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UBC Theses and Dissertations

A demand assigned multiple access strategy for land mobile satellite voice services Powell, Chris J. 1992

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We accept this thesis as conformingto  t requ ed standardA DEMAND ASSIGNED MULTIPLE ACCESS STRATEGYFOR LAND MOBILE SATELLITE VOICE SERVICESbyCHRIS J. POWELLBSc. (Hons), The University of British Columbia, 1989A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of Electrical EngineeringTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1992© Chris J. Powell, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of ^Electrical EngineeringThe University of British ColumbiaVancouver, CanadaDate^March 11, 1992DE-6 (2/88)AbstractDevelopment of land mobile satellite systems is progressing rapidly, and implementationof new voice and data services for North America is scheduled for early 1994. In order tomake the best use of the bandwidth allocated for these services, efficient demand assignedmultiple access (DAMA) protocols must be employed. Efficiency achieved in terms of higherchannel utilization and availability translates into more revenue for network management andbetter service for network subscribers.In particular, mobile voice services are examined, and a new blocked-calls-queued dis-cipline, which processes calls in batches, designed specifically for dispatch radio via satelliteis analyzed. Computer simulation is used to examine several batch service disciplines, and itis thereby shown that the new system meets the objectives of efficiency in providing a highlevel of performance by exploiting traffic characteristics unique to dispatch radio rather thanadapting conventional techniques used in telephony.In addition, a technique for integrating mobile radio service and mobile telephone servicein a dynamic resource sharing strategy using a common DAMA channel pool is introduced.The new strategy attempts to reserve a small margin of free channels for blocked-calls-dropped telephone traffic, while permitting the remaining channels to be shared betweenradio and telephone on a first come first served basis. It is shown that, without degradingthe performance of either traffic source, the proposed integrated system achieves higherthroughput than any other system of traffic integration found in the literature which isapplicable to these services.iiContentsAbstract^ iiList of Tables viiList of Figures^ viiiList of SymbolsAcknowledgment^ xivDedication xvChapter 1 Introduction^ 11.1 Background  11.1.1 Historical Perspective ^  11.1.2 Current LMSS Development ^ 31.1.3 Typical LMSS Network Configuration ^ 41.2 Motivations and Objectives ^  61.2.1 Motivations ^  61.2.2 Objective 1: MRS DAMA Strategy ^ 71.2.3 Objective 2: Integrated Network Strategy  81.2.4 Overall Contribution to LMSS Communications ^  81.3 Review of Previous Work ^ 91.3.1 Comparison of MRS and MTS Traffic ^ 91.3.2 Mobile Radio Service DAMA Protocol  101.3.3 Integrated MRS and MTS Dynamic Channel Allocation^ 131.4 Overview^  15iiiChapter 2 Description of MRS Protocol^ 162.1 Dispatch Service Disciplines for Batch Processing ^  162.2 MRS Subnet Operation ^  192.3 Description of MRS Delay Characteristics ^  22Chapter 3 Modelling and Analysis of a Single MRS Subnet^293.1 Single MRS Subnet Delay Model ^  293.2 Single MRS Subnet Operation  303.3 Delay Analysis ^  323.3.1 Comparison of FCFS and OW Batch Service Ordering ^ 323.3.2 Closed Batch Subnet Configurations ^  323.3.3 Open Batch Subnet Configurations  383.3.4 Open and Closed Batch System Comparison ^  443.4 Summary^  48Chapter 4 Integrated MRS and MTS Network^ 514.1 Dynamic Channel Allocation ^  524.1.1 The Reserved Margin Strategy ^  524.1.2 Comparison of Integrated Service S trategies ^  544.2 Integrated Network Operation ^  554.3 Integrated Network Model  574.3.1 MTS Traffic Model ^  574.3.2 MRS Network Model for Multiple Dispatch Subnets ^ 574.3.3 Integrated Network Model Parameters ^  59iv4.4 Simulation Modelling ^  614.4.1 MRS and MTS Performance Objectives ^  614.4.2 Methodology^  624.5 Results ^  634.6 Summary and Observations ^  78Chapter 5 Conclusion^ 805.1 Summary  805.2 Future Work ^  81Bibliography 84Appendix A Model Validation and Verification^ 90A.1 Open Batch MRS Subnet Model ^  91A.2 Closed Batch MRS Subnet Model  97A.3 Integrated Network Model ^  100Appendix B Simulation Modelling and Data Analysis^ 104B.1 Notes on Methodology ^  105B.2 Confidence Intervals  106Appendix C Source Code^ 109C.1 FC.sim ^  109C.2 call.sim  114C.3 checkin.sim ^  116C.4 disp.sim  117C.5 init.sim ^  119C.6 main.sim ^  120C.7 mrt.sim  121C.8 read.sim ^  122C.9 report.sim  125C.10 reset.sim ^  127C.11 timeout.sim  128viList of TablesTable 1^Savings in Signalling Overhead with a CB System ^ 22Table 2^Fixed MRS Model Parameters ^  30Table 3^Variable MRS Model Parameters  31Table 4^Location of Minimum Delay in MRTs per Dispatcher for CBSystems ^  37Table 5^Location of Minimum Delay in MRTs per Dispatcher for OBSystems ^  44Table 6^Comparative Results of Various Channel Allocation Strategies ^ 55Table 7^Fixed Network Model Parameters ^  60Table 8^Variable Network Model Parameters  60Table 9^High Performance CB Dynamic Allocation Improvements . . . ^ 66Table 10^High Performance OB Dynamic Allocation Improvements . . . ^ 66Table 11^Low Performance CB Dynamic Allocation Improvements ^ 68Table 12^Low Performance OB Dynamic Allocation Improvements ^ 69Table 13^Mean Number of Free Channels for High Performance Model ^ 71Table 14^Mean Number of Free Channels for Low Performance Model . . ^ 72Table 15^Optipal Batch Sizes ^  74Table 16^CB and OB Variance Comparison ^  75Table 17^Channel Queuing Delay^  76viiList of FiguresFigure 1^WARC-87 L-band Allocation (MHz) ^ 3Figure 2^Network Configuration ^  5Figure 3^North American Spot-beam Coverage^ 6Figure 4^Batch Formation Queuing Diagram  17Figure 5^Single Call Processing Timing Diagram ^ 18Figure 6^Closed Batch Call Processing Timing Diagram ^ 19Figure 7^Closed Batch Flowchart ^  24Figure 8^Open Batch Flowchart  25Figure 9^CB Subnet: Single Dispatcher Delay ^  33Figure 10^CB Subnet: Two Dispatcher Delay  34Figure 11^CB Subnet: Four Dispatcher Delay ^  35Figure 12^CB Subnet: Eight Dispatcher Delay  36Figure 13^CB Subnet Delay Curve Comparison for 1, 2, 4, and 8 Dispatchers ^ 38Figure 14^OB Subnet: Single Dispatcher Delay ^  39Figure 15^OB Subnet: Two Dispatcher Delay  40Figure 16^OB Subnet: Three Dispatcher Delay ^  41Figure 17^OB Subnet: Four Dispatcher Delay  42Figure 18^OB Subnet Delay Curve Comparison for 1, 2, 3, and 4 Dispatchers ^ 43Figure 19^CB and OB Single Dispatcher Delay ^  45Figure 20^CB and OB Two Dispatcher Delay  46Figure 21^CB and OB Four Dispatcher Delay ^  47Figure 22^Reserved Margin Channel Allocation  56vu'Figure 23^High Performance CB Channel Capacities ^ 64Figure 24^High Performance OB Channel Capacities  65Figure 25^Low Performance CB Channel Capacities ^ 68Figure 26^Low Performance OB Channel Capacities  69Figure 27^High Performance CB and OB Channel Capacities ^ 71Figure 28^Low Performance CB and OB Channel Capacities ^ 72Figure 29^Closed Batch High and Low Performance Models ^ 77Figure 30^Open Batch High and Low Performance Models  78Figure 31^Open Batch, Single Dispatcher Markov Chain ^ 91Figure 32^Comparison of OB Simulation Model Results with Markov ChainModel ^  96Figure 33^Closed Batch, Single Dispatcher Markov Chain ^ 97Figure 34^Comparison of OB Simulation Model Results with Markov ChainModel ^  100Figure 35^MTS Population versus Blocking Probability ^ 102Figure 36^MTS Population versus Utilization Factor  103Figure 37^CB Low Performance Network with 95% Confidence Intervals ^ 108ixList of Symbols0 — a matrix consisting entirely of zerosAMSC — American mobile satellite corporationb — batch sizeCB — closed batchcR — number of radio channels for a fixed channel allocation mobile radio networkcr — number of telephone channels for a fixed channel allocation mobile telephone networkDAMA — demand assigned multiple accessDCS — DAMA control centreDOC — Department of Communicationsd — number of dispatchersE[ I — expected valueei — column matrix which contains all zeros except in position i where there is a 1FAX — facsimileFDM — frequency division multiplexingFCFS — first come first servedGHz — gigahertzi — denotes an indexINMARSAT — International Marine Satellite Organizationj — denotes an indexKu-band — 12/14 GHzL-band — 1.5/1.6 GHzLMR — land mobile radioLMSS — land mobile satellite servicesm — number of mobile telephone terminalsMDS — mobile data serviceMHz — megahertzmin — minuteMRS — mobile radio serviceMRT — mobile radio terminalms — millisecondMSAT — mobile satelliteMSS — mobile satellite systemsMTS — mobile telephone serviceMTT — mobile telephone terminaln — number of mobile radio terminalsN — mean number of customers in a Markov chainNASA — National Aeronautics and Space AdministrationNCC — network control centren — number of mobile radio terminalsOB — open batchOW — oldest job firstp — state probability matrixpH — telephone service blocking probabilitypi — the limiting probability of state i in an imbedded Markov chainpy — the limiting probability of state ij in an imbedded Markov chainp.d.f. — probability density functionPSTN — public switched telephone networkQ — infinitesimal generator matrixR — mean number of free telephone channels realized in an integrated network after mobile radio servicetraffic has been increased as much as possible, while mobile telephone traffic has been held constantRM — specified margin of free telephone channels to be reservedRE'S — remote position sensings — seconds — number of spot-beams• — a Markov chain state• — a Markov chain stateSCADA — supervisory control and data acquisitionxiT — mean number of free telephone channels realized in an integrated network after mobile telephoneservice traffic has been increased as much as possible, while mobile radio traffic has been heldconstantT — mean time spent in system by a customer in a Markov chainTc — mean time between the time a dispatch radio call is initiated and the time service commencesexcluding the mean time to wait for a free channel to come available at the DAMA control centerTcA — mean time for a channel assignment to reach a dispatcherTcR — mean time for a channel request to reach the DAMA control centerTm — control message serializing delayTMI — Telesat Mobile IncorporatedTp — earth station to earth station propagation delayTQ - mean time spent in queue by a customer in a Markov chaintQc — mean time to wait for a free channel to come available at the DAMA control centerTQc — mean wait for a channel allocation per callTR — mean time for the call request to reach the dispatch centreTs — mean time to complete service for leading calls in the same batchTsetw, — mean time between the time a dispatch radio call is initiated and the time service commencesTv — mean time to verify a mobile radio terminal is set up on an assigned channelTv, — mean verification delay for an open batch call joining a. batch for which service has not begunTSB — mean verification delay for an open batch call joining a batch for which service has begunTwR — mean waiting time associated with batch formationTwc — mean time waiting to receive a channel assignmentTwD — mean time waiting for a dispatcher to service the batch -WARC — World Administrative Radio Conference• — mean of the random variable XX — random variable representing the number of open batch calls that arrive after batch service startsbut have still not commenced serviceA% — change in percentAm — change in the number of mobile telephone terminalsxiiAn — change in the number of mobile radio terminalsA — mean overall call arrival rate for a Markov chainA — mean arrival rate for a Markov chain client which is not queued or in serviceAR - mean individual mobile radio terminal call rateAT - mean mobile telephone call rate- mean rate of mobile radio call service for a single channel— mean rate of mobile telephone call service for a single channelri — the limiting probability of state i in a continuous time Markov chainAii — the limiting probability of state ij in a continuous time Markov chainp — channel or server utilization factorAcknowledgmentI would like to express my thanks to my advisor, Dr. Victor Leung, whose support andguidance throughout my studies is sincerely appreciated.I would also like to express sincere thanks to the technical support staff for their helpin answering many questions and keeping the computer network up and running, the womenin the Electrical Engineering office for their frequent administrative assistance, and to manyother new friends who have made my stay a pleasant one.The financial support I received is also gratefully acknowledged. Many thanks to Dr.Leung for his Research Assistantships, the Department of Electrical Engineering for itsscholarships and Teaching Assistantships, and to the British Columbia Science Council andMicrotel Pacific Research for their contributions toward my Graduate Research in Engineeringand Technology award.Finally, the support and encouragement I received from my family and friends has beeninvaluable — especially from my parents who were with me at the start of this endeavourand without whom it would not have been possible.xivDedicationIn Memory of my Parents,Francis H. and Hilda G.XV1. Introduction1.1 BackgroundSatellite technology has progressed enormously since its inception. In the early days ofsatellite communication, the expense was high for both service suppliers and system users.Today the cost of the space segment is still high, but due to advanced technology offering af-fordable terrestrial transceivers and a rapidly expanding demand for mobile communications,services can be offered to a large, diverse population at a reasonable cost [1].1.1.1 Historical PerspectiveIn 1945, twelve years before the first Sputnik was launched, Arthur C. Clarke, a radarofficer with the Royal Air Force, first proposed communication systems using geosynchronoussatellites [2,3]. Since that initial vision, satellite systems have burgeoned from dream toreality.The American National Aeronautics and Space Administration (NASA) first tested voicetransmission from a satellite by broadcasting a tape-recorded message in 1958. Two yearslater the first active radio repeater was in orbit: .ad three watts of power and lasted onlyseventeen days. Finally, in 1963, the idea created in the imagination of Arthur C. Clarkewas realized as NASA launched the first geosynchronous communications satellite into orbit.From that time, satellite technology continued to progress rapidly, and in 1966 the firstmultiple access satellite with multidestination capability was introduced by COMSAT in theUnited States [4].1Despite the fact that satellite communications were very expensive at the time, the 1971World Administrative Radio Conference (WARC-71) allocated 1 MHz of L-band (4.6/1.5GHz) spectrum to maritime and aeronautical communications to open the way for thedevelopment of mobile satellite systems (MSS). Following the WARC-71 L-band allocation,the Canadian Department of Communications (DOC) developed the concept of the firstmultiple purpose MSS and, in 1972, Telesat Canada launched the ANIK — the world'sfirst domestic communications satellite. The DOC undertook the capital intensive ANIKproject in its commitment to Canadian national communications; nevertheless, the DOChoped that by achieving full utilization, economies of scale would make the project end upbeing economical [51. As it turned out, the ANIK project showed a virtually unprecedentedreturn on capital investment in the telecommunications industry. In the US at that time,legislation was in place which prohibited domestic satellites and restricted US satellite serviceproviders to COMSAT alone. However, following the ANIK's resounding success, a fury of•US legislation was passed that same year which broke the US domestic market wide open.By 1974 the first US domestic satellite was operational, and within months two additionaldomestic US satellites from two different carriers joined the first [4,6]. With the feasibilityof satellite communications firmly established, a new age of satellite communications began.In 1975, several Canadian government agencies were participating in the establishmentof the first maritime MSS by the International Maritime Satellite Organization (INMARSAT).A continued interest in MSS resulted in the DOC's formation of Telesat Mobile Incorporated(TMI) for the development and implementation of mobile satellite (MSAT) technology inCanada [5]. Comprehensive market studies and business plans were compiled by NASAin the US in 1983 and by the DOC in Canada in 1986, and pursuant to these, decisions2were made in both countries to proceed in a cooperative effort to provide commercial landmobile satellite systems (LMSS). The decisions to proceed were made despite the fact thatthere was limited spectrum available for the proposed services. It was hoped that WARC-87 would allocate sufficient L-band spectrum to easily accommodate LMSS, but despiteextensive lobbying by Canada and the US, only 14 MHz (on a primary or co-primary basis)was allocated in WARC-87 (Figure 1) [7-10], which fell short of that deemed a minimalrequirement by Canada and the US for LMSS in North America [11].Downlink1530 1533^1544^1555 1559Uplink1626.5^1631.5 1634.5^1645.5^1656.5^1660.5LMSSPrimary orCo-primary LMSSSecondaryNot LMSS orNot allocatedFigure 1 WARC-87 L-band Allocation (MHz)1.1.2 Current LMSS DevelopmentToday LMSS are under development on virtually every continent, and services arescheduled for introduction as early as 1994 [10-12]. In North America, a synergy of Canada'sTMI and the American Mobile Satellite Corporation (AMSC) has resulted in conciliatory3agreements to provide mutually compatible and complementary services to Canada and theUS by their respective carriers [10,13]. System compatibility allows each system to providebackup for the other, and provides for uninterrupted service to mobile vehicles roamingacross international boundaries [10-14].North American LMSS will provide a full range of voice and data services to mobile ve-hicles in rural and sparsely populated areas, and complement terrestrial systems predominantin more densely populated areas [15,16]. In addition, LMSS will service light aircraft, andcoastal and inland marine applications. Target markets encompass all areas of the privatesector and all levels of government. Among the services to be offered initially are mobileradio service (MRS) for private subnets with closed user groups, mobile telephone service(MTS) as an extension to the public switched telephone network (PSTN), mobile data service(MDS) for remote position sensing (RPS), supervisory control and data acquisition (SCADA),national paging, and facsimile (FAX), although services may be modified or augmented asmarket demand warrants [10,18].1.1.3 Typical LMSS Network ConfigurationA typical LMSS network (Figure 2) consists of a collection of mobile terminals com-municating with terrestria,t stations or other mobile terminals via fixed earth stations overa geosynchronous satellite [8,9]. The satellite provides connections between L-band linksto mobile terminals and Ku-band links to fixed earth stations. The L-band footprint of thesatellite will have multiple spot-beams to increase transmit and receive power and to facilitatefrequency reuse. It is expected that in North America, a modest frequency reuse factor ofbetween 1.3 and 1.7 is achievable [15,19,20].4Figure 2 Network ConfigurationA possible configuration for North American spot-beam coverage is illustrated in Figure3, where each spot-beam is the area covered by a single satellite transponder. Fixed earthstations include gateways, base stations, and data hubs which provide interfaces to the/PSTN, private voice dispatch networks, and data networks respectively. In addition, thenetwork control centre (NCC) is also a fixed earth station. Functions of the NCC includenetwork surveillance, performance monitoring, system administration, service billing, andthe management of satellite transponder resources [9,15,21,22]. The NCC also incorporatesa DAMA control system (DCS) to handle call processing and channel assignment functionsas specified by MRS and MTS voice service protocols [9,2315%,,,..^ ...I......^ .0".•••••■ ea •••Figure 3 North American Spot-beam CoverageThe NCC communicates with mobile terminals over L-/Ku-band signalling links, andwith other fixed earth stations over Ku-band signalling links for management and callcontrol purposes. Mobile telephone service is offered to each mobile telephone terminal(MTT) user on an individual basis. Mobile radio service, on the other hand, accommodatesprivate dispatch subnets, and service is extended to each individual mobile radio terminal(MRT) through its associated dispatch centre. Each dispatch centre is, in turn, attached toan appropriate base station which is under DCS control.1.2 Motivations and Objectives1.2.1 MotivationsA need for LMSS services has been firmly established, and government and industryworld wide are committed to providing first generation services in the near future. Even the6most conservative projections for the first generation of Canadian LMSS estimate over 60,000voice service subscribers. Worldwide, twelve satellites dedicated to MSS are scheduled forlaunch by the mid-1990s, and global estimates well in excess of one million terminals withinfive years of initial implementation are common [13,24]. Of the total number of terminals,voice users are expected to constitute thirty to forty percent, most of whom are likely tobe MRS subscribers.Faced with a large, rapidly expanding demand for LMSS, and limited available spectrum,efficient utilization of satellite transponder bandwidth is essential [10,22,25,26]. For circuitswitched voice services, DAMA protocols are particularly suitable, as they provide asatisfactory grade of service for a large number of users with respect to the number ofavailable channels. The major advantage of DAMA protocols is that they restrict resourceallocation to only those users which have immediate requirements.1.2.2 Objective 1: MRS DAMA StrategyThe objective is to evaluate the delay performance for a recently proposed blocked-calls-dropped, batch processing MRS DAMA protocol in [9] under the above network andspot-beam configurations (Figures 2 and 3). Various numbers of dispatchers and several batchservice disciplines are examined. In particular, the objective of analyzing the MRS DAMAstrategy is to show that the scheme for handlir dispatch radio traffic which is based on•the blocked-calls-queued service discipline, makes more efficient use of available bandwidththan other techniques proposed to date. Efficiency is measured by how well the overallperformance objectives of both system and user are met.From a users perspective, performance is based on ease of access to network channelresources. Since blocked MRS calls are queued for service, the measure of user performance7is given by the mean delay between call initiation and the time service commences [27].Network management, on the other hand, endeavors to maximize its return on investment.While in theory, the latter is roughly equated with throughput (ie. maximizing carried trafficload), revenue will decrease if users find services unsatisfactory. Thus, there is often atrade-off between the amount throughput and the desired level of user performance.If both the throughput and delay vary, it may be difficult to determine how effective aDAMA system works, particularly if one aspect improves while the other declines. Therefore,the approach taken in determining the amount of efficiency gained by the new scheme isto choose a fixed level of user performance criteria, then observe the amount of increasedthroughput obtained by the new system.1.2.3 Objective 2: Integrated Network StrategyThe objective here is to find an appropriate technique for radio and telephone trafficintegration and to evaluate its performance imprcvements in order to further satisfy LMSSperformance criteria. A new technique for integrating MRS and MTS under a single dynamicresource sharing system using a common DAMA channel pool is introduced. Analogous tothe previous discussion, the objective of the analysis of the proposed integrated strategy isto show that it is more efficient than any other applicable channel allocation scheme foundin the literature. A similar approach is taken with the integrated strategy also — desiredlevels of user performance are selected, then it is shown how additional throughput may beachieved by employing the integrated strategy over the fixed channel allocation method.1.2.4 Overall Contribution to LMSS CommunicationsThe current demand for LMSS and the overwhelming potential magnitude of LMSSservices combined with the scarcity of channel resources clearly indicates the necessity for8the development of efficient DAMA protocols of a highly practical nature. The new DAMAprotocol for MRS and the introduction of an efficient method for integrating heterogeneoussources of voice traffic constitute fundamental contributions to MSAT communications inboth efficient and practical resource management.1.3 Review of Previous WorkSince there are two major topics covered in this thesis, it is appropriate that an expositionof previous work be made in two separate divisions. Hence, subsequent subsections ofthis section deal separately with the new MRS protocol and the proposed technique forheterogeneous traffic integration. Before discussion commences, however, some backgroundon MRS and MTS call characteristics is necessary.1.3.1 Comparison of MRS and MTS TrafficThe MRS segment of LMSS will serve a collection of independent closed user groupdispatch subnets [28]. On the other hand, the MTS segment will serve a number ofindependent telephone subscribers. Dissimilar applications give rise to different servicerequirements. These differences are reflected in a variation of call characteristics betweenthe two services.Differences between MRS and MTS traffic are in call duration, call frequency, andnetwork connectivity. Telephone traffic typically has a mean call holding time of 2-3 minutes[29-31] while dispatch calls vary between 8-30 seconds, depending on application [32-34].While radio call holding times are generally shorter, they are often more frequent, and thustotal offered traffic (measured in Erlangs) per MRT may be similar to that offered by eachMTI'. Connectivity of MTS, like conventional telephony, is variable as a large populationof users generates calls independently [35]. However, MRS caters to private dispatch9applications with closed user groups where connectivity is inherently fixed. Furthermore,MRS communication is generally between individual MRTs and their respective dispatcher(s),unlike that of MTS which is between mobiles or a mobile and a PSTN subscriber [10,21].In addition to differences in traffic characteristics, MRS and MTS calls are serviceddifferently. Blocked MRS calls are queued for service at their respective dispatchers, whereasblocked MTS calls are dropped. Since no dispatch radio calls are dropped, the primarymeasure of MRS performance is given by the mean delay between the time when a callis initiated and the time service commences [27]. On the other hand, MTS performanceis determined by its blocking probability — the probability that an attempted call finds allchannels busy and is subsequently dropped [15].1.3.2 Mobile Radio Service DAMA ProtocolIn general, DAMA protocols require signalling for call management through call request,channel allocation, channel verification, and channel release upon call termination [36].Signalling represents overhead in system operation and costs in terms of revenue-producingtraffic carrying capacity. Therefore, efficient DAMA protocol design is concentrated in twoareas — minimizing signalling overhead, and maximizing the utilization of the demandassigned channel pool under constraints of customer satisfaction.Conventional methodology for handling radio dispatch systems is to treat radio callsin the same manner as telephone calls, by employing a blocked-calls-dropped servicediscipline [9,30]. However, when this technique is adapted to MRS, private dispatchnetworks endeavouring to make efficient use of their respective dispatchers find highlyutilized dispatchers forming a resource bottleneck; this translates into a high blockingprobability for a blocked-calls-dropped radio service. In this situation, calls are not only10limited by available channel resources, but also by the availability of their own subnetdispatchers (35]. Due to the higher call rate of MRTs over MTTs, repeated call requestsfrom blocked MRTs result in an excessive number of retries, and hence wasted signallingcapacity [9]. Signalling is particularly costly in satellite communications where propagationdelay is inherently long. Therefore, the handling of MRS by traditional telephony techniquesis unacceptable for LMSS applications. Nevertheless, very little research has been dedicatedspecifically to modelling and analysis of land mobile radio (LMR) traffic [35]; however, thatwhich is found in the literature is now summarized.Deferred channel assignment has been proposed as one possible modification to con-ventional call handling [23,37]. However, deferred channel assignment is not applicable toLMSS. In the case of MTS, deferred channel assignment, which does not assign a channeluntil the called party is off hook, is unacceptable since the one who initiates a call from thePSTN is charged for the PSTN segment of the call even though the LMSS network might notbe able to complete its portion of connection [9]. This type of deferred channel assignmentis also inapplicable to MRS since all calls must go through a dispatch center. Dispatchersonly make channel requests to serve MRTs that have call requests pending so they could notpossibly be busy or unavailable. Thus, anytime the DCS responds to a dispatcher channelrequest, there is certainty that the connection can be completed end to end. However, callqueuing at the dispatcher could be considered an alternate form of deferred channel assign-ment since a channel is not assigned when an MRT initiates a call but when a dispatcheris able to handle the call.Quite a number of new protocols were proposed during the upshot of terrestrial cellularcommunications, particularly in the early 1970s through to the early 1980s in the design11and implementation stages of cellular development. However, methodology arising fromthe cellular revolution is directly related to conventional terrestrial telephony and, therefore,inherits the same shortcomings when adapted to MRS, because the techniques are still basedon the assumptions of a large independent population, longer less frequent call characteristics,and variable connectivity. Among those strategies, a number propose a blocked-calls-queueddiscipline based on the Erlang-C traffic model [31,38-41].Although the Erlang-C model could be considered appropriate for telephone traffic, wherethere is a large independent population, it does not accurately represent MRS which consist ofa collection of closed user groups. While the total MRT population is large, each subnet hasa small population which must contend for proprietary dispatcher service [35]. Nevertheless,call queueing is appropriate for mobile dispatch applications since it eliminates the needfor repeated call requests, and thereby saves on signalling overhead. Accordingly, the newprotocol outlined in the next section incorporates call queuing as a fundamental componentof its design.In addition to work done in mobile telephony, some research has been done trunk radioapplications. With regard to subnet configuration, some trunk radio applications are verysimilar to proposed LMSS dispatch radio services and therefore tend to be more relevantthan telephony models. However, the underlying assumption of Erlang-C traffic is oftenthe basis for modelling of trunk radio applications as well [32,35,33]. Furthermore, trunkradio applications typically employ a drop out phase for reclaiming idle channels [42],where the drop out period is usually significantly less than round trip propagation delay forgeosynchronous satellite communications, so the corresponding methods are inappropriatefor LMSS. Finally, none of the systems attempt batch processing to save on signalling12overhead, which is particularly relevant in a satellite environment where long propagationdelays warrant special consideration. Therefore, a need for further research concentrated inthis area still exists.1.3.3 Integrated MRS and MTS Dynamic Channel AllocationThe objective of integrating two separate networks into one is that, in combination, betterperformance can be realized by both services [32]. Alternatively, it would be acceptableto improve the performance of one service, provided that the other suffered no servicedegradation. It is, however, important that a resource sharing strategy not only achievethe objective, but achieve it in a simple and practical manner. Simplicity is of paramountimportance in implementing satellite systems [27,36].There have been several attempts to model systems with heterogeneous traffic sources.Of those systems which are applicable to voice traffic, there are two distinct types. One typeassumes Erlang-B traffic is generated from both sources, although each source is assumedto have different call characteristics [43]. However, as previously discussed, the blocked-calls-dropped service discipline is inappropriate for dispatch applications. The other typeof system assumes Erlang-B traffic for telephone calls and Erlang-C traffic for dispatchradio. The Erlang-B is an acceptable model for telephone traffic, but once again, the Erlang-C model does not accurately represent the M # system being modelled. Nevertheless,problems faced when integrating an Erlang-B (telephone) and an Erlang-C (dispatch radio)system are relevant to the proposed strategy, because a common problem is encounteredwhen blocked-calls-dropped and blocked-calls-queued disciplines are combined.The problem is most simply explained by examining a simple method for combining thetwo traffic sources. Accordingly, the most obvious technique is considered which is to open13all available channels to both services on a first come first served basis. This system has theadvantage of being very simple; however, even when the two heterogenous systems performwell independently, the combined system exhibits undesirable behavior. An acceptable levelof performance is maintained by both traffic sources in such a network only when overalltraffic is low. When loads are increased, the Erlang-C source often maintains an acceptablelevel of performance but only at the expense of the Erlang-B traffic. As observed throughsimulation modelling in [44], performance degrades quickly for telephone traffic even at amodest channel utilization level of about 70 percent. Since a queue is most often presentat higher Erlang-C channel utilization levels, most free channels are consumed by queueddispatch calls, leaving few available for the blocked-calls-dropped telephone traffic. In asimilar analytical model developed in [45], telephone traffic is again shown to deterioraterapidly as most of the available channels are seized by queued traffic.One successful attempt to circumvent this prciblem was proposed by Peritsky [46][45].Peritsky tries to maintain a more evenly balanced system by introducing an artificial delay,r, to the dispatch traffic to afford a chance for incoming telephone calls to pick up a freechannel. Peritsky's premise is that forcing incoming dispatch calls to delay for a short timebefore requesting a channel gives an incoming Erlang-B call a chance to obtain a free channelbefore the channel is seized by Erlang-C traffic which most always has queued calls pending.If, after an initial delay, a channel is not available to serve a queued dispatch call, the leadcall in the queue must wait another r seconds before once again attempting to seize a freechannel. Peritsky also shows that an optimal 7 - may be estimated effectively.Some other attempts to integrate heterogeneous traffic sources have been presented[32,43,44,47]; however, none others have been found which actually show improvements14over separate channel allocation schemes. Furthermore, most are complex or make unrealisticassumptions in order to focus on some special case for which promise is shown. The reservedmargin strategy proposed in chapter 4, on the other hand, not only works well for the proposedLMSS network but can also be applied directly to the more classical problem of combining theubiquitous Erlang-B and Erlang-C traffic models, and in fact, is the best solution for solvingthis problem to date. A comparison between Peritsky's method and the newly proposednetwork integration strategy may be found in Chapter 4.1.4 OverviewA complete description and thorough analysis of the proposed MRS DAMA system aregiven in Chapters 2 and 3 respectively. Due to the highly intractable nature of the queuingmodels required for closed form analytical results, much of the protocol analysis is donethrough computer simulation modelling. This a common technique since the derivation ofsteady-state distributions is rarely possible with new communication system models [48].However, when applicable analytical models or numerical results are available, they are usedin simulation model verification. Chapter 4 looks at the proposed strategy for integratingMRS and MTS in dynamic shared channel allocation. Methodology is similar to that for theMRS system. The last chapter, Chapter 5, contains a summary and discussion of Chapter 3and Chapter 4 results, and includes suggestions for further research and development.Verification of simulation models, including analytic model comparisons, is coveredin Appendix A. Appendix B includes a brief description of general simulation modellingmethodology and discusses the generation of confidence intervals for simulation results.Finally, Appendix C includes some examples of simulation model source code.152. Description of MRS ProtocolThe new MRS protocol employs a blocked-calls-queued discipline and batched callprocessing. By employing a call queuing discipline, the proposed protocol saves signallingoverhead attributed to frequent retries of blocked calls. A further reduction in signallingoverhead achieved by the batch processing scheme is demonstrated below.2.1 Dispatch Service Disciplinesfor Batch ProcessingBatch processing is where dispatcher service for calls under the same spot-beam, andbelonging to the same subnet, are delayed until a predetermined threshold, with respect to thenumber of calls, is reached. Once the threshold is reached, a dispatcher request is made toprocess the entire batch of calls in succession by pipelining. If a dispatcher is not immediatelyavailable to process the new batch, it must wait in queue for the first available dispatcher.Figure 4 depicts a model of the batch formation and dispatcher queuing process: notice howbatches are formed independently under each spot-beam, but batches are channelled intothe same queue for dispatcher service; there is no distinction between subnet dispatchers —any dispatcher belonging to a particular subnet may serve any batch belonging to the samesubnet, regardless of the spot-beam under which the batch is formed.16 00I BATCHSPOT —+BEAM I lliiiI BATCHSPOTBEAM 2 : 111 1SERVICECOMMENCEMENT •••••DISPATCHERQUEUESPOT --b.BEAM b 11111 BATCHCALL^BATCH^DISPATCHERSARRIVALS FORMATIONQUEUESFigure 4 Batch Formation Queuing DiagramThe rationale for batch processing is that savings in signalling overhead can be achievedby eliminating some inband signalling requirements for channel assignment, confirmation,and relinquishment. A timing diagram for single call channel assignment is shown in Figure5. Single call channel assignment corresponds to a batch size of one, and is also applicableto MTS call servicing where each call is handled individually. Figure 6 presents a timingdiagram for more general batch call servicing, where the batch size may be greater thanunity. With regard to the two timing diagrams (Figures 5 and 6), T. is the control messageserializing delay, Tp is the propagation delay between two earth terminals, and b is the batchsize.Four alternative batching servicing strategies are considered here, although there aremany possible variations on these. The alternatives presented here encompass two broadclasses: closed batch (CB) and open batch (OB). In either system a channel is requestedwhen a batch is formed, and once a channel is seized, it is not relinquished until all calls17BaseStationTm+TpT.+TpTm+Tp3(T.+Tp)DCSMRTTm+Tpin the batch have been processed. In a CB system, if subsequent calls arrive during theprocessing of a batch, the new arrivals must wait to form a new batch, and the new batchmust queue for the next available dispatcher. Open batch systems are the same as CB systemsexcept subsequent call arrivals join the batch in dispatcher queue and are pipelined throughbefore the channel is relinquished.CALL IN^PROGRESSFigure 5 Single Call Processing Timing DiagramWhen several batches from a single subnet are queued for dispatcher service, the orderin which they are served may be made according to a number of different disciplines. Twobatch ordering disciplines are investigated here: first come first served (FCFS), and oldestjob first (OJF). The FCFS discipline serves batches in the order in which they completeformation, whereas the OJF discipline first serves the completed batch which contains theoldest individual call request.18CALL IN^PROGRESSDCSMRTL,bCALL REBaseStationTm+TpFigure 6 Closed Batch Call Processing Timing Diagram2.2 MRS Subnet Operation •In operation, a single subnet consists of a number of MRTs distributed over the satellitecoverage area. MRTs illuminated by different spot-beams (Figure 3) must communicatewith the dispatch centre through their respective satellite transponders. When a mobile userinitiates a call, the MRT sends a call request to the DCS at the NCC via the L-/Ku-band19signalling channel of the user's respective spot-beam, using the slotted Aloha or sloppy Alohaprotocol [49]. Instead of allocating a channel in response to the call request, the DCS simplyacknowledges receipt by returning a standby indication to the MRT, and relays the requestto the dispatch centre via the base station to which the dispatch centre is attached [8]. Callrequests are queued at the dispatch centre and displayed on dispatchers' consoles, sortedaccording to the originating spot-beam, and ordered by the time of arrival. When a sufficientnumber of call requests from the same spot-beam have accumulated in queue to form a batch,the completed batch is entered into a dispatcher request queue and ordered according to theactive service discipline (either the FCFS or OJF). When a dispatcher comes available, thedispatch centre requests the DCS to allocate a channel under the appropriate spot-beam.Channel requests could be generated automatically by the dispatch centre using a pre-selected batch size, or manually under dispatcher control, before being relayed to the DCSvia the base station over the Ku-band signalling channel. Each channel request is queued atthe DCS for the first available voice channel under the required spot-beam. Once a channelhas been assigned, the DCS broadcasts the channel allocation to all the MRTs in the batch,as well as signalling the base station, which then sequentially verifies the presence of theMRTs on the assigned channel by pipelining a series of queries. Once channel verification iscomplete, the dispatcher can then select each MRT in sequence to talk with the mobile user.Once each MRT completes its call, it is free to initiate a new call. Upon clearing a batch ofcalls, the dispatcher proceeds with call termination, and via its associated base station, thedispatch centre reports to the DCS to relinquish the channel. The channel is then available toanother user, and the dispatcher is ready to handle the next batch of calls. Once a dispatcheris again seized, it contacts the DCS to request another channel from the DAMA channel pool.20Figure 5 illustrates signalling timing for individually processed call requests, whereasFigure 6 illustrates the more general timing of the CB MRS DAMA signalling sequence.Timing for the OB system is more complex because the batch size is not fixed (it has aminimum size only), and additional calls may join the batch currently being served. Forthose call requests arriving in an OB system before channel assignment, batch treatment issimilar to a CB system with the exception of the variable batch size. A call request arrivingat an OB system after service has begun requires signalling confirmation on an individualbasis; in this case, confirmation is done immediately prior to call servicing.Since larger batch sizes result in greater savings in signalling overhead, dispatchers couldbe encouraged to use the largest batch size possible that meets the objectives of their subnet— perhaps by implementing a tariff structure. In Figure 6, it can be seen that the inbandL-band signalling overhead for a CB system is given by(b + 3)T„, + 4Tp (2.1). Note that call requests are also made in L-band but use sideband signalling channels,and that call notifications, channel requests, and channel assignments made to dispatchersare all in Ku-band. The amount of bandwidth saved by reducing signalling overhead usinga CB system is shown as a percentage of the bandwidth used for actual call servicing inTable 1, where it is assumed that T ni = 50 ms and Tp = 250 ms [9,27]. The amount saved,as a percent, is calculated from the difference between the amount of signalling overheadrequired by batches consisting of a single call and that required by batches of the given size.The savings in overhead are expressed as a percentage of the expected channel resourcesrequired to service the batch of calls. Given an expected call holding time of 20 seconds,21the percentage of overhead for a CB system is calculated as follows:(b + 3)T. + 4TP X 100%20b (2.2)where the percentage of overhead is determined on a per call basis. Note that by usingthe above values for T. and Tp and taking the limit as b -4 oo in (2.2), the percentage ofoverhead is bounded below by 0.25%. Correspondingly, the maximum achievable increasein usable bandwidth is bounded above by 5.75% — the difference between the maximumpercent overhead using single call processing and the minimum obtainable. These figuresrepresent significant resource savings. As can be seen in Table 1, the majority of possiblesaving is achieved with a relatively small batch size.Batch Size Overhead (%) Saving (%) % of TotalPossible Saving1 6.00 0.00 02 3.13 2.67 46.43 2.17 3.83 66.65 1.40 4.60 80.08 0.95 5.05 87.812 0.73 5.27 91.720 0.54 5.46 95.0Table 1 Savings in Signalling Overhead with a CB System2.3 Description of MRS Delay CharacteristicsIn analyzing a dispatch subnet, the objective is to determine delay characteristics as ameasure of required user performance. The average call setup delay, Tsetup , is defined asthe mean time between call initiation at an MRT and commencement of conversation with22a dispatcher; it consists of the following components:Tsetup = TR + TWB + TWD + TWC + Tv -I- Ts^(2.3)where• TR is the mean time for the call request to reach the dispatch centre,• TWB is the mean waiting time associated with batch formation,• TWD is the mean time waiting for a dispatcher to service the batch,• Tur is the mean time waiting to receive a channel assignment,• Tv is the mean time to verify all MRTs in the batch are set up on the assigned channel,• 7's is the mean time to complete service for leading calls in the same batch.Figures 7 and 8 show the flow of a single call through the proposed CB and OB systemsrespectively, where nonzero instances of the components of Tse/up are indicated in boldsquare boxes.As previously defined, let Tp be the satellite propagation delay between any pair offixed or mobile earth stations, and let T. be the serializing delay for a signalling message.Assuming signalling messages do not encounter collisions and are free of errors, thenTR = 2(T,, + Tp )^ (2.4)is the time required for round trip messages (a request and acknowledgment).Similarly,TWC = TCR + Tqc + TCA^ (2.5)where TCR = TCA = Tm + Tp. TCR and TCA are the times required for a channel requestand channel assignment respectively, and TQc is the additional time required for channel23Batch started? Start new batchTime for call request to reach dispatch centerThreshold reached? Walt to form a batchDispatcher free?^ Walt for free dispatcherChannel requestChannel available?Channel assignmentChannel verification<First call In batch?Service callWalt for free channelTime to process callsCall completion )Request dispatcherRequest channelCall initialization )Figure 7 Closed Batch Flowchart24Batch started? Start new batchRequest dispatcherVService callTime for call request to reach dispatch centerBatch In service? Threshold reached? Wait to form a batchWait for free dispatcherRequest channelChannel requestChannel available? Wait for free channelChannel assignmentChannel verificationFirst call in batch? Time to process callsCall initialization Call completionFigure 8 Open Batch Flowchart25assignment queueing at the DCS should no channels be readily available for assignment. Inthe case of a CB discipline with pipelined channel verification signalling,= (b + 1)T„, + 2Tp^(2.6)where b is the number of MRTs in a batch (see Figure 6).For OB systems, Tv is considerably different. Let TVA be the mean verification delay fora call joining a batch before the batch service begins, and let TvB be the mean verificationdelay for a call joining a batch already in service. For calls that come in before batch servicecommences, TVA is given by equation (2.6) with the batch threshold size, b, replaced by themean number of calls actually in the batch before service commences. For each call thatarrives after batch service has begun,TvB = 2( 1)(Tm Tp) (2.7)where x is the mean of a random variable, X, where for each new call request that arrives aftera batch has started service X represents the number,of calls that arrive after batch service startsbut still have not commenced service at the time the new call arrives. The factor of 2(Tm+Tp)represents round trip verification signalling done for each new arrival on an individual basis,as discussed in Section 2.2. New call arrivals continue to be processed until an idle periodoccurs under the spot-beam being serviced, at which time the dispatcher surrenders thechannel. For an OB system, Tv is a weighted average of TvA and TVB . However, sinceneither the expected number of calls in an open batch before service commencement northe probability density function (p.d.f.) for the random variable X are known, a closed formsolution for Tv for OB systems cannot be derived.For the ith call in CB system, the time spent waiting for leading calls in the same batchto complete is the sum of the service times of those i-1 previous calls, which, on average26is simply (i — 1) • E[call holding time]. Further averaging over the waiting times for all bcalls in a batch yieldsb — 1Ts = 2^E[call holding time] (2.8). Again, however, for OB systems the lack of knowledge about the call arrival distributionprohibits the development of a closed form solution for Ts. If the call arrival distributionwere known, then Ts could be calculated similarly to the open batch calculation with theexpected number of leading calls substituted for b in equation (2.8), where the expectationaccounts for the expected residual service time for a call in service when a new call arrives.Finally, calculation of TWB, TWD, and TQc are not straightforward since they areinterdependent. TWB could be calculated similarly to Ts with the substitution of expected callinterarrival time for expected call holding time if the appropriate probability distributionscould be determined. By using a finite population model, however, each time a call requestenters the system the MRT that generated the call is no longer free to generate new calls,which results in a slowing of overall arrival rate. Similarly, each time a call is completed,an MRT that was engaged in a call becomes free to generate calls again, so the overallcall rate increases. Therefore, a varying arrival rate due to the finite population model,means that the expected call interarrival time is dependent on queue length distributionsfor batch formation, dispatcher waiting, and channel assignment queues. Interdependenciesare further complicated by the introduction of propagation and message delays, and channelresource competition between different private dispatch networks, each of which might havea different configuration. Even under the assumption of infinite population homogeneoussubnets, multiple tiered queuing, batch processing, and long propagation delays result in aformidable queuing model not given to closed form analysis. Hence, in the next chapter the27delay characteristics of single subnet with various configurations are analyzed through theuse of computer simulation.I283. Modelling and Analysisof a Single MRS SubnetThe analysis of a single dispatch subnet focuses on determining delay characteristics asthe measure of user performance. Analysis concentrates on the expected performance underthe assumption of stationarity where it is well known that channel utilization in stochasticsystems must be strictly less than unity for stability [29,50]. In order to determine relevantdelay characteristics, a network model is constructed.3.1 Single MRS Subnet Delay ModelThis chapter considers an instance of a single private subnet in order to gain insight intothe general operation and performance of the proposed MRS DAMA protocol. Specifically,call processing delay of a single dispatch subnet, defined now as Tc = Tsetup — TQc, isconsidered. The overall delay of an MRS network which includes TQC, and is made upof many independent subnets operating under the proposed DAMA protocol competing fora fixed number of channels, is subsequently considered in Chapter 4. The analysis of callprocessing delay for a single subnet provides an understanding of the relationships betweendelay and offered dispatch traffic, batch size, and batch servicing discipline. For a morecomplete discussion of the advantages of call queuing on the sideband signalling channels,the reader is referred to [9].The initial analysis is done under the assumption that there is a sufficient number ofchannels available under each spot-beam such that channels are always available upondispatcher request. Thus, TQC = 0 as channel assignment is immediate. As a result, the29Call rate per MRT (AR)Mean call holding time (1IpR)Number of spot beams (s)Control message serializing delay (T,i )Propagation delay (Tp ).001 calls/sec.20 sec.450 ms250 msTwc component in Tc is equal to 2(T,,z + Tp ). Ignoring TQc for the moment does not detracta great deal from the usefulness of the individual subnet analysis, since system behavioris such that TQc remains relatively small when considering subnets of a practical size (seeChapter 4).3.2 Single MRS Subnet OperationThe model under consideration has a number of both fixed and variable parameters.Fixed model parameters are related to the general MRS satellite network architecture and tocall characteristics; they are summarized in Table 2. Variable parameters, shown in Table3, are related to an individual dispatch subnet where a wide variety of configurations arerequired for comparative performance analysis.Table 2 Fixed MRS Model ParametersA dispatch subnet is represented as a collection of n independent MRTs, each of which isassumed to generate calls with exponentially distributed interarrival times, at rate AR = 0.001calls/s, and have a mean call holding time of 11pR = 20s, where call holding times are alsoexponentially distributed [9,30,33,37]. Overall, the total offered traffic per MRT is 0.02Erlangs in the absence of queuing, which is typical for LMR applications [51]. Call queuingtemporarily stops queued MRTs from generating calls and thus slows the call arrival processso that a lower level of offered traffic per terminal is actually realized.30Number of dispatchers (d) 1 - 8Batch size (b) 1-12 Number of MRTs (n) 12d - 92dTable 3 Variable MRS Model ParametersThe MRT population is distribt•. uniformly under s = 4 spot-beams, and is served byd identical dispatchers. In keeping with the small number of terminals in each individualsubnet, a finite population model must be used in MRS subnet modelling; similar networkconfigurations employed in LMR applications are also modelled in this fashion [35]. Aconsequence of the finite population model is that the overall call rate varies over timeas MRTs either waiting for service, or in service, cannot generate new calls (see Section2.3). The assumptions of exponential interarrival and service times are accepted as goodapproximations derived from empirical observations of real LMR traffic [30,52].The number of spot-beams is fixed, and is consistent with the proposed satellite coveragein Canada (Figure 3). Subnet configuration is varied by changing the number of dispatchersand the number of MRTs. The latter change also has the effect of varying the offered traffic.In subsequent analysis, both the subnet configuration and the batch size are varied, and theresultant effects on delay are observed for each service discipline. It is important to note thatfor a CB system, d may be greater than s as several batches might be served simultaneouslyunder one spot-beam. On the other hand, for an OB system d must be less than or equal tos since at most one batch may be present under each spot-beam, and a dispatcher servinga particular spot-beam continues to serve all calls arriving at that beam until there is anidle period. If d were greater than s, then d — s dispatchers would never be utilized inan OB system.313.3 Delay AnalysisIn order to determine an optimal strategy, the effects of dispatch network traffic, batchsize, subnet size, number of dispatchers per subnet, and batch service discipline are examined.In some restricted cases of much simplified network models, some numerical or closed formsolutions exist for delay analysis. However, due to the complexity of the proposed system,and the uncertainty in related probability distributions, no general closed form solutionsexist. As an alternative, discrete event computer simulation is used as the primary toolof analysis. Nevertheless, simplified analytic models have been used to verify simulationmodel execution where possible (see Appendix A).3.3.1 Comparison of FCFS and OJF Batch Service OrderingEmpirical results obtained via simulation indicate virtually no significant statisticaldifference in delay characteristics between systems employing the FCFS discipline and thoseusing OJF. These results are consistent with the Nilarkovian nature of the traffic and the callservice distributions. Therefore, in subsequent analysis, OJF models are not considered, andFCFS models are selected for their efficiency in execution and ease of implementation. Thus,the only two models used for subsequent analysis are the FCFS CB and FCFS OB systems,but the results apply equally well to OJF systems. Henceforth, discussion will only referto CB and OB systems but it is understood that either FCFS or ON service ordering mayequally well be in effect.3.3.2 Closed Batch Subnet ConfigurationsEach variable system parameter may assume a range of values in order that many subnetconfigurations may be examined. Figures 9 through 12 show resultant delay characteristics inrelation to the number of MRTs per dispatcher in a CB subnet with 1, 2, 4, and 8 dispatchers.321614128co0 642016141210The respective curves in each figure show results from experiments with batch sizes of 1, 2,3, 5, 8, and 12, and thereby illustrate the effects of different batch sizes on Tc.10 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 9 CB Subnet: Single Dispatcher DelayExcept for the case where b = 1, the general shape of the curves indicates that delay islong for small MRT populations with respect to the number of dispatchers, but delay decreasesas the number of MRTs per dispatcher (offered traffic) increases. Eventually, a minimumdelay is reached, and further increases in the MRT population cause delay to rise once again.331614126-10-8-42010 20 30 40 50 60 70 80 90MRTs per Dispatcher-16-14-12-6Figure 10 CB Subnet: Two Dispatcher DelayFor small populations, most of the delay is attributed to the time it takes to form a batch, TWB•When b = 1, there is no batch formation delay. In the extreme (implausible) case, wherethere is a nonzero population of fewer MRTs (under each spot-beam) than required to forma single: batch, the resultant batch formation delay is infinite since no batch can be formed.When the MRT population is increased to a number larger than the batch size, delaybecomes finite. Further increases in population cause delay to decrease as batches are formedmore quickly. However, if the population is increased too much, delay begins to rise onceagain as dispatchers become fully utilized, and TwD becomes the dominant component ofthe overall delay. For very large populations, note that Tc increases linearly with respect341614-12-b=12 -16-14-12-10-8-6b=5-4- b=3b=2b=1,^I 10 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 11 CB Subnet: Four Dispatcher Delayto the MRT population due to the finite population model. Another consequence of thefinite population model is that the delay remains bounded regardless of how large a subnetpopulation becomes because call request simply accumulate in queue until equilibrium isreached. At equilibrium where the rate of calls generated by those MRTs not in queue norengaged in calls is balanced by the rate of call completions.Further note that the lines at the right side of each graph are slightly splayed due tooverhead processing delays being proportionally larger for smaller batch sizes. The spacingbetween the lines narrows as the batch size is progressively increased due to less dramaticsavings in signalling overhead for each successive increase in batch size (Table 1).235-16-14-12-10-8-6b=8b=5b=3b=2b=1,42016141210>, 8ca10 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 12 CB Subnet: Eight Dispatcher DelayCloser examination of Figures 9 through 12 reveals that for any given batch size, theoptimal number of MRTs per dispatcher corresponding to the minimum delay is fairly constantwith respect to the number of dispatchers (see Table 4). Hence, it appears that the ratio ofMRTs to the number of dispatchers is an important indicator of subnet delay performance.•This is because a high number of MRTs per dispatcher results in long dispatcher delays(large TwD). This finding is, in fact, consistent with other research investigating similarlyconfigured LMR dispatch networks [35,53].36BatchSizeNumber of Dispatchers1 2 4 81 12 12 12 122 34 32 32 323 44 36 36 365  56 44 44 408 66 52 48 4812 80 62 52  52Table 4 Location of Minimum Delay in MRTs per Dispatcher for CB SystemsWhile the delay minima are of a similar range with respect to MRTs per dispatcher, theabsolute delay is shorter for larger subnets, due to the much accelerated batch formationprocess, as shown in Figure 13 The largest difference in delay occurs between single anddouble dispatcher systems, then progressively smaller differences are observed with eachadditional dispatcher. For any constant ratio of MRTs per dispatcher and fixed batch size, asthe number of dispatchers is increased (yielding a proportional rise in absolute population)the rate at which the delay decreases begins to diminish. Initially, additional dispatchersresult in great improvements in overall delay, but after four dispatchers, improvements comemore slowly. It appears that little is gained by having more than eight dispatchers, and aspreviously noted, LMSS are likely to serve a collection of smaller private dispatch subnetsso large subnets are not consistent with the system being modelled.37d=1d=2d=412--16-14d=8 -12-10421614-8-610›, 8coa)6100 200 300 400 500 600 700 800Number of MRTsFigure 13 CB Subnet Delay Curve Comparison for 1, 2, 4, and 8 Dispatchers3.3.3 Open Batch Subnet ConfigurationsDelay curves for OB subnets with d = 1,2,3,4 are shown in Figures 14 through 17respectively. Subnets with more than four dispatchers are not considered since at most fourcan be utilized at any moment. If more than four dispatchers 'were assigned to a single subnetwith a fixed MRT population, the delay curves would be identical to Figure 17, regardlessof how many more dispatchers were added.The general rationale for the shape of the OB curves is essentially the same as for CBsystems; however, there are some behavioral differences. First of all, as subnet size gets large(right hand side of figures), the delay seems to grow almost identically in Figures 14, 15, and38161412- 1 0-8-642010 20 30 40 50 60 70 80 90MRTs per Dispatcher-16-14-12Figure 14 OB Subnet: Single Dispatcher Delay17, regardless of batch size. This is in contrast to CB systems whose linear tails were splayeddue to differences in the average overhead per call for different batch sizes. Since overloadedOB systems tend to hold channels open for long periods of time, the vast majority of callsthat arrive do so while a batch is already in service; therefore, the number of unservicedcalls remaining in an open batch when a new call arrives tends to be the same regardless ofthe number of calls required to form the batch initially. As a result, the overhead associatedwith most OB calls is also the same, regardless of size designated for batch formation. Ifa batch stays open for a very long time, the signalling overhead saved due to the initialbatch size becomes much less relevant in the long run. However, once again it is recognized3910 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 15 OB Subnet: Two Dispatcher Delaythat subnets with over-utilized dispatchers are not realistic, and degenerate into subnets withpermanently assigned channels, which is simply frequency division multiplexing (FDM).In Figure 16, while the delay curves still have the same general shape as the precedingfigures, a slightly different phenomenon is observed at very high utilization: the right endsof the delay curves in Figure 16 turn upward in much more erratic fashions than thosein previous figures. This rapid rise in delay is the result of spot-beam starvation. Spot-beam starvation occurs when there is a sufficient amount of traffic generated under a propersubset of the spot-beams to keep all subnet dispatchers continually busy, while call requestsgenerated under the other spot-beams go without service.401614-161412108642010 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 16 OB Subnet: Three Dispatcher DelaySpot-beam starvation is not observed in either Figure 14 or Figure 15 because therange of values on the horizontal axis does not extend to a sufficiently large population.Correspondingly, starvation occurs at a much higher MRT per dispatcher ratio in a singledispatcher subnet than it does in a two dispatcher subnet, and the ratio is higher for a twodispatcher subnet than for one with three dispatchers. The reason that starvation only occursat much higher MRT per dispatcher ratios when there is one or two dispatchers is that theabsolute number of terminals per spot-beam is the critical factor. For example, supposethe are two subnets, each with 80 MRTs per dispatcher, but one has a single dispatcherand the other has three dispatchers. The subnet with one dispatcher has only 20 MRTs41 b=8b=5b=3b=2b=11614121614121086420642010 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 17 OB Subnet: Four Dispatcher Delayunder spot-beam which do not generate enough traffic to continually tie up the dispatcher, sono starvation occurs. The subnet with three dispatchers has 60 MRTs under each spot-beamwhich generate enough traffic to tie up a dispatcher for extended periods of time, so starvationmay occur. On the other hand, starvation is not c! served in Figure 17 where there are fourdispatchers because there is exactly one dispatcher available for each spot-beam, so it is , notpossible for any to go without service. Nevertheless, spot-beam starvation does not cause aproblem for subnets of any practical size, regardless of the number of dispatchers, becausethe population level at which it occurs is where dispatchers are hopelessly over-utilized andfar above the population that minimizes the call setup delay.42040 80 120 160 200 240 280 320 360Number of MRTs161412108642d=416d=1^d=214d=312,.. 10cE>. 8asT)o6Similar to those cases of CB subnets, it is observed that on an MRT per dispatcher basisthe location of the minimum delay on OB delay curves is fairly consistent with regard batchsize, though not quite as consistent as for CB systems (see Table 5). In addition, the loci ofminima for OB systems tend to be where there is a smaller number of MRTs per dispatcher.Figure 18 combines Figures 14 through 17 on the same scale for ease of comparison, andonce again it is seen that the minimum delay for a given batch size is always found withsubnet with a greater number of dispatchers, although for OB systems d is constrained tobe less than or equal to s.Figure 18 OB Subnet Delay Curve Comparison for 1, 2, 3, and 4 Dispatchers43BatchSizeNumber of Dispatchers1 2 3 41 12 12 12 122 36 32 28 243 42 36 32 285 52 44 40 368 62 48 44 4012 74 56 48 44Table 5 Location of Minimum Delay in MRTs per Dispatcher for OB Systems3.3.4 Open and Closed Batch System ComparisonIn order to facilitate comparison between CB and OB systems, Figures 19 through 21are provided. Figures 19 through 21 each combine two previous figures: respectively theycombine Figures 9 and 14, 10 and 15, and 11 and 17.For small batch sizes, the minimum delays are roughly equal for both CB and OB systems.It appears, however, that CB systems offer larger subnet sizes at optimal delay, although OBsystems always yield lower minimum delay for larger batch sizes. For a single dispatchersubnet (Figure 19), OB systems always perform better than CB systems in terms of delaycharacteristics, with increasing advantage for larger batch size with respect to the absolutedifference in delay. This is primarily due to the ability of OB systems to occasionally servicenew incoming calls without waiting for a new batch to form, so a dispatcher has opportunityto flush all calls through under the spot-beam it is currently serving before relinquishing thechannel. Closed batch call arrivals, on the other hand, must always wait for batch formation,and this delay is most often long when the total MRT population is small or batch size islarge. A two dispatcher subnet (Figure 20) behaves very similarly to a single dispatcher44b=12\\\b=8\1111b=5b=3"\b=1, ^20-8-6-4-14-12-1 0- b=2OBCB1412subnet, except minimum delays achieved by the larger population two dispatcher subnetsare significantly less.16^ -1610 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 19 CB and OB Single Dispatcher DelayIn the case of four dispatcher subnets (Figure 21), the delay curves are somewhatdifferent. For small populations, the OB systems still perform better, but as the populationincreases, CB systems outperform their OB counterparts when small batch sizes are employed.For larger batch sizes, OB systems begin to show better performance once again.The reason for good OB performance at low traffic levels is the same as that given forone and two dispatcher subnets. As the population is increased, however, small batch CBsystems have the advantage of being able to use more than one dispatcher to service a single4516- -16 14 -1412 -1210>. 8caa)- 10-8-642010 20 30 40 50 60 70 80 90MRTs per DispatcherFigure 20 CB and OB Two Dispatcher Delayspot-beam if high traffic fluctuations so warrant. The ability to apply any combination ofdispatchers to any spot-beam is equivalent to statistical multiplexing for closed batches, since"batch arrivals" may be served by the first available dispatcher. The advantage of statisticalmultiplexing is well documented [29], and plays an important role here in reducing theoverall delay for CB systems.An important observation of Figure 21 is that the minimum delay for the CB systems isoften the same or less than for OB systems when small batch sizes are used. Moreover, theloci of the CB minima tend to occur at larger population levels than their OB counterparts.As batch size increases, OB minima become smaller than those of CB systems. Therefore,46-16b=12b=811 11b=5b=3b=2b=1, --10 20 30 40 50 60 70 80 90MRTs per Dispatcher-14-12-1086420OBCB16141210C5 8C)6Figure 21 CB and OB Four Dispatcher Delayit appears that either a CB or an OB system may be selected for optimal performance in afour dispatcher subnet, depending on its configuration and batch size.With larger batch sizes, batch formation delay increases dramatically. For CB systems,TWB becomes more significant than the saving in TWD due to statistical multiplexing. Thus, asbatch size increases, OB systems tend to have shorter overall delay than CB systems. Openbatch systems gain advantage by being able to process all calls queued under a particularspot-beam before relinquishing a channel. Therefore, the delay of those calls which arriveduring batch service is shortened greatly, since they do not have to wait for a new batch toform. With larger batch sizes this effect becomes more important; not only is batch formation47delay longer for larger batches, but a greater number of additional calls are likely to arriveduring batch servicing of a larger batch. As more calls arrive during batch servicing, morecalls per batch avoid the long delay associated with large batch formation.For very high population levels, where dispatchers are fully utilized, TwD is the dominantdelay component. The amount of overhead associated with an OB system at full dispatcherutilization is slightly smaller than the overhead associated with a CB system with a batchsize of two, as is reflected in the relative positions of the OB and CB linear tails at the righthand side of Figure 21. The overhead associated with each call in an OB system with fullyutilized dispatchers who never realize breaks in servicing once batches are open is2(T,, + Tp) (3.1)For CB systems, the overhead per call is given by dividing Equation (2.1) by the batchsize, b:(b + 3)Tni + 4Tpb(3.2)By equating the two formulae given in Equations (3.1) and (3.2), substituting the valuesgiven in Table 2 for T„, and Tp , and solving for b, the following result is obtained:b 2.1.This result corresponds to the observation that the linear tails of the OB systems in Figure21 converge just below the tail of the CB system using a batch size of two. For larger batch•sizes, the smaller overhead associated with CB systems result in lower delays relative to OBsystems at full dispatcher utilization.3.4 SummaryBy dealing with the simplified case of a single subnet which does not face channelcompetition from other subnets, several insights into the behavior of the new MRS protocols48have been obtained. Insights have been gained by experimenting with a wide range ofcombinations of MRT population size, the number of dispatchers, batch formation strategy,batch service ordering discipline, and batch size.It is observed that the number of MRTs per dispatcher (dispatcher load) is often morerelevant in considering delay performance than the absolute MRT population itself, becausecompetition for dispatcher service within a subnet can result in large delay. However,very low or very high MRT to dispatcher ratios constitute extreme, implausible networkconfigurations and are therefore not considered realistic candidates for network configuration.When there are only a few MRTs for each dispatcher, dispatchers are under-utilized and batchformation delay is often large. Very high MRT per dispatcher ratios, on the other hand, resultin over-utilized dispatchers where long queues for dispatcher service result and delay is alsolong. It is important to note, however, that small absolute populations (Figures 19 and 20)tend to show large delay characteristics even for a reasonable MRT per dispatcher ratiobecause calls are still generated too slowly; thus, dispatcher utilization is often very loweven when delay is high.Whether batches are ordered for service by the FCFS or the OJF discipline has little effecton subnet delay characteristics. However, considerable differences are observed between CBand OB systems. When subnets are small (one or two dispatchers), OB systems alwaysexhibit superior delay characteristics over their CB counterparts, regardless of batch size ornumber of MRTs per dispatcher. As the number of dispatchers increases, the minimum delayfor CB systems is often smaller than that of similar OB systems, depending on batch sizeand offered traffic.Open batch systems always perform much better than CB systems when traffic is low.49When the batch size is large, OB systems again have an advantage by being able to clear allcalls under a given spot-beam, which tends to reduce batch formation delay. However, forlarge subnets with high traffic, CB systems often perform better due to the advantage of beingable to statistically multiplex batch arrivals. In addition, the nature of CB systems allowsmore dispatchers than spot-beams to be employed, although very large networks are unlikely.Increasing batch size also results in greater savings in signalling overhead per call,although the most dramatic increases in savings occur at relatively small batch sizes (seeTable 1. Moreover, the utilization of small batch sizes generally contributes to more favorabledelay characteristics, particularly at low traffic levels. A unit batch size performs best at lowtraffic levels. Although single sized batches do not offer any signalling overhead saving,at very low traffic levels resource conservation does not present a problem. Alternatively,batch formation time-outs might be used for larger batch sizes when traffic is low and channelresource competition is minimal. A batch formation time-out would allow partially formedbatches to request a dispatcher some specified time after the first call request in the batchhas been received.In consideration of all of the above factors, the results enable the estimation of theoptimal batch size and service discipline to achieve a desired performance objective for agiven network size and number of dispatchers. Overall, an understanding of the effects ofthe new MRS protocol applied to a single network has been achieved. In addition, the delayanalysis of a single subnet affords a good point of departure in further investigating thebehavior of the protocol when applied to multiple subnets in a network where competitionexist for a finite number of channels.504. Integrated MRS and MTS NetworkHaving analyzed the delay characteristics of a single subnet, the analysis of delaycharacteristics associated with an MRS network consisting of a collection of similar subnetsin channel resource competition remains to be done. Still further, an investigation of theeffects of integrating MRS and MTS traffic into a single network must also be performed. Thebehavior of an MRS network in isolation is obtained in the course of analyzing an integratednetwork, where the behavior of separate MRS and MTS networks with fixed channel poolallocations form the basis of comparison for the proposed integrated strategy.If given a finite number of channels to distribute between two traffic sources, the simplestallocation method would be to partition the channels into two fixed size channel pools —one for each service. However, if the two sources generate the same type of traffic then,as is well documented, overall performance for both networks improves by combining theminto a single network with equal access to all channels [50]. Improved performance is due toa statistical smoothing which occurs as high and low fluctuations in one traffic source tendsto cancel fluctuations in the other. However, as previously discussed, when networks withheterogeneous traffic sources are combined, one might improve at the expense of the otherunless some measure of control is introduced into the system.In particular, it has been shown that Erlang-B traffic may be sacrificed to improvedErlang-C performance [44]. While LMSS MRS traffic is not modelled as Erlang-C, the MRSsystem does employ call queuing, and simulation results indicate that, once again, blocked-calls-cleared telephone traffic performance deteriorates rapidly in favour of queued dispatch51radio service, as queued calls seize channels as soon as they come available. The new strategyproposed here, however, balances the two services and allows more total throughput without adegradation of the performance of either system. In addition, the new reserved margin systemcan be applied to other blocked-calls-dropped and blocked-calls-queued services equally wellas the proposed LMSS voice network.4.1 Dynamic Channel Allocation4.1.1 The Reserved Margin StrategyIn examining the problem of integrating MRS and MTS traffic, the behavior of thetelephone traffic is first examined, where an Erlang-B traffic model is assumed. The blockingprobability of the Erlang-B model, pB, is related to the offered traffic, p, and the number ofavailable channels, n, by the following formula:p/n!PB = nE plk!k=0(4.1). Suppose there are 30 channels dedicated to telephone traffic and a blocking probabilityof 0.01 is desired. Given these parameters, the offered traffic utilizes p = 20.3 channelson average. Conversely, an average of 9.7 channels — almost one third of the availableresources — are left unused. Since calls are only dropped when all 30 channels are inservice, there are periods where the number of free channels is considerable larger thanthe mean. It is apparent that a large margin of free channels is maintained only in orderto ensure that all channels are not busy more than 1% of the time. In theory, an averageof an additional 9.7 channels of capacity could be made available to dispatch radio withoutdegrading telephone service, provided preemptive priority could be given to telephone service52for up to the full 30 channels. However, preemptive priority is entirely infeasible, so a moremoderate system for sharing is in order.The basic premise of the new channel allocation scheme is to reduce the mean numberof free channels required when combined with radio service, and thereby provide additionalchannel capacity for call servicing. In keeping with the overall objective, however, theutilization of the available free channels must be such that overall service improves. In anintegrated network, the idea is to tentatively maintain a small margin of free channels at alltimes for telephone traffic, where the mean number of free channels is considerably less thanthat given by the Erlang-B model. If there are more free channels available than stipulated,dispatch traffic may use them to service calls in queue. Blocking of telephone traffic onlyoccurs when telephone calls or batch services do not complete quickly enough to maintainthe desired margin, but new telephone traffic is generated quickly enough to consume thosechannels in reserve.Combining both MRS and MTS by sharing a common channel pool, rather than allocatingseparate channel pools, allows channels unused by one service due to a traffic lull to be usedby the other service if the latter is simultaneously experiencing a high statistical fluctuationin its traffic level. The ability of the system to statistically multiplex may be more clearlyillustrated by example. Suppose there are two separate 30 Erlang-B networks, each requiringa blocking probability of 0.01. Given these constraints, a maximum of 20.3 Erlangs of trafficcan be handle by each network, for a total of 40.6 Erlangs of traffic. On the other hand, asingle network with 40.6 Erlangs of traffic requires only 53 channels to maintain the sameblocking probability of 0.01. Therefore, the combined network provides the same level ofservice with 7 fewer channels, which may be allocated elsewhere. Though more difficult53to analyze, an analogous situation occurs when an Erlang-B and Erlang-C networks arecombined. Therefore, a smaller free channel margin is required by the combined networkthan two networks in isolation.With regard for telephone service, it should be noted that the margin of free channelsis independent of current traffic load (the number of channels currently dedicated to MTScall servicing) because of the memoryless property of exponentially distributed interarrivaltimes under the Erlang-B traffic model. In other words, the expected rate of telephonetraffic is constant regardless of how much is currently in service. Hence, it is reasonable toexpect that the free channel margin should be held fairly constant, regardless of current load.Differences may occur, however, when the balance between dispatch and telephone trafficchanges the channel relinquish process (discussed below). Thus, the problem is reduced tofinding the optimal value for the tentative free channel margin when given particular levelsof telephone and radio traffic and their respective performance criteria in terms of blockingprobability and delay.Since an analytical closed form solution for the system is not known, the optimalfree channel margin must be determined experimentally through discrete event computersimulation.4.1.2 Comparison of Integrated Service StrategiesAn application of the reserve margin is now shown in comparison with two other methodsfor integrating Erlang-B and Erlang-C traffic: separate channel pool divisions and Peritsky'smethod [46]. Some of the numerical values given in Peritsky's paper are contradictory, sothey cannot be verified. Nevertheless, by reproducing his method as it is described, ratherthan accepting the results as presented, it may be verified that the system does in fact work.54However, the system proposed above performs better than Peritsky's method, even whenapplied to his own traffic model. In addition, the new system is much simpler to implement.Peritsky analyses a model with 40 channels available to share between both services.The traffic model he uses for his analysis assumes a mean telephone call holding time of3 minutes, 1/30 Erlangs of traffic generated per MTT, and a resultant telephone blockingprobability of 5 percent. For dispatch traffic, a mean call holding time of 15 seconds isassumed, where the mean delay is less than one holding time, and traffic generated by eachMRT is 1/120 Erlangs. Given these traffic characteristics, a pure Erlang—B network with32 channels accommodates 802 MTTs, and a pure Erlang-C network with 8 channels alsoaccommodates 802 MRTs. The numbers of terminals that can be accommodated by separatechannel pool divisions are compared to the numbers of terminals that can be accommodatedby shared channel strategies at the same performance levels in Table 6, the effectiveness ofthe new method is clearly shown.Channel AllocationMethodNumber ofMTTs(Erlang-Btraffic)Number ofMRTs(Erlang-Ctraffic)Separate Channel Pools 802 802Peritsky's Method 819 819Proposed Method 832 832Table 6 Comparative Results of Various Channel Allocation Strategies4.2 Integrated Network OperationWhen a dispatcher requests a channel to service a batch, the DCS allocates a channel onlyif the number of free channels is greater than the predetermined telephone reservation margin,otherwise the channel request is placed in queue until a sufficient number of channels become55Drop telephoneservice requestDispatcherchannel request }Allocate channel toserve dispatch batchn > RMQueue dispatcherrequestAllocate channel toserve telephone callRelease channel to DAMA channel pooln > RM(Telephonechannel requestn > 0available such that the margin can be maintained, at which time queued channel requestsare served in order of arrival. A requests for telephone service, on the other hand, is servedimmediately if any channel is available.Channels are reallocated at the time of channel release. As each MRS batch or MTScall completes service a channel is relinquished and returned to the DAMA channel pool forsubsequent reallocation. If the number of free channels is less than the specified margin, areleased channel is used to reinstate the margin, otherwise it is used to serve any queuedradio calls (see Figure 22).Channel(s) available^Channel(s) availableto radio or telephone to telephone onlyFigure 22 Reserved Margin Channel Allocation564.3 Integrated Network ModelThe model used for analyzing the reserved margin channel allocation scheme in an MTSand MRS integrated LMSS network consists of an Erlang-B traffic source for telephone anda collection of subnets operating under the new MRS protocol detailed above. The definitionof the MTS traffic model is straightforward; however, the determination of an appropriatemodel for a collection of MRS subnets operating in a combined network with a finite numberof channels is much more complex. In order to achieve the optimal performance for an MRSnetwork, it is necessary to determine the best subnet configuration for a desired level ofperformance. Given a fixed number of channels and a mean delay requirement, the optimalnetwork configuration is the one which allows the most throughput with respect to the numberof calls that can be handled at the given level of performance.4.3.1 MTS Traffic ModelThe Erlang-B traffic model is generally accepted as a realistic representation of indepen-dent telephone traffic when the number of terminals is large in comparison with the numberof available channels [35]. However, MTS traffic is not modelled identically as Erlang-B;slight differences are inherent because MTS traffic is subject to signalling and propagationdelays which add to the exponentially distributed holding time. With respect to overhead,each telephone call is handled as if it were a single sized closed batch radio call as shownin Figures 5 and MRS Network Model for Multiple Dispatch SubnetsIn the face of a combinatorial explosion, and limited computational resources, anexhaustive search for the optimal network configuration cannot be performed. Hence, thefirst step in limiting the number of possible combinations is to assume homogeneous subnet57configurations. This is a reasonable assumption since subnets that are either too small or toolarge exhibit unfavourable delay characteristics, and are considered implausible. In practice,more moderately sized subnets are more suitable for the MRS services being offered, and arelikely to be more easily manageable from an administration standpoint. Very small subnetscould be serviced simply by MTS, whereas large subnets will demand dedicated channelsunder each spot-beam.Given the assumption of homogeneous subnet configurations, systematic attempts toachieve a globally optimal network configuration further result in the derivation of implausiblesubnets where there is an inordinately large number of dispatchers. This is a consequence ofa predominant trend to completely eliminate dispatcher wait by allowing enough dispatchersfor the maximum possible number of batches. In other words, if no constraints are placed onconfiguration parameters, the number of dispatchers increases until no dispatcher contentionexists. Hence, intelligent choices must be made in selecting a subnet configuration. Sinceactual subnets desire well utilized dispatchers, the number of dispatchers must be fixed to areasonable number relative to the offered traffic. Upon fixing the number of dispatchers, thenumber of MRTs per dispatcher is estimated effectively by examining results in the previouschapter.The :question still remains as to how the number of dispatchers is determined. A subnetmust not be too small, nor excessively large, and for realistic analysis, it must facilitatecomparison between CB and OB systems. Therefore, a subnet configuration with fourdispatchers is selected. This moderate sized subnet configuration allows CB systems to takeadvantage of statistical multiplexing, and OB systems to serve batches simultaneously underall spot-beams if necessary. In addition, delay performance has been shown to improve most58rapidly when the first increases in the number of dispatchers are made, so four dispatchersprovides good overall performance. Furthermore, OB systems cannot take advantage of morethan four dispatchers when there are four spot-beams, but with exactly four there is no riskof starvation. Overall, the four dispatcher subnet model strikes the best balance betweenfeasibility, comparability, and performance.Given subnets with four dispatchers, the best operating range in consideration of bothdelay and dispatcher utilization perspectives is in the range of 35 to 55 MRTs per dispatcher(see Figure 21). For the network model, 44 MRTs per dispatcher is selected since it isclosest to the middle of the range where the MRTs can be distributed uniformly over thefour spot-beams, and this configuration performs well over a wide range of batch size.The determination of the best batch size for a given performance level is investigated byexperimentation.4.3.3 Integrated Network Model ParametersA list of fixed model parameters for both MRS and MTS in a combined system is shownin Table 7, and a list of variable parameters is shown in Table 8. The batch servicingdiscipline may also be either closed or open.The mean MTS call holding time is typical for telephone service [31], but this valuehas been selected specifically such that the offered traffic per MIT is 0.02 Erlangs =- thesame as the per MRT offered traffic for MRTs in the absence of queuing. Having the sameoffered traffic per terminal is not essential, but it makes some comparisons between the twoservices more simple. In the literature, comparisons of traffic handling capacities betweenheterogeneous traffic sources are often made by comparing the number of terminals that areaccommodated; however, these same comparisons are often made between terminals which59offer considerably different levels of traffic and, therefore, might be misleading [54,53].When each type of terminal offers approximately the same amount of traffic, comparisonscan be made easily because the number of terminals for a given service is a reasonablerepresentation of the level of offered traffic. Nevertheless, there is no one standardizedmethod for comparing heterogenous traffic, and there is considerable disagreement in theliterature as to which method is best [35,53]. However, the direct comparison betweenMRS and MTS traffic handling capacities is of secondary consideration; the performanceenhancement of combined network services is of paramount importance.MTS mean call holding time, 11 FT^ 120 sControl message serializing delay, Tn, 50 msPropagation delay, T,,^ 250 msMRT call rate, AR .001 calls/sMRS mean holding time, II/IR^ 20 sNumber of spot beams, s 4Number of dispatchers per subnet, d^ 4Number of MRTs per dispatcher 44Total number of channels^ 35Table 7 Fixed Network Model Parameters•Number of subnets in the network 1 - 50MTS call rate, AT .02 - .20Batch size, b 1 - 20Size of reserve channel margin 1-10 Table 8 Variable Network Model Parameters60The propagation delay, message serializing delay, MRT mean call rate, MRT mean callholding time, and the number of spot-beams are identical to those used in Chapter 3, andthe rationale for selecting these parameters is discussed there. The rationale for choosing theselected subnet configuration, including the number of dispatchers, the number of MRTs perdispatcher, and the use of homogeneous subnets has been discussed previously.In actual implementation, LMSS transponders are expected to provide several hundredchannels for voice services [15]. Nevertheless, the total number of channels used in thesimulation model analysis here is 35. While less than the expected number of channels inactual implementation, 35 channels is the upper functional limit given the constraints of theavailable computer resources (see Appendix B). This is a sufficient number to illustrate thedynamic channel allocation scheme.4.4 Simulation ModellingBefore it is possible to determine the degree of improved performance offered by theproposed MRS and MTS integrated network strategy, a basis for comparison must beestablished. The basis is established by first observing the performance of separate MRSand MTS networks with a separate channel pool for each service. The merit of the proposedsystem may then be determined by observing the level of improvement over the separatechannel pool method.4.4.1 MRS and MTS Performance ObjectivesA level of performance, in terms of both blocking probability for MTS and delay forMRS, must be established for comparison purposes. Two different combinations of networkperformance are examined here:611. MRS delay = 2 minutes, MTS blocking Probability = 0.012. MRS delay = 5 minutes, MTS blocking Probability = 0.05For convenience, these two models are subsequently referred to as the high performancemodel (shortest delay and smallest blocking probability) and the low performance modelrespectively.A blocking probability of 0.01 is often used in the analysis of telephone traffic, and 0.05is not uncommon. In fact, in many mobile networks, the blocking probability far exceeds0.05 during the busy period [55]. The delay of two to five minutes is assumed acceptablefor MRS. It is common within heavily utilized urban dispatch environments to be faced withdispatcher delays of this order. Furthermore, since LMSS is rurally oriented, delay of afew minutes is a great improvement in many circumstances, especially considering that noservice of any kind may have been previously provide.4.4.2 MethodologyIn examining the fixed allocation scheme, several channel divisions are used. Startingwith zero channels for MRS and 35 for MTS, the number of MRS channels is incrementedby 5 while the number of MTS channels is correspondingly decremented by 5, until thereare no channels available to MRS and 35 available to MTS — eight static divisions in all.For each division, as much MRS and MTS traffic as possible is applied to each of the tworespective channel pools until the desired levels of performance can no longer be maintained.The experiment is repeated for each of the four possible combinations of performance levelsand batch servicing disciplines. Experimentation with various batch sizes is also undertakento ensure the most effective batch size is chosen in minimizing delay for each case.62In order to determine the additional number of terminals that can be serviced usingdynamic allocation, the above process is repeated with some modification. For eachexperiment, the channel pools are merged into a single pool of 35 channels and trafficlevels are set according to the results obtained under the separate channel allocation scheme.Then, only the MRS traffic is increased while the batch size and free channel margin arevaried until the highest level of throughput is achieved. Experimentation ceases when thespecified performance level can no longer be maintained in the face of increasing traffic. Theexperiment is then repeated, except the MRS traffic is held constant and the MTS traffic isincreased until performance degrades below the specified level.The level of MRS traffic is varied by increasing or decreasing the number of subnetspresent in the network, whereas the MTS traffic level is varied by increasing the rate atwhich calls come in, AT (see Appendix B). Experimentation over a wide range of batchsizes and free channel margins provides the best performance that may be realized for eachcombination of offered MRS and MTS traffic. In practice, a trade-off between an increasein one type of offered traffic against the other could be made, but for illustration purposeschanges in each type of traffic are examined independently.4.5 Results0Figures 23 through 26 show the results obtained for each respective performance leveland service discipline combination. Static and dynamic allocation results are included in thefigures for comparison. The downward sloping lines in the figures represent the number ofMTTs while the upward sloping lines represent the number of MRTs. The horizontal axesrepresent the size of the MRS channel pool, cR, under the fixed allocation scheme, whereit follows that the size of the MTS channel pool, cT, under the fixed allocation is 35 — eR63Dynamic AllocationFixed Allocation..,///\ // .-,..._9000800070006000500040003000200010000(for an overall total of 35 channels). As more channels are dedicated to MRS, more MRTsare accommodated; at the same time, more MRS channels means fewer for MTS, and aresultant decrease in the number of MTTs. Hence, as the number of terminals under oneservice increases, the number under the other declines.9000800070000rac 6000._Ets 5000I-i.. 4000a).c)E 3000=z200010000..., ..., .., ..,5^10^15^20^25^30Number of Dispatch Channels (cR )Figure 23 High Performance CB Channel CapacitiesThe solid lines in each pair of sloped lines represents the number of terminals that canbe accommodated under the fixed allocation scheme, whereas the dashed lines represent thenumber of terminals that can be handled using the dynamic strategy. As outlined in themethodology of the previous section, a change shown in the number of terminals of onetype is dependent upon the traffic being held constant for the alternative service. Numerical64Dynamic AllocationFixed Allocation900080007000CaTa 6000.'6 5000146 4000E▪ 3000z2000100005^10^15^20^25^30Number of Dispatch Channels (cR)Figure 24 High Performance OB Channel Capacitiesquantities corresponding to the graphs in Figures 23 through 26 are found in Tables 9 through12 respectively. The definition of symbols used to head columns in Tables 9 throughl4 areas follows:n — number of MRTs• An — increase in n• m — number of MTTs• Am — increase in m• A% — percent increase659000800070006000500040003000200010000Radio TelephoneStatic Dynamic  Static DynamiccR n An A%  cT m Am A%0 0 0 0 35 4879 0 05 927 487 53 30 4028 312 810 1980 663 33  25 3192 401 1315 3174 908 29 20 2382 492 2120 4245 777 18 15 1606 503 3125 5459 738 14 10 883 422 4830 6524 492 8 5 270 315 11635 7590 0 0 0 0 0 0Table 9 High Performance CB Dynamic Allocation ImprovementsRadio TelephoneStatic Dynamic Static DynamiccR n An A% CT m Am A%0 0 0 0  35 4879 0 05 1072 162 15 30 4028 110 310 2143 138 7 25 3192 132 415 3209 516 16 20 2382 299 1320 4406 369 8 lf, • 1606 240 1525 5475 423 8 10 883 254 2930 6538 465 7 5 270 211 7835 7646 0 0 0 0 0 0Table 10 High Performance OB Dynamic Allocation Improvements66Figures 23 and 24, and Tables 9 and 10 show that significant increases in traffic handlingcapacity can be achieved by employing dynamic channel sharing between the two services.Results are excellent for both CB and OB service disciplines with the high performancemodel. When the low performance model is examined, it appears that the CB disciplinecontinues to work well (Figure 25, Table 11), although improvements are not quite aspronounced. On the other hand, the OB systems show little or no improvement; in fact,they often show degradation in performance (Figure 26, Table 12). This phenomenon isfurther discussed below.For CB and OB comparison, Figures 23 and 24 have been combined in Figure 27(high performance models), and Figures 25 and 26 have been combined in Figure 28 (lowperformance models). Notice that in each of the new figures, the line showing the numberof MTTs under static allocation is the same for CB and OB systems, so those lines aresuperimposed. In Figure 27 it can be seen that, while both CB and OB systems offer higherthroughput with dynamic allocation, there are some performance differences. In particular,an OB system offers greater capacity than a CB system under fixed allocation. However,under dynamic allocation, CB systems significantly surpass their OB counterparts in traffichandling capacity. Differences in traffic handling capacity are even more noticeable with thelow performance model shown in Figure 28; here it can be seen that a CB system outperformsan OB system regardless of which channel allocation method is employed.6705^10^15^20^25^30Number of Dispatch Channels (cR ), 900080007000600050004000300020001000900080007000en03 600015 50005 4000E 3000zz20001000Dynamic AllocationFixed AllocationFigure 25 Low Performance CB Channel CapacitiesRadio TelephoneStatic Dynamic Static DynamiccR n An A% cT m Am A%0 0 0 0 35 5882 0 05 1251 159 13 30 4908. 82 210 2494 170 7 25 3960 143 315 3877 531 14 20 3019 314 1020 5122 571 11 15 2105 248 1225 6516 524 8 10 1231 250 2030 7755 409 5 5 439 176 4035 9154 0 0 0 0 0 0Table 11 Low Performance CB Dynamic Allocation Improvements68Dynamic AllocationFixed Allocation7000cco 6000•Ea; 5000i—"6 4000la").oE 3000z5^10^15^20^25^30Number of Dispatch Channels (cR )Figure 26 Low Performance OB Channel CapacitiesRadio TelephoneStatic Dynamic Static DynamicCR n An A% CT in Am A%0 0 0 0 35 5882 0 05 1258 -4 0  30 4908 30 110 2491 -180 -7 25 3960 40 115 3726 3 0  20 3019 11 020 4936 158 3 15 2105 87 425 6349 23 0 10 1231 332 2730 7584 -11 0 5 439 83 1935 8981 0 0 0 0 0Table 12 Low Performance OB Dynamic Allocation Improvements69When considering CB systems, greater improvements in traffic handling capacity areseen in the high performance model than in the low performance model. The reason for thisis largely due to factors inherent in the achievement of the desired MTS blocking probability.There must be a much higher mean percentage of under-utilized channels in an Erlang-Bmodel when the blocking probability is small. For example, if there are 30 channels availablefor service requiring a blocking probability of 0.01, then an average of 9.7 channels wouldbe free; alternatively, a service offering a blocking probability of 0.05 results in a mean ofonly 5.2 free channels. Hence, as one might expect from this example, a small Erlang-Bblocking probability affords a higher number of potential free channels for sharing than alarge blocking probability. Tables 13 and 14 show the number of mean free channels for thehigh performance and low performance models, respectively.In the tables, following the columns indicating the number of channels given under thestatic allocation scheme, is a column showing the mean number of free channels using afixed MTS channel pool of the given size when meeting the given blocking probability. Thenext columns show first the specified free channel margin for which an attempt is made tomaintain, and second the mean free margin that is actually obtained. Tables 13 and 14 usethe following symbols (not previously defined) in column headings:• (1 p)cT — mean number free channels for a fixed channel allocation telephone networkwith the given number of channelsR — mean number of free telephone channels realized after MRS traffic had beenincreased as much as possible, while MTS traffic was held constant• T — mean number of free telephone channels realized after MTS traffic had beenincreased as much as possible, while MRS traffic was held constant709000 -8000 -7000 -6000 -5000 -4000 -E 3000 -=z2000-5^10^15^20^25^30Number of Dispatch ChannelsOBCB9000800070006000500040003000200010000Figure 27 High Performance CB and OB Channel CapacitiesHigh Performance ModelStatic Allocation Strategy Dynamic Allocation StrategyClosed Batch^I^Open BatchCT (1 — p)cT R T RM RM T R30 9.7 6.9 8.1 4 9 8.6 8.325 8.9 4.8 6.1 3 8 7.9 7.520 8.0 3.1 4.3  3 6 5.9 5.115 6.9 2.8 3.4 3 5 5.0 4.310 5.5 1.9 2.4 2 4 3.5 3.55 3.6 1.6 1.7 1 2 2.4  2.4Table 13 Mean Number of Free Channels for High Performance Model71900080007000cn6 6000"E5000F-115 4000asE 3000z20001000090008000700060005000400030002000100005^10^15^20^25^30Number of Dispatch ChannelsFigure 28 Low Performance CB and OB Channel CapacitiesLow Performance ModelStatic Allocation Strategy Dynamic Allocation StrategyClosed Batch I^Open BatchcT (1 — p)cT R T RM RM T R30 5.2 4.7 4.9 5 11 5.8 5.925 5.0 3.7 3.9 4 10 5.6 5.720 4.8 2.8 3.0 3 8 4.8 4.815 4.4 2.5 2.4 3 6 4.6 4.310 3.8 1.8 1.7 2 4 3.5 3.45  2.8 1.5  1.9 1 3 2.4 2.2Table 14 Mean Number of Free Channels for Low Performance Model72Note that the number of free channels which the system attempts to maintain (RM) is notgenerally equal to the actual mean number of free channels that is realized (R or 7). Supposethat M is the number of free channels desired and that at some time there are exactly RM freechannels on reserve. Further suppose that all other channels are being used. If a telephonecall arrives before any of the calls in service is complete, then one channel is used to servethe incoming call and only RM — 1 free channels remain. More incoming telephone callsmay reduce the margin even further. Blocking occurs when additional telephone calls arrivebut there are no more free channels in reserve. On the other hand, if traffic is low and there isno queue to service dispatch batches, the actual number of free channels may be greater thanRM. Hence, it is apparent that the observed mean number of free channels is generally notequal to the specified minimum number of free channels which the system strives to maintain.Open batch systems, however, do not behave as predictably as CB systems. The reasonfor the apparent inconstant behavior of OB systems is due to their variable batch sizecapability. Since batch sizes are not fixed, calls joining a batch which has not completedservice add to the time a dispatcher hold a channel. When channels are often held forrelatively long periods of time, dispatchers queued for channel allocation find larger batchesaccumulating in queue due to extended channel waiting delays. Batches which are larger atservice commencement ultimately result in still longer channel holding time and, hence, theproblem compounds until equilibrium again is reached.Table 15 shows the optimal batch sizes used for each service discipline and performancemodel in the experiments. In the case of OB systems, there are two numbers for each case.The first number is the minimum batch formation threshold, and the second number (inparenthesis) is the mean number of calls processed in a batch before the dispatcher actually73relinquishes an assigned channel. Note that for the high performance model, the actualnumber of calls processed in an OB averages between 10 and 16, and the number of callsper OB in the low performance model is approximately four times as high.cR High Performance Low PerformanceClosed Open Closed Open5 4 1 (16) 7 2 (65)10 4 1 (15) 7 3 (62)15 4 1 (12) 8 4 (60)20 4 1 (11) 8 4 (50)25 4 1 (12) 8 5 (47)30 4 1 (10)  8 5 (40)35 4 1 (10) 8 5 (38)Table 15 Optimal Batch SizesWhen performance levels are kept high, open batches remain relatively small, but asperformance is allowed to drop, large batches result and detrimental effects become evident.However, the underlying cause of performance degradation is more easily understood byconsidering the process of channels being relinquished on batch service completion. Becauselarge batches cause dispatchers to hold channels for extended periods of time, the timeperiods between channel relinquishment are extended. As a result of an infrequent channelrelinquishment process, the dynamic channel allocation system cannot react quickly enoughto adjust to changing traffic intensities, and both services can end up adversely affected dueto frequent traffic imbalances that cannot take advantage of the statistical smoothing of thedynamic allocation system.Open batch systems have another major disadvantage associated with them. The problemmay be explained by examining the variance in the mean delay. Table 16 shows comparisons74between the delay variances of OB and CB systems in relative terms, where the varianceratio is defined as the OB delay variance divided by the CB delay variance.cR Variance Ratio (CB variance (min 2 ))High Performance Low Performance5 6.23 (1.02) 6.75 (3.48)10 2.98 (0.93) 5.34 (2.51)15 1.43 (0.97) 3.82 (2.72)20 2.23 (1.07) 5.49 (2.35)25 1.93 (1.02) 4.65 (2.43)30 4.54 (0.39) 4.61 (2.20)35 2.21 (0.89) 5.15 (2.30)Table 16 CB and OB Variance ComparisonOne reason for the larger OB variance is the channel queuing delay. Define tQc as themean absolute channel request delay at the dispatcher between the time a channel is requestedand the time it is assigned. Note the difference between tQc and TQc, where the latter is themean channel request delay per call. Table 17 shows the tQc and TQc for each number ofradio channels. For CB systems, tQc translates directly into TQC, since all calls in a closedbatch face the same absolute channel request delay.0On the other hand, OB calls that arrive after a dispatcher has been seized (it is assumeda channel is requested immediately upon receiving a dispatcher) do not have to wait the fulllength of the absolute channel request delay. Open batch calls that arrive after a channelrequest has been made do not have to wait the full tQc, and those calls which arrive after achannel has been assigned face no channel queuing delay at all. This wide relative variabilityof channel queuing delays combined with a large tQc accounts for the much larger delay75variance in OB systems. Table 17 shows a comparison between tQc for CB and OB systemsunder the fixed channel allocation scheme. An analogous situation occurs with the dispatcherdelay, TWD •Number ofRadioChannlestQcHigh Performance Model Low Performance ModelCB OB CB OB5 11.6 104.8 67.2 555.310 12.4 63.9 31.4 421.115 12.4 51.1 68.1 408.320 18.4 139.9 68.2 435.325 18.0 95.4 73.7 460.530 15.6 60.3 63.4 428.035 14.8 117.9 65.4 506.1Table 17 Channel Queuing DelayThe variance for OB systems is always larger than similar CB systems, and the differencesare more pronounced with the low performance model. The problem with a large variance,even with systems exhibiting favourable performance in terms of mean delay, is that widevariations in delay at the MRT level are likely to cause users to viewed the system asunreliable. Therefore, inconsistent service is likely to lead to customer dissatisfaction — akey concern in performance evaluation for overall network design.Since the batch size is fixed in CB systems, they do not experience the same shortcomingsas OB systems. Consistently small batch servicing times allow for fast adjustment under thedynamic allocation strategy, and provide a more uniform service to MRTs.76Low Performance ModelHigh Performance ModelAside from comparisons between CB and OB systems, a comparison relating the lowand high performance models for each of the two batch service disciplines is also considered.Figure 29 combines Figures 23 and 25 to compare low and high performance models for CBsystems, and Figure 30 combines the OB performance model graphs from Figures 24 and26. It is observed that even though the high performance model offers greater improvement,but as expected the low performance model is ultimately capable of handling more traffic.9000800070006000500040003000200010000a,03 60005000"C) 4000ir)E 3000z20005^10^15^20^25^30Number of Dispatch Channels90008000700010000Figure 29 Closed Batch High and Low Performance Models779000800070006000500040003000200010000Low Performance ModelHigh Performance Model7000Cocas 6000ti 5000F-18 40004.)3000z20001000 -0900080005^10^15^20^25^30Number of Dispatch ChannelsFigure 30 Open Batch High and Low Performance Models4.6 Summary and ObservationsA model of the integrated MRS and MTS network is constructed which is consistentwith the proposed LMSS network configuration. The MRS segment operates under the newdispatch radio protocol discussed above, and thc•MTS segment is modelled as an infinitepopulation Erlang-B traffic source. The networks are combined under two different channelallocation strategies (static and dynamic), and the results are compared.Under all traffic divisions and performance model combinations, CB systems usingdynamic allocation show improvements in dispatch and telephone traffic throughput overstatic channel pool division. Increased throughput in CB systems is achieved with no sacrifice78in performance. Qualitatively, OB systems show similar behavior with the high performancemodel, but no real improvement with the low performance model.Closed batch systems using the proposed dynamic channel allocation scheme performbetter than any static system or any OB system model. In addition, CB systems offer asmaller variance in call delay. While it would seem that CB systems are always the clearfavourite, OB systems still offer better service when traffic levels are relatively low.The dynamic channel allocation system works by reducing the mean number of freechannels required to ensure adequate blocking probability for blocked-calls-dropped traffic.Table 13 and 14 summarize the reductions in the mean number of idle channels for thedifferent levels of offered traffic. From these tables, it can be seen that the tentative marginof free telephone channels, M, can be either smaller or larger than the actual mean numberof free channels realized depending on service discipline and performance level. Increasesin traffic due to varying MRS or MTS traffic also have an effect on the mean numberof free channels. The difference is often small, but usually results in a smaller numberof free channels being necessary when radio traffic is increased. This is due to the factthat radio calls are considerably shorter than telephone calls. Shorter calls means morefrequent call completions and, ultimately, more rapid adjustments in the free channel marginto accommodate changing traffic. The speed of margin adjustment is fundamentally relatedto the size of the free channel margin; if adjustments could be made instantaneously, thenthe tentative free channel margin would never have to be greater than unity, since as soonas a telephone call seized the free channel, another channel would be made available.795. ConclusionBoth the new MRS protocols and the proposed reserve margin dynamic channel allocationstrategy provide means to make more efficient use of available bandwidth for LMSS voiceservices. The MRS protocol conserves bandwidth by reducing inband signalling requirementsby processing calls in batches, and reducing sideband signalling by queuing blocked calls toavoid repeated call requests. Further conservation of bandwidth is achieved by employingthe dynamic channel allocation scheme use to combine radio and telephone which takesadvantage of channels that often remain idle when used in a telephone only, blocked-calls-dropped, network.5.1 SummaryGiven an integrated MRS and MTS network, the selected subnet configuration, any levelof offered traffic, and one of the two performance levels, CB systems under the reservedmargin dynamic allocation system perform better than any OB system or any system understatic allocation. In addition, it appears that CB systems are robust when faced with variousperformance levels.When offered traffic is low, OB systems might offer lower delay. Regardless of whichservice discipline is employed, time-outs might be used to provide better service at low trafficlevels, and priorities might be incorporated to service urgent messages at any traffic level.The batch size might also be adapted dynamically to reflect the current traffic load. If theload is light, a smaller batch size can be used to reduce the batch formation delay. With80regard to the dynamic channel allocation system, the tentative free channel margin mightalso be adjusted to adapt to changes in the load balance between MRS and MTS traffic.An interesting consequence of the integrated system, is that greater additional throughputis achieved when required blocking probability is small. This is due to the fact that, onaverage, more channels must be free to maintain a small blocking probability and thereforemore channels can be utilized under the reserve margin dynamic allocation scheme.Intelligent choices have been made in constructing a model from that which is knownabout planned LMSS voice services and in consideration of available computing resources.While no model is ideal, the results here clearly indicate the superiority of the analyzedsystems. The effectiveness of the reserved margin strategy and the CB systems during thebusy period allows us to relax some of the network parameter constraints selected earlier.It follows that subnets need not be constrained to having fewer dispatchers than the numberof spot-beams. The proposed reserve margin dynamic allocation strategy not only facilitatesadditional throughput over static allocation for all CB systems, but is also intrinsically simpleto implement. In addition, the strategy is easily adapted to other systems of heterogeneoustraffic where offered traffic is a combination of blocked-calls-dropped and blocked-calls-queued disciplines. By virtue of the fact that CB systems exhibit optimal throughput whenusing a batch size greater tlian unity, the batching strategy is shown to work effectively. Thereserved margin dynamic channel allocation strategy is also shown to improve throughput.Overall, the systems constitute innovative and practical contributions to efficient use ofscarce channel resources for LMSS.5.2 Future WorkDue to the constraints of both time and computational power, an exhaustive study has by81no means been done. Nevertheless, insights gained here into system behavior may be usedas a foundation for further study. Several aspects of the system may be further investigated.First of all, only two possible batch service disciplines have been tested, and there mightbe some better than the FCFS-OB system. One possibility is a hybrid of the CB and OBsystems where batches remain open until service begins, but once a channel is allocated thebatch closes to new arrivals. This system might provide a combination of advantages of theCB and OB systems, allowing statistical multiplexing within subnets and at the same timepreventing excessively long channel holding times.A greater range of performance models could also be investigated. Additionally, amethod for relating blocking probability to delay in order that the channel margin maybe adjusted to maintain equal levels of performance at all times. This would allow systemperformance to be truly balanced between services. In reality, the most effective performancemeasure would be a cost function which can be applied to maximize LMSS revenue. In orderto achieve the best cost function, a degree of adaptability might also be incorporated, wheretime-outs and priorities might be used, and where the batch size, batching strategy, and freechannel margin might also be modified dynamically also.Larger simulations might be considered to more accurately represent an entire LMSSsystem. Since larger systems tend to behave more efficiently than proportionally smallerones due to statistical smoothing, the benefits of the dynamic allocation strategy may not beas pronounced in a large network. On the other hand, a larger network has a much faster andmuch more uniform channel relinquishment process which would allow the system to adaptmuch more quickly. Hence, it might be the case that even a proportionally much smallernumber of free channels is required to achieve the desired result. Furthermore, the proposed82system performs better when a smaller blocking probability is desired; therefore, it might bepossible to considerably enhance system performance without sacrificing throughput.A system that also incorporates a third service into a shared dynamic channel allocationscheme might also be considered. In particular, a method for integrating mobile data serviceto further enhance overall LMSS network bandwidth utilization may be possible..83Bibliography[1] K. G. 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Model Validation and VerificationIn order to determine the correct operation of a software project, both validation andverification are required. Validation is to ensure that the correct model is being built, whereasverification is to ensure the model is being built correctly [56,57].There are no actual systems against which to compare either the subnet or integratednetwork model, since the systems are new. Therefore, MRS model validation is implicitin the model description which is provided in previous chapters and validated againstthe open literature to the extent possible. Validation of the MTS model is complete byaccepting the assumption of Erlang-B traffic which is widely regarded as a reasonablyaccurate representation of telephone traffic.Model verification, on the other hand, is still essential to ensure there are no softwarebugs which produce errors in program output. Some standard software verification techniquesinclude independent program module testing, redundant collection of program statistics toensure consistency, program execution step-throughs, and the use of predetermined test suites.All of these techniques have been employed as a matter of routine coding, except for thelast one. Predetermined test suites cannot be used because no results can be determined inadvance for any input. In addition, no closed form analytic solutions or numerical resultsexist for the particular G/G/m/n queuing systems involved in subnet modelling. Nevertheless,if the models are simplified, some mathematical models may be constructed and their resultscompared to the simulation models. This is the objective in the next sections.90• •••• •• • •A.1 Open Batch MRS Subnet ModelA single spot-beam OB MRS subnet employing a single dispatcher with no signallingoverhead (propagation and serializing delays) and no channel assignment delay may bemodelled by the imbedded Markov chain as shown in Figure 31. In the figure, n is the totalnumber of MRTs in the subnet, b is the batch size, A is the call rate per individual MRT, andis the call service rate. Before proceeding to analyze the Markov chain, some theoretical(n-1)X11Figure 31 Open Batch, Single Dispatcher Markov Chainresults are required. First, by inspection it is noted that the Markov chain of Figure 31 isa finite state, irreducible, aperiodic chain.Proposition B.1. All states of an irreducible aperiodic Markov chain are either:i. positive recurrentii. transient•Corollary B.2. All states of a finite state irreducible aperiodic Markov chain are positiverecurrent.Corollary B.2 indicates that the Markov chain of Figure 31 is positive recurrent.Proposition B.3. Sufficient conditions for the existence of a stationary distribution of aContinuous-time Markov Chain are:91i. the Markov Chain is irreducibleii. the Markov Chain is positive recurrentThe Markov chain is irreducible by inspection and positive recurrent by Corollary B.2;therefore, the limiting distribution exists.Propositions B.1 and B.3, and Corollary B.2 are offered without proof. For a morecomplete discussion of limiting distributions of Continuous-time Markov chains, includingproofs see references [20,50,58,59].Define pi as the limiting probability of the chain being in state Si. Now, since the limitingdistribution exists, the Chapman-Kolmogorov equations are reduced to the following set ofbalance equations: For states Si through Sb_i= nApo + [1 — (n —^ (A.1)752 = (n^+ [1— (n — 2)A]p'2^(A.2)P.? = (n — j 1)ApZi j + [1 — (n — j)A]pli^3 < j < b — 1^(A.3)The equations (A.1) through (A.3) may be more simply expressed as(n - j 1)PJ - (n - j) PJ-1and, solving recursively in terms of 190,- (n - j) Po^1 < j < b - 1^ (A.5)Investigating states So through Sb_j, the balance equations arePo = (1 — n A )po + (1 — p)pl^ (A.6)92v <j< b-1^(A.4)= [1 — (n — 1)A — IL]P1 + /'P2^ (A.7)P2 = (n — 1)Api + [1 — (n — 2)A —^+ pp3^(A.8)pi = (n — j 1)Api_i + [1 — (n — j)A —^+ ppi+i 3< j < b — 1^(A.9)Simplification of equations (A.6) through (A.9) yieldsAn (—)po (A.10)\ AP2 = [(n — 1 )(—) + lipi (A.11)[(n — j 1) )^ — (n — j + 2)(—)Pi-2 3 j b^(A.12)recursively solving equations (A.10) through (A.12) in terms of po,k+1= nPo^(Api^ (n — j)! (n — j k)!k=01 < j < b^(A.13)Finally, for states S b through S„.] the balance equations are as follows:^Pb = (n — b 1)A(Pb:--i + Pb) + ([1 — (n — b)A —^ PPb+1^(A.14)p = (n j + 1)Api _i + [1 — (n — j)A^PP1+1^< j < n^(A.15)93and by simplifying and solving recursively in terms of poj-1(^kk +1PJ — (nnf°j)! kb AII^(n - j + k)!^b < j < n^(A.16)Further, the dispatcher utilization factor, p, may be calculated as follows:p = 1 —b-1(PO E p") ).J=1Now definePo{j = 0^ri = p'j + pj^1 < j < b^(A.17)Pi^b < j < nso that 7rj represents the limiting probability that there are j customers (calls) in the systemat any time. By combining equations (A.5), (A.13), and (A.16) the following result isobtained:j-1k+1A^2222(n —j) [ 1^J(n —.-1 )!^(IL)^(n^k)!k=0J-1n-J)! Ej—b (A) (n - j + k)! b < j < n(^k=However, there are only n equations, but n+ 1 unknowns. In order to solve for the ri anadditional equation is required. By recognizing the fact that all probabilities must sum to1.0, the additional equation,(A.19)Omay be used. The limiting distribution for the Markov chain may now be solved by combining=1 < j < b(A.18)equations (A.18) and (A.19):b-1 )--1 p I) k-I-1^.= [1 +4-1=1 n^12 (n - j) (1 + (n - j - 1)! E^(rz -3 + 0!)-1-k---0 \ j-1^k+ 1^ E (L) (n - j + k)!i) k=j—bn.E(A.20)94The expected number of calls in the system is simplyN = Ejri^ (A.21)j=i. Still further, the average call arrival rate, A, may be calculatedA =^ (A.22). Finally, by Little's law, N=AT, the mean time spent in the system, T, can be found. Themean delay, TQ, is simply the mean time spent in the system minus the mean service timewhich is given by 1/µ. Thus, the mean delay is given byN 1TQ = - /7, (A.23)orTQ N — p^ (A.24)A9512b=12_ b=8b=5b=3- b=2b=1 ,  10-2801^i^III^i ^09020 30 40 50 60 70MRTs per Dispatcher-4SimulationMarkov Chain21614Figure 32 Comparison of OB Simulation Model Results with Markov Chain ModelFor b=1, note that the result is identical to an M/M/1/n queuing system. Figure 32 showsa comparison of the results of the delay derived from the Markov chain, and that determinedempirically through simulation modelling when signalling overhead is omitted, where A andu have been set to .001 and .05 respectively, in accordance with Table 2. The error bars onthe simulation model curves represent 95% confidence intervals. Slight aberrations in thecurves are largely due to limitations of the graph plotting software used. It is clear, however,that the simulation model corresponds almost identically with the theoretical model.96A.2 Closed Batch MRS Subnet ModelA Markov chain representation of a single spot-beam CB subnet without signallingoverhead may also be constructed. Figure 33 show one possible representation. Each statein this model has two associated subscripts; a state Sy is defined such that i is the number ofcall requests in the system, and j is the number of calls requests eligible for service. A callis eligible for service if it is belongs to a completely formed batch. A closed form solutionfor this system is not given; however, numerical solutions may be determined.• • •• • •Figure 33 Closed Batch, Single Dispatcher Markov Chain•First of all, recognize that the Markov chain of Figure 33 is a finite state irreducibleaperiodic chain and, therefore, has a unique limiting distribution. Thus, the Chapman-Kolmogorov differential equations describing the rates of state transitions may be reducedto a set of balance equations. Let py be the limiting probability that the chain is in state Sid,97and assume b > 2, then for 0 < k < n — b — 1, there are the following set of equations:—7240,0 +^= 0^ (A.25)n40,0 — (n — 1)Api,o + pp2,1 = 0^ (A.26)— [(n — 1)A +^+ pp2,2 = 0^ (A.27)(n — k — b +1)APk+b—i,k — [(n — k — b)\ ii1Pk+b,k+i 11Pb+k-Fi,k+2 = 0^(A.28)(n — k — b 1)Apk+b—i,k-Fi — [(n — k — b)\ /11Pk+b,k+2 PPb+k+1,k+3 = 0^(A.29)(n — k — b +1)APk+b—i,k+b-2 — [(n — k — b)A + PiPk+b,k+b-1 fiPb+k+1,k+b 0 (A.30)(n — k — b + 1)Apb+k—i,k-1 — [(n — k —^P1Pb+k,b+k iiPb+k-Fi,b+k-Fi = 0 (A.31)Apn-1,n-2^n —1 = 0^ (A.32)•APn-1,n—b /tPn,n = 0^ (A.33)If m is the total number of states, then there are m equations and m unknowns. In matrixnotation,Qp = 0^ (A.34)98where Q is an m xm infinitesimal generator matrix, and p is an mx 1 matrix of unknownstate probabilities, and whereb- 2rn = b(n — b+ 2) 2— L(j + 1)(j +_ o (A.35)However, the first of the balance equations, (A.25), is linearly dependent on the others.Therefore it is replaced withEpi ,,j = 1^(A.36)all i,jwhich holds true since all probabilities sum to unity. The resulting system of linear equationsisQp = el^ (A.37)where el is a zero vector with the exception of a 1.0 entry in the first position. This systemof equations is solved using standard numerical methods employing Gaussian eliminationand back substitution with row and column pivoting for numerical stability. Then, in orderto determine the limiting probability distribution, note that,O, 1 2, ..., j^0 < j < b7rj =^Pj,k^k = 3 —b+1,j —b+2,...,j^b< j <nThe utilization factor is calculated as followsp = 1 — Epoi=oFinally, the delay is calculated similarly to that of OB systems yielding,T,^N — p—^lip(A.38)(A.39)(A.40)99b=580 90>,ca 8a)620b=810-C--161412b=3- b=2b=1,10 20 30 40 50 60 70MRTs per Dispatcherb=12-16-14-12-10- 8- 642^ 0SimulationMarkov ChainOnce again, for b=1, note that the system is identically an M/M/1/n queuing system.The results of the delay derived numerically from the Markov chain model are comparedto the results of the simulation model in Figure 34. The individual MRT arrival rate anddispatcher service rate are set to .001 and .05 respectively, in accordance with Table 2. Theerror bars on the simulation model curves represent 95% confidence intervals. Once again,the simulation model performs almost identically to the theoretical model.Figure 34 Comparison of OB Simulation Model Results with Markov Chain ModelA.3 Integrated Network ModelThe integrated network model consists of both dispatch radio and telephone trafficsources. The radio traffic is made up of a collection of either CB or OB MRS subnets which100are constructed identically to the models described above. Hence no further verification forMRS models is given. Mobile telephone traffic, on the other hand, is modeled as Erlang-Bsource, and verification is presented here.Figures 35 and 36 compare theoretical results of telephone traffic with simulation modelresults in the absence of signalling overhead. The theoretical model used is Erlang-B.The Erlang-B model is an infinite population model where the rate remains constant forthe duration of the model's lifetime and the rate is directly proportional to the population.Simulation model MTS traffic is varied in simulation runs by varying the traffic arrival rate,and therefore, the independent variable in the comparisons is the MIT population. Figures35 and 36 show population versus blocking probability respectively and channel utilizationfactor. Ninety-five percent confidence intervals are included for the simulation models,however, the simulation model and theoretical model curves are virtually superimposed,reflecting the accuracy of the simulation model implementation of the Erlang-B system.The probability of blocking for the Erlang-B M/m/n n-server loss model is well known.It is given bypnPB =^n! E Lkkik=0 •(A.41)where p = it and A is the mean call arrival rate, is the mean call service rate per channel,and n is the number of channels available [20,50,59]. The mean channel utilization, p, maybe calculated directly form A and Once again, the accuracy of the simulation models canbe seen by their close adherence to the presented theoretical results.101SimulationErlang-B1.• 0.7=.o013- 0.50)ci 0.4o03 0.6800^1600^3200^6400^12800Number of MTTsFigure 35 MTS Population versus Blocking Probability102SimulationErlang-Bn=20201918171615141312111020191817= 1ca 68 .1■1,0131211109800^1600^3200^6400^12800Number of MTTsFigure 36 MTS Population versus Utilization Factor•103B. Simulation Modellingand Data AnalysisAll simulation models are written in the SIMSCRIPT 11.5 1 programming language,and executed on Sun SPARC 11 2 Workstations under the UNIX3 operating system. TheSIMSCRIPT language is chosen over a general purpose programming language for its builtin queuing and scheduling control structures, its statistics gathering capabilities, and its nearlyself-documenting source code. Built in features help keep programming models small andthereby reduce coding and debugging time, and enhance program reliability. In furtherconsideration of SIMSCRIPT, it provides a greater degree of flexibility than most othercomparable simulation languages and lends itself well to large complicated models [57].A simulation model consisting of only MRS traffic which is made up of 52 subnets with44 MRTs per dispatcher each and using a closed batch size of 8, requires over 7 megabytesof computer memory and 3.4 hours of CPU time. In theory, larger model could be run withthe given computer resources, but experience has shown that larger models rarely surviveto run through to normal completion. In addition, time constraints dictate that much larger•models are not practical given the number of test runs that may be made to achieve anydegree of statistical reliability over the large number of network configurations tested.1^SIMSCRIPT is a registered trademark of CACI2^SPARC is a registered trademark of Sun Microsystems3^UNIX is a registered trademark of AT&T104B.1 Notes on MethodologyIn varying the traffic levels for an MRS subnet model, the MRT population is variedon an MRT per dispatcher basis; increments of 4 to 8 MRTs per dispatcher are used. Thismeans that larger increases in absolute population are made when there are a greater numberof dispatchers. However, the number of MRTs per dispatcher has been shown to be the morerelevant measure of subnet load than absolute population.When several subnets are combined under the integrated network strategy, the subnetconfiguration is fixed with 44 MRTs per dispatcher, so each subnet is under a fixed trafficload. In order to make adjustments to MRS traffic within a combined network the numberof subnets is varied. When there are only a few subnets, adding or removing one subnetconstitutes a fairly large proportional change in overall MRS traffic. When there are manysubnets varying the number of subnets makes more gradual proportional changes. Whileit is desirable to be able to make small proportional changes in order to fine tune networkperformance, this is not always possible in practical model implementation.When varying the number of subnets, one must keep in mind that there are practicallimits to the number of subnets that may be accommodated by a given number of channels.A model with 35 available channels and enough subnets present to maintain full channelutilization reaches is sufficiently large that it reached the upper limit of given computerresource functionality. Experience has shown that larger models will rarely run though tonormal completion.Traffic variations for the MTS segment are simply made by adjusting the rate at whichnew calls enter the system. Since the rate is specified by a single real number, very fine trafficadjustments may be made. In addition, the simple manner in which MTS calls are generated105does not pose a computational constraint on the system being modelled; the number of MRSsubnets is the limiting factor.B.2 Confidence IntervalsThe results of Appendix A show a strong correlation between the given analytical modelsand computer simulation results. However, underlying those results is the assumption thatthe output from several simulation runs is representative of the expected output of all possibleruns. One common method used to establish an estimate of the expected behavior is to makeseveral test runs and then calculate a confidence interval about the mean value of a particularoutput parameter. This is the approach taken above.A confidence interval for a population parameter is an interval calculated from a samplestatistic which estimates the population parameter with some degree of confidence. Theconfidence level is given as the probability that the population parameter falls withinthe calculated interval [60]. With regard to analyzing simulation model output, however,calculating a confidence interval for an output parameter may not provide the desired result.Computer simulations must often run for an initial period of time before statistics are collectedin order to eliminate initialization bias. Several methods have been proposed to controltransient effects [61-63]; "however, one primary method has been applied to models usedhere. Successive identical test statistics from consecutive simulation blocks of executionare compared in order to determine how long it takes for transient effects to subside.This determination is done in part by comparisons among the test statistics and in partby comparison of the test statistics to the known analytic results given above. If transienteffects are not negated, the confidence intervals that are calculated may contain initialization106bias. All calculations are based on experiments with a single subnet since each subnet ina group behaves similarly.The degree of confidence may be increased by examining more samples of simulationoutput; however, the magnitude of the simulation model and the available computer resourcesconstrain the number of test runs that may actually be performed. The number of runs thatshould be made was determined by selecting the size of the confidence interval. A reasonablysmall 95% confidence interval could be obtained for the simulation models. Figures 32 and 34show 95% confidence intervals for single MRS subnet simulation results for delay. These twofigures exemplify typical confidence intervals for all similar figures presented above. Ninety-five percent confidence intervals for MTS simulation models are shown in Figures 35 and 36.Only 90% confidence intervals could be achieved for the integrated network. A typical curvewith confidence intervals is given below (Figure 37). Figure 37 is a modification of Figure25 showing only the results of MRS modelling but including 95% confidence intervals forthe number of MRTs in the network.0107,Dynamic AllocationFixed Allocation9000800070006000500040003000200010000cncTO 6000I 5000F-' 2 4000coE 3000z20005^10^15^20^25^30Number of Dispatch Channels (CR)90008000700010000Figure 37 CB Low Performance Network with 95% Confidence Intervals108IC. Source CodeThe following source code is provided as an example of the software used in creatingsimulation models; it is the CB MRS subnet model employed above. The model is madeup of several parts, each of which is maintained in a its own source file. Source files arecompiled separately, then subsequently linked together to form a single executable version.Each of section that follows constitutes a single source file.C.1 FC.simThis file constitutes the simulation model preamble.PreambleNormally mode is undefinedDefine secs to mean daysResources includeDISPATCHER^•Permanent entitiesEvery QUEUEhas an ARRIVAL.COUNT,has a COMPLETION.COUNT,has a BATCH.FORMATION.COUNTER,has a CURRENT.BATCH,may have a PENDING.TIMEOUT,owns a CALL.REQUEST.SET109Define ARRIVAL.COUNT,BATCH. FORMATION. COUNTER,COMPLETION. COUNTas integer variablesDefine PENDING.TIMEOUT,CURRENT.BATCHas pointer variablesDefine CALL. REQUEST. SETas setsEvents includeRESTART,FINAL.REPORTProcesses includeCHECK.POINTEvery MRT.CALLhas a BEAM.IDhas a CURRENT.MRTEvery DISPATCHhas a BEAM.ID,has a BTIMEEvery MRThas a BEAM.IDDefine BEAM.IDas an integer variableDefine BTIMEas a double variable •Define CURRENT.MRTas a pointer variableTemporary entitiesEvery CALL.REQUESThas an INITIATION.TIME,110has a HOLDING.TIME,has an CALL.ID,has a MY.BATCH,belongs to a CALL.REQUEST.SETDefine HOLDING.TIME,INITIATION.TIMEas double variablesDefine CALL.ID ,MY.BATCHas pointer variablesEvery BATCHhas a NEXT.CALL,has a SIZE,may have a CURRENT.DISPATCHDefine NEXT.CALL,CURRENT. DISPATCHas pointer variablesDefine SIZEas an integer variableDefine NUM. DISPATCHERS,MRT.CALL.IAT,NUM.SPOT.BEAMS,NUM.TIMEOUTS,NUM.QUEUED,BATCH.SIZE,NUM.MRTS.PER.DISP,REQUEST. TOTAL,CALL. ARRIVAL. STREAM,HOLD. TIME. STREAMas integer variablesDefine IAT,TWB,TWD,TWS,111CHANNEL. SETUP. TIME,CHANNEL.TEARDOWN.TIME,END.OF.RUN,SERVICE.TIME,MEAN.HOLDING.TIME,RESTART. TIME,GLOBAL.DELAY,RUN.LENGTH,LAST. CALL. TIME,CHECK.IN.TIME,TIMEOUT.PERIODas double variablesTally MEAN.GLOBAL.DELAY as the mean,GLOBAL.DELAY.SD as the std.devof GLOBAL.DELAYTally MEAN.IAT as the mean,IAT.SD as the std.devof IATTally MEAN.SERVICE.TIME as the mean,SERVICE.TIME.SD as the std.devof SERVICE.TIMETally MEAN.TWB as the mean,TWB.STD.DEV as the std.devof TWBTally MEAN.TWD as the mean,TWD.STD.DEV as the std.devof TWDTally MEAN.TWS as the mean,TWS.STD.DEV as the std.devof TWSDefine NUM.IATS to mean 61Define NUM.DELAYS to mean 31Define NUM.LENS to mean 26112Define MRT.CALL.RATE to mean 0.001Define CNTL.MSG.SER.DELAY to mean 0.050Define PROPAGATION.DELAY to mean 0.250Define .ACTIVE to mean 0Define .ASLEEP to mean 1Define .WAITING to mean 2Define INI.FILE to mean Unit 1Define OUT.FILE to mean Unit 2Define STDOUT to mean Unit 6Define STDERR to mean Unit 98EndC.2 call.simThis file constitutes a process of an individual MRT call.Process MRT.CALLGiven BEAM.ID and CURRENT.MRTDefine BEAM.ID as an integer variableDefine CURRENT.MRT as a pointer variableDefine .DELAY as a double variableDefine .CALL.REQ as a pointer variableCreate a CALL.REQUEST called .CALL.REQLet CALL.ID (.CALL.REQ) = MRT.CALLLet IAT = time.v - LAST.CALL.TIMELet LAST.CALL.TIME = time.vLet INITIATION.TIME(.CALL.REQ) = time.vFile .CALL.REQ in CALL.REQUEST.SET(BEAM.ID)Add 1 to NUM.QUEUEDAdd 1 to ARRIVAL.COUNT(BEAM.ID)Add 1 to BATCH.FORMATION.COUNTER(BEAM.ID)If BATCH.FORMATION.COUNTER(BEAM.ID) = 1Create a BATCH called CURRENT.BATCH(BEAM.ID)NEXT.CALL(CURRENT.BATCH(BEAM.ID)) = .CALL.REQEndifIf BATCH.FORMATION.COUNTER(BEAM.ID) = BATCH.SIZESIZE(CURRENT.BATCH(BEAM.ID )) = BATCH.SIZEActivate a DISPATCHcalled CURRENT.DISPATCH(CURRENT.BATCH(BEAM.ID))'giving CURRENT.BATCH(BEAM.ID) and time.vnowBATCH.FORMATION.COUNTER(BEAM.ID) = 0EndifMY.BATCH(.CALL.REQ) = CURRENT.BATCH(BEAM.ID)Suspend114.DELAY = time.v - INITIATION.TIME(.CALL.REQ)Remove .CALL.REQ from CALL.REQUEST.SET(BEAM.ID)Subtract 1 from NUM.QUEUEDLet HOLDING.TIME(.CALL.REQ) =exponential.f(MEAN.HOLDING.TIME,HOLD.TIME.STREAM)Work HOLDING.TIME(.CALL.REQ) secsGLOBAL.DELAY = .DELAYLet SERVICE.TIME = HOLDING.TIME(.CALL.REQ)Reactivate the DISPATCHcalled CURRENT.DISPATCH(MY.BATCH(.CALL.REQ)) nowDestroy the CALL.REQUEST called .CALL.REQAdd 1 to COMPLETION.COUNT(BEAM.ID)Reactivate the MRT called CURRENT.MRT nowEnd•115C.3 checkin.simThis file constitutes a process for giving positive feedback of program execution atspecified constant simulated time intervals.Process CHECK.POINTDefine .CP as a pointer variableUse STDERR for outputPrint 1 line withtime.v thusCHECK POINT: time = ***********Activate a CHECK.POINT called .CP in CHECK.IN .TIME secsEnd.•116C.4 disp.simThis file constitutes a process of an MRS subnet dispatcher.Process DISPATCHGiven CALL.BATCH and BTIMEDefine CALL.BATCH as a pointer variableDefine BTIME as a double variableDefine .TWD as a double variableDefine .TWS as a double variableDefine I as an integer variableLet .TWD = time.vRequest 1 DISPATCHER(1)Let TWD = time.v - .TWDIf CHANNEL.SETUP.TIME > 0.0Work CHANNEL.SETUP.TIME secsEndifLet .TWS = time.vFor I = 1 to SIZE(CALL.BATCH) doLet TWS = time.v - .TWSLet TWB = BTIME -INITIATION.TIME(NEXT.CALL(CALL.BATCH))Reactivate the MRT.CALLcalled CALL.ID(NEXT.CALL(CALL.BATCH))nowNEXT.CALL(CALL.BATCH) =S.CALL.REQUEST.SET(NEXT.CALL(CALL.BATCH))SuspendLoopIf CHANNEL.TEARDOWN.TIME > 0.0Work CHANNEL.TEARDOWN.TIME secsEndif117Relinquish 1 DISPATCHER(1)Destroy the BATCH called CALL.BATCHEndto118C.5 init.simThis file constitutes a subroutine for initializing simulation variables and entities.Routine INITIALIZEDefine I as an integer variableCreate every QUEUE(NUM.SPOT.BEAMS)Create every DISPATCHER(1)Let U.DISPATCHER = NUM.DISPATCHERSFor I = 1 to NUM.SPOT.BEAMS doBATCH.FORMATION.COUNTER = 0LoopLet NUM.QUEUED = 0Let LAST.CALL.TIME = 0.0Let MRT.CALL.IAT = 1.0 / MRT.CALL.RATELet END.OF.RUN = RUN.LENGTH + RESTART.TIMEIf CHANNEL.SETUP.TIME = -1.0Let CHANNEL.SETUP.TIME =(BATCH.SIZE + 2) * CNTL.MSG.SER.DELAY +3 * PROPAGATION.DELAYEndifIf CHANNEL.TEARDOWN.TIME = -1.0Let CHANNEL.TEARDOWN.TIME =CNTL.NeSG.SER.DELAY + PROPAGATION.DELAYEridifEnd119C.6 main.simThis file constitutes the main procedure of the simulation model.MainDefine I and J as integer variablesDefine .NUM.MRTS.PER.BEAM as an integer variableCall GET.PARAMETERSCall INITIALIZEActivate a CHECK.POINT nowSchedule a RESTART in RESTART.TIME secsSchedule a FINAL.REPORT in RESTART.TIME + RUN.LENGTH secsLet .NUM.MRTS.PER.BEAM =(NUM.DISPATCHERS * NUM.MRTS.PER.DISP) / NUM.SPOT.BEAMSFor I = 1 to NUM.SPOT.BEAMS doFor J = 1 to .NUM.MRTS.PER.BEAM doActivate a MRT giving I nowLoopLoopStart simulationEnd120C.7 mrt.simThis file constitutes the process of a single MRT.Process MRT given BEAM.IDDefine BEAM.ID as an integer variableHereWait exponential.f(MRT.CALL.IAT,CALL.ARRIVAL.STREAM)secsActivate a MRT.CALL giving BEAM.ID and MRT nowSuspendJump backEnd•121C.8 read.simThis file constitutes a subroutine which reads and initialization file to obtain externallyspecified simulation parameters.Routine GET.PARAMETERSDefine .QUIT as an integer variableDefine .FIELD as a real variableDefine .NAME as a text variableLet CALL.ARRIVAL.STREAM = 1Let HOLD.TIME.STREAM = 3Let RESTART.TIME = 0.0Let BATCH.SIZE = 1Let CHANNEL.SETUP.TIME = -1.0Let CHANNEL.TEARDOWN.TIME = -1.0Let MEAN.HOLDING.TIME = 20.0Let NUM.MRTS.PER.DISP = -1Let NUM.DISPATCHERS = -1Let NUM.SPOT.BEAMS = -1Let TIMEOUT.PERIOD = -1.0Let RUN.LENGTH = -1.0Let CHECK.IN .TIME = -1.0Open INI.FILE for input, name = "SIM.ini"Use INI.FILE for input.QUIT = 0eof.v = 1Read .NAMEWhile eof.v <> 2 doRead .FIELD•If .NAME = "num.dispatchers"Let NUM.DISPATCHERS = int.f(.FIELD)Else if .NAME = "call.arrival.stream"Let CALL.ARRIVAL.STREAM = int.f(.FIELD)Else if .NAME = "hold.time.stream"122Let HOLD.TIME.STREAM = int.f(.FIELD)Else if .NAME = "check.in.time"let CHECK.IN .TIME = .FIELDElse if .NAME = "restart.time"Let RESTART.TIME = .FIELDElse if .NAME = "num.spot.beams"Let NUM.SPOT.BEAMS = int.f(.FIELD)Else if .NAME = "mean.holding.time"Let MEAN.HOLDING.TIME = .FIELDElse if .NAME = "batch.size"Let BATCH.SIZE = int.f(.FIELD)Else if .NAME = "timeout.period"Let TIMEOUT.PERIOD = .FIELDElse if .NAME = "run.length"Let RUN.LENGTH = .FIELDElse if .NAME = "channel.setup.time"Let CHANNEL.SETUP.TIME = .FIELDElse if .NAME = "channel.teardown.time"Let CHANNEL.TEARDOWN.TIME = .FIELDElse if .NAME = "num.mrts.per.disp"Let NUM.MRTS.PER.DISP = .FIELDElseUse STDERR for output .Print 1 line with .NAME like thisUnknown parameter: *************************.QUIT = 1Endif endif endif endif endif endif endif endif endifendif endif endif endifStart new input recordIf eof.v <> 2Read .NAMEEndifLoopIf NUM.MRTS.PER.DISP = -1Print 1 line thusnum.mrts.per.disp not specified.QUIT = 1EndifIf NUM.DISPATCHERS = -1123Print 1 line thusnum.dispatchers not specified.QUIT = 1EndifIf NUM.SPOT.BEAMS = -1Print 1 line thusnum.spot.beams not specified.QUIT = 1EndifIf TIMEOUT.PERIOD = -1.0Print 1 line thustimeout.period not specified.QUIT = 1EndifIf RUN.LENGTH = -1.0Print 1 line thusrun.length not specified.QUIT = 1EndifIf CHECK.IN.TIME = -1.0Print 1 line thuscheck.in .time not specified.QUIT = 1EndifIf .QUIT = 1StopEndifEnda124C.9 report.simThis file constitutes and event to print a summary of simulation execution, includingtest statistics.Event FINAL.REPORTUse STDOUT for outputPrint 14 lines withRESTART. TIME,CHECK.IN.TIME,NUM.DISPATCHERS,NUM. SPOT. BEAMS,CHANNEL.SETUP.TIME,CHANNEL.TEARDOWN.TIME,MEAN.HOLDING.TIME,BATCH.SIZE,MRT.CALL.RATE,NUM.MRTS.PER.DISP,CNTL.MSG.SER.DELAY * 1000,PROPAGATION.DELAY * 1000,RUN.LENGTH like thisLength of time before resetting statisticalvariables = ****.***Length of time between checkpoints = **********.*Number of dispatchers = ***Number of spot beams = ***Length of time to set up channel = **.**** secsLength of time to tear down a channel = **.**** secsMean holding time "for an MRT call = ***.** secsBATCH SIZE = ***MRT call rate = **.***** calls per secondNumber of MRTs per disp = *****Contol message serializing delay = ****.**Propagation.delay = ****.**Length of run = ***************.* secsprint 5 lines with MEAN.SERVICE.TIME,MEAN. GLOBAL. DELAY,125MEAN.TWB, MEAN.TWD, MEAN.TWS thusMEAN SERVICE TIME: ****.***^MEAN DELAY: *****.***TWB• ****.***^TWD: ****.***^TWS• ****.***StopEnd126C.10 reset.simThis file constitutes an event which resets variables used for gathering statistics. Theevent is scheduled to occur when the model reaches a state of equilibrium.Event RESTARTDefine I as an integer variableReset totals ofIAT,SERVICE. TIME,GLOBAL.DELAYFor I = 1 to NUM.SPOT.BEAMS doLet ARRIVAL.COUNT(I) = 0Let COMPLETION.COUNT(I) = 0LoopNUM.TIMEOUTS = 0End127C.11 timeout.simThis file constitutes an event which may be used to schedule a time-out for batchformation. It has not been used in the above analysis.Event TIMEOUTGiven BEAM.ID and PART.BATCHDefine BEAM.ID as an integer variableDefine PART.BATCH as a pointer variableAdd 1 to NUM.TIMEOUTSSIZE(PART.BATCH) = BATCH.FORMATION.COUNTER(BEAM.ID)BATCH.FORMATION.COUNTER(BEAM.ID) = 0Activate a DISPATCHcalled CURRENT.DISPATCH(PART.BATCH)giving PART.BATCHnowEnd•128


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