEE Vehicular Technology Conference (VTC-Spring'06), M e l b o u r n e , A u s t r a l i a , M a y 2006. B o o k C h a p t e r s • E n r i q u e Stevens-Navarro , C h i Sun , and V i n c e n t W . S . W o n g , " A Survey of A n a l y t i c a l M o d e h n g for C e l l u l a r / W L A N Interworking , " i n Emerging Technologies in Wireless LAN: Theory, Design and Deployment, edited by B e n n y B i n g , Cambr idge Univers i ty Press, I S B N 978-0-521-89584-2, 2008. • J ie Zhang , E n r i q u e Stevens-Navarro , V i n c e n t W . S . Wong , H e n r y C . B . C h a n , and V i c t o r C M . L e u n g , "Protoco ls and Decis ion Processes for V e r t i c a l Handovers , " i n Unlicensed Mobile Access Technology: Protocols, Architectures, Security, Standards and Applications, edited by Y . Zhang , L . Y a n g , J . M a , A u e r b a c h Pub l i ca t i ons , C R C Press , 2008.

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