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Performance evaluation of the movable-slot TDM protocol and its application in metropolitan area networks Hon, Lenny Kwok-Ming 1987

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P E R F O R M A N C E EVALUATION OF T H E MOVABLE-SLOT T D M P R O T O C O L AND ITS APPLICATION IN M E T R O P O L I T A N A R E A N E T W O R K S by L E N N Y K W O K - M I N G H O N B . S c , Chinese Universi ty of Hong K o n g , 1985 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C I E N C E i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S Department of Elect r ica l Engineering We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A July , 1987 © L e n n y K w o k - M i n g H o n , 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of &iPetrifjO EneLAP&rii\i The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 DE-6(3/81) Abstract Movable-slot t ime-division mult iplexing ( M S T D M ) is a medium access control protocol for the integration of voice and data i n local area networks. In this thesis, the performance of this protocol is evaluated through mathematical analysis and simulat ion. Its application i n metropoli tan area networks is also studied. For the performance evaluation, a non-preemptive pr ior i ty queueing model is first proposed for analysing the mean data delay characteristic of the slotted non-persistent carrier-sense mult iple access w i th collision detection ( C S M A / C D ) pro-tocol. T h e n this analyt ical approach is extended to the slotted M S T D M protocol w i t h non-persistent data packet transmission, and its mean data delay performance is obtained. Numer ica l results from the analysis are shown and discussed. Moreover, s imulat ion study of the M S T D M protocol is performed. Through the s imulat ion results, the effects of this protocol on the general delay performances of voice and data are discussed. It is found that i f first voice packets, which are generated at the beginning of talkspurts, are given a shorter retransmission delay than data packets, the channel-acquisition delay for voice sources can be reduced without sacrificing the data delay performance significantly. The simulat ion results are also used to verify the analytical results. A s the comparisons show, the accuracy of the analysis is high although it is based on a simple approximate model . For the application of M S T D M i n metropoli tan area networks, a scheme which alleviates the distance and transmission rate constraints associated w i t h this pro-tocol is described. The approach is to divide the stations i n a large area into regional groups, each operating in a different frequency band. E a c h group forms a i i sub-network which is part of the metropolitan area network. A n access protocol is proposed for interconnecting these sub-networks. Also an analysis which finds the optimum number of sub-networks for interconnection is presented. The criterion is to minimize the mean data delay for communications in a sub-network. iii Table of Contents Abstract ii List of Figures vi List of Tables viii Acknowledgements ix 1 Introduction 1 1.1 Background 1 1.2 Objective and Outline of the Thesis 5 2 Performance Analysis of C S M A / C D and MS T D M 8 2.1 CSMA/CD 9 2.1.1 Protocol Description 9 2.1.2 Analytical Model 10 2.1.3 Delay Analysis 12 2.1.4 Numerical Results 14 2.2 M S T D M 16 2.2.1 Protocol Description 16 2.2.2 Analytical Model 21 2.2.3 Delay Analysis 24 2.2.4 Numerical Results 30 2.3 Summary 37 3 Simulation of M S T D M 38 3.1 Description of the Simulation Model 39 3.2 Simulation Results and Discussions 42 iv 3.3 Summary 5 6 4 M S T D M Network for a Metropolitan Area 57 4.1 Homenet Network 58 4.2 Description of the Access Protocol 61 4.2.1 Interconnection 61 4.2.2 Other Related Issues 65 4.3 Optimum Number of Homenets 66 4.3.1 Analysis 66 4.3.2 Numerical Results • 69 4.4 Summary 73 5 Conclusions 4^ Appendix A 77 Appendix B 80 References 89 v List of Figures 2.1 Packet transmission using the slotted non-persistent C S M A / C D protocol . 9 2.2 Non-preemptive priori ty queueing model for C S M A / C D 11 2.3 D a t a delay-throughput characteristics for C S M A / C D (k — 2) 15 2.4 Fi rs t voice packet transmission using the slotted non-persistent M S T D M protocol 18 2.5 Subsequent voice packet transmission 18 2.6 Packet formats for M S T D M 20 2.7 Periodic transmission of voice packets and their repositioning when delayed by other transmission 22 2.8 Non-preemptive priori ty queueing model for M S T D M 23 2.9 Remaining transmission time seen by a class 1 arrival 26 2.10 D a t a delay-throughput characteristics for M S T D M (a = 0.0125, k = 3) . . 32 2.11 D a t a delay-throughput characteristics for M S T D M (a = 0.05, k = 2) 33 2.12 D a t a delay versus fraction of data load for M S T D M (a = 0.0125, k = 3) .35 2.13 D a t a delay versus fraction of data load for M S T D M (a = 0.05, k = 2) . . . 36 3.1 Delay characteristics of data packets when both first voice packets and data packets use B E B for retransmission (a — 0.0125, k — 3) 43 3.2 Delay characteristics of voice packets when both first voice packets and data packets use B E B for retransmission (a — 0.0125, k = 3) 44 3.3 Delay characteristics of data packets when both first voice packets and data packets use B E B for retransmission (a = 0.05, k = 2) 45 3.4 Delay characteristics of voice packets when both first voice packets and data packets use B E B for retransmission [a — 0.05, k = 2) 46 v i 3.5 Delay characteristics of data packets when first voice packets r i s e LIB and data packets use B E B for retransmission (a = 0.0125, k = 3) 49 3.6 Delay characteristics of first voice packets when first voice packets use LIB and data packets use B E B for retransmission (a = 0.0125, k = 3) . . . 50 3.7 Delay characteristics of voice packets when first voice packets use LIB and data packets use B E B for retransmission (a = 0.0125, k = 3) 51 3.8 Delay characteristics of data packets when first voice packets use LIB and data packets use B E B for retransmission (a — 0.05, k — 2) 52 3.9 Delay characteristics of first voice packets when first voice packets use LIB and data packets use B E B for retransmission (a — 0.05, k = 2) 53 3.10 Delay characteristics of voice packets when first voice packets use LIB and data packets use B E B for retransmission (a = 0.05, k = 2) 54 4.1 Homenet network on a subsplit cable system 60 4.2 Inter-homenet packet transfer of bursty data 62 4.3 Link set-up for conversation between two stations in different homenets . . 64 4.4 Mean data delay for transmission within homenet as a function of the number of homenets at pv = 0 70 4.5 Mean data delay for transmission within homenet as a function of the number of homenets at pv = 0.2 71 4.6 Mean data delay for transmission within homenet as a function of the number of homenets at pu = 0.4 72 vii List of Tables B.l 95% Confidence intervals for the C S M A / C D simulat ion results shown i n Figure 2.3 (fc = 2) 80 B.2 95% Confidence intervals for the M S T D M simulat ion results shown in Figure 2.10 (a = 0.0125, fc = 3) 83 B.3 95% Confidence intervals for the M S T D M simulation results shown i n Figure 2.11 (a = 0.05, Jfc = 2) 86 v i i i Acknowledgements I would like to thank my supervisor, D r . H . W . Lee, for his encouragement and advice. F inanc ia l support from his N S E R C grant No . A5986 is also gratefully acknowledged. ix Chapter 1 Introduction 1.1 Background The concept of local area networks (LANs) emerged when there was a dramatic increase in the number of small independent computing systems, especially in the form of microcomputers, as a result of the continuing decline in the cost of comput-ing hardware. In an establishment, these machines may be dedicated to perform specific functions. However, there is a need for them to communicate with each other in order to exploit the advantages of functionally distributed computing and share the resources effectively. This communications network is regarded as a L A N which interconnects locally distributed computing systems. Generally, a L A N should satisfy a broad set of requirements such as the ones listed as below [1]: • high data rates (typically 1 to 10 Mbps); • geographic distance spanning from one hundred meters to a few kilometers; 1 CHAPTER 1. INTRODUCTION 2 • abi l i ty to support a few hundred independent devices; • good rel iabi l i ty; • fair access to the network by al l devices; • easy instal lat ion of a small system, w i th graceful growth as the network evolves; • ease of reconfiguration and maintenance; and • low cost. The design of L A N s involves two important issues which are the topology of configuration and the coordination of access to the network (or the medium access control protocol) [2]. They are often closely related to one another. T w o general classes of physical l ink topologies are the r ing and the bus. In the r ing topology, the access methods typical ly employed are slotted-ring technique [3] and impl ic i t token-passing [4]. In the bus topology, the more common ones are contention technique [5] and explicit token-passing [6]. These protocols provide access by the nodes to the transmission medium i n a distributed coordination w i th packet-switched communications. One of the most successful designs of L A N s , which attempt to meet the re-quirements listed above, is the Ethernet [7]. It employs a bus communications channel which provides a passive broadcast medium. The access protocol used is the carrier-sense mult iple access wi th collision detection ( C S M A / C D ) protocol. It is a contention protocol which allows a number of users to share a single channel i n a random access manner w i th no central control. CHAPTER 1. INTRODUCTION 3 The L A N was primarily designed for data service. However, office automation has necessitated the integration of voice and data into a single L A N . There are two potential advantages of this implementation: • cost savings gained from the sharing of the transmission and the switching facilities; and • provisions of more sophisticated services to the users. Yet integrating voice and data creates a new set of communications problems, which are mainly due to their different traffic characteristics. Voice is periodic traffic that requires real-time delivery while data is bursty traffic that can tolerate long delays. Therefore, to make the integration possible, new medium access control protocols have to be applied, which can fulfil the different requirements for both voice and data traffic in LANs. There have been many new protocols proposed in this research area. When applied to a (implicit or explicit) token-passing or a slotted-ring network, they take the advantage of the round-robin approach in the access method, which bounds the channel access delay, to meet the demands of the periodic traffic from voice sources [8] [9]. However, because the channel access delay in contention technique is unbounded, it is not suitable for integrating voice and data. Usually it has to form a hybrid with the reservation scheme to suit this task [10]. Because of the popularity of applying the C S M A / C D protocol in LANs, typified by the numerous Ethernet installations, it can be a very attractive feature if these C S M A / C D LANs can be upgraded to provide voice and data services with minimal CHAPTER 1. INTRODUCTION 4 changes i n the system. The enhancement can be achieved by applying the movable-slot t ime-division mult iplexing ( M S T D M ) protocol to the network [11] [12]. It is a simple var iat ion on C S M A / C D , which enables voice and data integration i n a ran-dom access manner and has an upper bound on voice packet delay. In this protocol, data sources follow the same set of rules for transmission as i n C S M A / C D . There-fore, i n migrat ing from a C S M A / C D L A N to a M S T D M L A N , i t is not necessary to modify the data stations. New voice stations and voice /da ta hybr id stations can be added onto the network simply by tapping to the passive transmission medium. A s a result, M S T D M lends itself to be an attractive protocol for the integration of voice and data. L A N s are l imi ted by their geographic distance. They can work well over a dis-tance of a few kilometers. However, as they elongate, problems such as performance degradation and decline in reliabil i ty occur [13]. Solving the distance l imi ta t ion problem can increase the attractiveness of the office information system so that of-fice branches located at distant locations i n a metropol i tan area can become part of the network and can share information of voice and data [14-17]. Moreover, differ-ent companies can participate i n the same metropoli tan area network ( M A N ) and exchange information w i t h each other, in addit ion to communicat ing wi th in their own premises through the M A N . If the M A N supporting voice and data services can be expanded to the community, the local telephone subscriber loops can even be replaced by the network. Besides, new and advanced services such as home banking and home shopping can be provided in cooperation w i th the banking and merchan-dising companies. However, back to the problem addressed at the beginning, we first have to solve the distance constraint associated w i t h the networks before these CHAPTER 1. INTRODUCTION 5 new concepts can be put into realization. The introduct ion above has briefly reviewed the evolution from L A N s providing data-only service to M A N supporting voice and data integration. In the following parts of the thesis, attention is focused on the M S T D M protocol. The performance of this protocol is evaluated through mathematical analysis and simulat ion, for its applicat ion i n L A N s [18-20]. The method of applying the protocol to the M A N s , which have the potentialities to provide the services as described i n the previous paragraph, is also studied [21]. Because of the sui tabil i ty of the analyt ical model and the close relationship between C S M A / C D and M S T D M , a minor part of the thesis is devoted to the performance analysis of the C S M A / C D protocol. 1.2 Objective and Outline of the Thesis There have been some analyses on the performance of C S M A / C D in the literature, e.g. [22], [23] and [24]. In the first part of Chapter 2, a non-preemptive priori ty queueing model is proposed for analysing the mean delay-throughput performance of the slotted non-persistent C S M A / C D protocol. Th i s analyt ical model presents a simpler way of performance evaluation than the previous works. We shall see later that al though it is a simple approximate model, it provides very promising explicit results which are verified by simulation. Unl ike C S M A / C D , there has been no analyt ical result of the data delay per-formance of M S T D M before. In the second part of Chapter 2, a queueing model, which is similar to the one for C S M A / C D , is formulated for analysing the mean delay-throughput characteristic of data packets for the slotted M S T D M protocol CHAPTER 1. INTRODUCTION 6 with non-persistent data packet transmission. Numerical results are obtained from the analysis and compared with simulation results. The comparisons show that the analytical model proposed yields accurate results for the data delay performance of M S T D M . The M S T D M protocol can be considered as a more general case of the C S M A / C D protocol, which allows the integration of voice and data. Without voice, M S T D M degenerates to C S M A / C D . The purposes of including the performance analysis of C S M A / C D here are twofold. One is to look into the data delay performance of this more 'specific' protocol directly in our new approach. Another is to show the accuracy of this modeling approach before we apply it to analyse the M S T D M protocol. The analysis of M S T D M gives only the mean of data delay, but not its higher moments as well as any information on voice delay characteristics. In order to have a thorough understanding on the characteristics of M S T D M and to provide a means for verifying the delay analysis in Chapter 2, simulation was performed for this protocol. Since the first voice packet generated at the beginning of a talkspurt from an active voice source uses C S M A / C D as a data packet in the M S T D M system, we may give the former a shorter retransmission delay than the latter so as to reduce the channel-acquisition time for voice sources, as explained in Section 2.2.1. In the simulation studies, the same as well as different retransmission scheduling al-gorithms were applied to data packets and first voice packets. In each case, the effects of the M S T D M protocol on the delay performances of data packets, first CHAPTER 1. INTRODUCTION 7 voice packets and subsequent voice packets were obtained i n terms of the mean and the standard deviation of their delay. Chapter 3 shows the s imulat ion model, the s imulat ion results and the discussions. Because M S T D M is a bus contention protocol, its efficiency decreases inversely w i th the transmission rate and the channel length. The protocol works well on local area networks where the distance between the stations at the two ends is typical ly less than a few kilometers and the bit rate is in the order of 1 to 10 M b p s . W h e n it is applied to a metropoli tan area network w i t h a distance being an order of magnitude longer, the transmission rate should be decreased by an order of magnitude i n order to mainta in the same efficiency. However, this is incapable of providing adequate data and voice services to such a large community of users. In Chapter 4, a scheme which was proposed i n [16] to enable the M S T D M protocol to be applied efficiently to a large network is described. The approach is to divide the system into a number of broadband local area networks called homenets. However, the method for inter-homenet communications is not clearly examined i n [16]. In this thesis, we enhance the scheme by proposing an access protocol for the interconnection of homenets. It facilitates the communications between stations i n different homenets for both voice and data services. T h e issues about traffic control and addressing are also mentioned. Moreover, based on the analyt ical results obtained for M S T D M i n Chapter 2, we find the op t imum number of homenets for interconnection, which minimizes the mean data delay wi th in homenet. F ina l ly , Chapter 5 contains the conclusions which review the major results of the research work. Chapter 2 Performance Analysis of CSMA/CD and MSTDM In this chapter, a non-preemptive priori ty queueing model is first proposed for the performance evaluation of the slotted non-persistent C S M A / C D protocol . T h e n it is extended to a more 'general' voice/data model for the M S T D M protocol, a var i -at ion on C S M A / C D , which enables voice and data integration i n a random access manner w i t h an upper bound on voice packet delay. For each of the two protocols, the analysis yields explicit results for the mean delay-throughput characteristics of data packets. Numer ica l results are presented and discussed. A s comparisons w i th s imulat ion results show, the accuracy of the analysis is high although it is based on a simple approximate model . 8 CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 9 other transmission collision successful packet transmission i i i I I i i I I I l I 1 I I I I (> one arrival) Figure 2.1: Packet transmission using the slotted non-persistent C S M A / C D proto-2.1.1 Protocol Description The slotted non-persistent C S M A / C D protocol is considered here. In this proto-col , the t ime axis is (mini-)slotted w i th slot size equal to the end-to-end channel propagation delay (r second). Transmission can only be started at the beginning of a slot. A l l data sources are synchronized to follow this restriction. W h e n a data source has a packet ready for transmission, it senses the channel and proceeds as follows (also see Figure 2.1). 1. If the channel is sensed idle, i t initiates transmission of the packet. 2. If a collision is detected during transmission, the transmission is aborted and the packet is scheduled for retransmission at some later t ime which is deter-col . 2.1 CSMA/CD CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 10 mined by a retransmission scheduling scheme. T h e n the data source repeats the algori thm. 3. If the channel is sensed busy, the data source reschedules the transmission of the packet to some later t ime using the retransmission scheduling scheme and repeats the algori thm. 2.1.2 Analytical Model We assume, i n the following, that the number of data sources i n our C S M A / C D system is infinite and they collectively form an independent Poisson source w i th an aggregate mean packet arr ival rate of A2 packets/second. Moreover, the system is stable so that the input rate of data packets is equal to the output rate. There are two types of events that happen i n the channel. They are (successful) data packet transmission and data packet collision. We attempt to consider them as two independent processes and we term packet collision as transmission of collision packet. B y means of a suitable retransmission scheduling scheme [25], we assume that the probabil i ty of successful transmission i n a contention slot is maintained to be constant, which is independent of the number of packets i n the system. This constant probabil i ty is denoted by a factor l/v. Therefore, the mean arrival rate of collision packets is Ax = {y — 1)A 2 packets/second. If T is so small i n the C S M A / C D system that the durat ion of a collision can be neglected, we can approximate the system by the M / G / l queue because the arr ival of data packets is Poisson. A s we now consider packet transmission and packet coll ision as two independent processes, we attempt to model each of them w i t h the CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 11 Figure 2.2: Non-preemptive priori ty queueing model for C S M A / C D . M / G / l queue and they together form a non-preemptive pr ior i ty queueing system (as shown i n Figure 2.2) i n which collision packets have a higher pr ior i ty of transmission than data packets. T h e mean arr ival rate of the former is A i packets/second whereas that of the latter is A2 packets/second. A s the analyt ical model is priori t ized, (successful) data packet transmission cannot occur while collision packet is present, which implies collision of data packets i n the system. However, the model is non-preemptive so that a data packet w i l l be transmitted unt i l completion i f it can acquire the channel successfully, i.e. no coll ision occurs at the beginning of the transmission. Under a stable condit ion of the model , the rat io of the number of data packet transmissions to the total of the two types of channel events is \Jv on the average. In the next section, we shall use this model to find the delay-throughput perfor-mance of the slotted non-persistent C S M A / C D protocol. CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 12 2.1.3 Delay Analysis For the M / G / l model w i th two non-preemptive priorities like the one shown in Figure 2.2, we denote the packets i n the higher priori ty queue as the class 1 packets and the ones i n the lower pr ior i ty queue as the class 2 packets. The lengths of class 1 packet and class 2 packet are respectively rhi and ra2, which may be random variables of any distr ibut ion i n second. The mean wai t ing t ime ( W 2 ) of class 2 packets i n this model (see Append ix A) is given by 2(1 — A 1 m 1 ) ( l — Xiffii — A 2 m 2 ) where m~i and m 2 are the mean lengths of class 1 packets and class 2 packets respectively, and m j and m 2 are the second moments. To model the C S M A / C D protocol, we assume the length of collision packets, i.e. the collision recovery time, is a mult iple of the end-to-end channel propagation delay T. Therefore, m i — mi — kr (2-2) where k is an integer. Because of propagation delay, the channel w i l l not be sensed idle right after a packet has been successfully transmitted. Thus , the length of class 2 packet is longer than the actual length of data packet by some propagation delay. We assume the difference is one end-to-end channel propagation delay. Therefore, m 2 = m + T (2.3) where m is the length of data packet and is assumed to be a mult iple of r . A s the channel is slotted, a packet has an addit ional wai t ing time of half a slot, i.e. r / 2 , on CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 13 the average. Th i s factor is not characterized by our analyt ical model. To make the correction, we have to add the term r / 2 to the mean wai t ing t ime of data packets i n (2.1). The mean delay of data packets is defined as the sum of the mean packet wai t ing t ime and the mean packet transmission time. For simplicity, here we let the length of data packets be constant, i.e. m = m. Us ing (2.1) to (2.3) and replacing A i w i th — l ) , we obtain the normalized mean delay (Dn) of data packets after d iv id ing the mean delay by m and it is given by P d [ f c W ^ - l ) + ( l + a) 2] a , n 2[1 - kpda{u - 1)]{1 - pd[l + a + ka{u - 1)]} 2 { ' } where Pd = A 2 m is the data throughput and a = r/m is the normalized end-to-end channel propagation delay. Note that as a goes to zero, (2.4) can be approximated by the M / D / l delay equation (see e.g. [26]) which is given by B " = 1 + 2 ( T ^ ) - <2-5> To find the m a x i m u m data throughput that the C S M A / C D system can achieve, we have, from our queueing model, that Aimx + A 2 m 2 < 1 (2.6) if the system is stable. This implies that for the C S M A / C D system, P d < l + a[k{v-l) + l) • (2'7) If retransmission is optimized by means of a suitable adaptive retransmission sche-dul ing scheme, the probabil i ty of successful transmission i n a contention slot is CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 14 l / e , i.e. \jv = l / e , which is the max imum for the slotted random access protocol [22] [25]. Therefore, substi tuting u = e into (2.7), we have P d < 1 + a[k(e- 1) + 1] • ( 2 - 8 ) 2.1.4 Numerical Results We use (2.4) to obtain the mean delay-throughput characteristics for data pack-ets of constant length. In the following examples, the collision recovery time is twice the end-to-end channel propagation delay, i.e. k — 2. A l s o we assume that retransmission is optimized so that we have v = e. Figure 2.3 shows the analytical results together w i t h the s imulat ion results for a=0.001, 0.01, 0.05, 0.1 and 0.2 respectively. We see from the figure that the curves obtained from both methods are very close to one another for each value of a. The results show that the performance of the C S M A / C D protocol declines w i t h a being increased. F r o m light to medium load (relative to the m a x i m u m throughput achievable for a particular a) of data traffic, the mean delay of data packets is quite small . However, it increases rapidly as the traffic becomes heavy. Th i s is a well-known characteristic for the performance of data packets using random access protocol for transmission. Moreover, the m a x i m u m throughput that can be achieved increases w i t h a being reduced because less channel capacity is wasted i n collisions and removals of signal propagation after successful packet transmissions. W h e n a is equal to 0.001, the delay curve of the C S M A / C D protocol is almost identical to the one obtained from the M / D / l delay equation in (2.5). Our s imulat ion model for the slotted non-persistent C S M A / C D assumes an in -CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 15 I 1 I L D = a-0.001 Data throughput Figure 2.3: Data delay-throughput characteristics for C S M A / C D (k = 2). CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 16 finite populat ion of data sources which collectively form an independent Poisson source. T o obtain the simulat ion results shown in Figure 2.3, we assume the length of data packets is constant and it takes the t ime of one end-to-end channel propaga-t ion delay to have the effects of signal propagation removed from the channel after a successful packet transmission. The adaptive retransmission scheduling algori thm that we use i n the simulation is binary exponential backoff. A s comparisons w i th the s imulat ion results show, the accuracy of our analysis turns out to be high a l -though it is based on a simple queueing model. The 95% confidence intervals for the C S M A / C D simulat ion results shown i n Figure 2.3 are listed i n A p p e n d i x B . l , together w i t h the analyt ical results for easy comparisons. 2.2 M S T D M 2.2.1 Protocol Description Speech from an active voice source consists of alternating intervals of talkspurt and silence. Dur ing talkspurt , voice packets are generated from digitized voice; however, there are none i n a silent period. The M S T D M protocol enables voice and data i n -tegration i n a random access manner [11][12]. A s it is a var iat ion on C S M A / C D , data packets are treated exactly the same in this protocol as i n C S M A / C D . More-over, the first voice packet generated at the beginning of a talkspurt from an active voice source follows the C S M A / C D protocol as a data packet. We consider here the slotted non-persistent M S T D M which has the same set of rules for both data packets and first voice packets as those given i n section 2.1.1 CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 17 W h e n speech energy is detected at the beginning of a talkspurt , transmission of the first voice packet is activated as soon as voice bits of the first voice sample arrive. Depending on the wai t ing time of this packet, there is a variable number of voice bits in i t . Ye t there is a m a x i m u m number of voice bits, say S, that can be placed i n the packet, because the packets generated by voice sources are constrained to have a fixed length as explained later. If there are more than S voice bits coded when the channel is acquired, only the last S bits are transmitted and the earlier ones are discarded; thus, the speech at the beginning is clipped. However, we shall see in the next chapter that we can give first voice packets a shorter retransmission delay than data packets i n order to reduce the channel-acquisition t ime for voice sources. In this way, the chance of voice bits being discarded is considerably decreased, yet the performance of data packets is not deteriorated significantly. After a voice source has successfully transmitted its first packet, it plans on t ransmit t ing its next packet in a fixed time T which is its period of transmission (Figure 2.4). W i t h i n a period, new voice bits arrive and fill up the data area of the voice packet. Subsequent voice packets i n a talkspurt after the first one follow a subset of the C S M A / C D rules. W h e n a voice source has a packet (other than the first one i n a talkspurt) ready for transmission, it senses the channel and proceeds as follows (also see Figure 2.5). 1. If the channel is sensed idle, it initiates transmission of the packet without listening to the channel. 2. If the channel is sensed busy, the voice source refrains from transmission and keeps on listening to the channel. W h e n the channel becomes idle, i t initiates CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 18 other transmission collision successful first voice packet transmission second voice packet transmission i i V// / / A 1 1 1 • • • • 1 1 1 1 A 1 \ 1 \ 1 \ (> one arrival) Figure 2.4: First voice packet transmission using the slotted non-persistent M S T D M protocol. other transmission voice packet transmission Figure 2.5: Subsequent voice packet transmission. CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 19 transmission of the packet without listening to the channel. (Note that the rules above represent the 1-persistent C S M A without collision de-tection protocol.) For the slotted M S T D M , a l l voice sources are synchronized to start transmission only at the beginning of a slot as data sources. In the following, we call the sub-sequent voice packets i n a talkspurt after the first one simply as voice packets and that first one as the first voice packet. We find that a voice packet may experience collision w i th data packet(s) and/or first voice packet(s) in the vulnerable inter-val . Moreover, extra voice bits keep on arr iving during the wait ing t ime of a voice packet, wh ich cannot be carried i n the data area of the packet. To overcome these problems, voice packets have a specific packet format which is shown i n Figure 2.6, together w i t h the format of data packets for comparison. It consists of a preempt area, a header area, a data area and an overflow area. W h e n a voice source initiates transmission of a voice packet, it places a signal (which forms the preempt area of the packet) on the transmission media but does not send information during the vulnerable interval. Th i s interval is long enough for data sources as well as voice sources t ransmit t ing their first voice packets to detect a coll ision, stop transmitt ing, and have the effects of their transmission removed from the channel before the voice source begins t ransmit t ing useful data. A s first voice packets use C S M A / C D , they do not have a preempt area. If we restrict the length of data packets to be equal to or less than that of voice packets, the m a x i m u m wai t ing time incurred by a voice source is never greater than one voice packet transmission t ime after it has successfully transmitted the first CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 20 preempt packet data overflow area header area area (a) voice packet (b) data packet Figure 2.6: Packet formats for M S T D M . voice packet i n a talkspurt . A s voice bits arrive continuously, the overflow area is used for accommodating those voice bits which arrive while a voice source is wai t ing for transmission, and i t is long enough to carry a l l of the extra voice bits while a voice source is delayed by as much as one voice packet transmission time. The voice source loses the privilege of not listening while t ransmit t ing after a talkspurt is over. In the next talkspurt after a silent period, the first voice packet has to be t ransmit ted according to the whole set of the C S M A / C D rules. A l s o , coll ision among voice packets never occurs because voice sources plan on t ransmit t ing their next packet one period after they have successfully acquired the channel. For the transmission of the subsequent voice packets i n a talkspurt after the first one, a data source cannot delay a voice source enough to make it collide wi th CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 21 another voice source. Figure 2.7 shows the si tuation when the periodic transmission of voice packets is delayed by a data source. We see that voice sources appear to acquire T D M slots for transmission. Yet these periodic slots are repositioned when other transmissions interfere w i th them. Tha t is why it is called movable-slot T D M protocol. 2.2.2 Analytical Model In the following, the phrase 'data packets' includes both actual data packets and first voice packets. W e assume the former and the latter have the same retransmission delay dis t r ibut ion so that they behave without any difference from each other i n the system. There are three types of events i n the M S T D M channel. They are voice packet transmission, (data) packet collision and (successful) data packet transmission. We know from the protocol description that collision of voice packet w i th data packet has no effect on the voice packet transmission because useful information is not sent i n the preempt area of voice packet. Thus , a voice source t ransmit t ing voice packet is oblivious of data packet transmission and once the channel becomes idle, a ready voice source can acquire the channel successfully. Voice packet transmission has, therefore, the highest pr ior i ty of acquiring the channel among the three types of channel events, but it is non-preemptive as voice sources listen before t ransmit t ing. F r o m section 2, we see that the performance of data packets for C S M A / C D can be approximately analysed by a non-preemptive priori ty queueing model. Here we attempt to extend this model to include voice packets for formulating an approx-CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 22 <1 • • • PD PB,+i • • • i \ J \ 1 \ 1 \ 1 \ 1 \vA VB D VA VB VA VB VA — packet arrival from voice source A VB — packet arrival from voice source B D — bursty data packet arrival PAI — ith packet from voice source A PBJ — jth packet from voice source B PD — data packet Figure 2.7: Periodic transmission of voice packets and their repositioning when delayed by other transmission. CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 23 buffer size = i Figure 2.8: Non-preemptive pr ior i ty queueing model for M S T D M . imate model for the M S T D M protocol. T h e n we solve for the delay performance of data packets. O u r extended model as shown in Figure 2.8 is the M / G / l sys-tem w i t h three non-preemptive priorities. Queue 1 which has the highest pr ior i ty of transmission contains voice packet. The next priorities are queue 2 and then queue 3, which contain collision packets and data packets respectively. Note that queue 1 is single-buffered whereas the other two have infinite storage. Wi thou t queue 1, the model i n the present case is identical to the one i n Figure 2.2. We have the same assumptions for data packets and collision packets here as those given in section 2.1.2. Assuming the number of active voice sources i n our system is large (but finite), we attempt to replace the process of voice packet generation by an independent CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 24 Poisson source. However, not a l l the voice packets generated by this source con-tr ibute to the voice traffic i n our model as we shall see below. For the M S T D M protocol, we know that there is no contention of voice packet transmissions, since at most one voice packet can be wait ing for transmission at a time. To characterize this property i n our model , we assume that queue 1 is single-buffered so that any voice packet arr ival from the Poisson source is blocked off and lost while one voice packet is wai t ing for transmission i n the queue. On ly those voice packets that get into the queueing system for transmission form the voice traffic for our analysis. In the next section, we shall make use of this model to analyse the data delay performance of the M S T D M protocol w i t h voice throughput i n the channel as a system parameter. 2.2.3 Delay Analysis For the queueing model shown in Figure 2.8, we denote the packet i n queue i as the class i packet where i =1, 2 or 3. We assume that the lengths of the three classes of packets, which are denoted by m u ra2 and m 3 for classes 1, 2 and 3 respectively, are constant for simplifying the analysis. Moreover, the mean packet arr ival rates at the queues are A i , A 2 and A3. Under a stable condition, the throughputs of class 2 and class 3 packets are A 2 m 2 and A 3 m 3 respectively. To calculate the throughput of class 1 packets, we first denote their mean wait ing time in queue 1 by Wi- Since queue 1 has only one buffer, a l l packet arrivals are s imply blocked off i f it is occupied. F r o m the t ime that a class 1 packet leaves the queue for transmission to the next arr ival , the CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 25 V A < > class 1 arr ival Figure 2.9: Remaining transmission time seen by a class 1 arr ival . mean durat ion is l / A i because the interarrival t ime is exponentially distr ibuted. The mean number of class 1 arrivals at the queue is, by expectation, given by 1 Ax Thus , the throughput of class 1 packets is A j r o i / ( l + AiVK x) . (2.9) Define Pi -Ajmi -, pi = A 2m 2, ps — A 3m 3 . (2.10) i + AiWy We are next going to find the mean wai t ing times of class 1, 2 and 3 packets i n the queues, which are respectively denoted by V 7 1 , H / 2 and W3. Class 1 Assume there is a class 1 arr ival while another class 1 packet is being transmitted as shown i n Figure 2.9. Let Y\ denote the remaining transmission time seen by the CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 26 arr iv ing class 1 packet. Now, e - A i ( m 1 - t / ) ( ' ^ _ g - A i y \ Prob [Yi < y|packet length = mi] = _ _ A i m i (2.11) and its probabi l i ty density function is f(y|packet length = m i ) = _ e _ A i m i • (2.12) Thus , Yi = / yf(y|packet length = m i ) dy Jo m i (2.13) 1 - e - * i m i Xi ' Similar ly , the mean remaining transmission times of class 2 and class 3 packets seen by a class 1 arrival (which successfully goes into queue 1) are, respectively, TT m 2 1 1 - e~x^ A i and (2.14) ^ 3 = — • (2.15) 1 - e-^m* A i v 1 Thus , the mean wai t ing time of class 1 packets is given by W1 = p i F i + p2Y2 + p3Y3 . (2.16) F r o m (2.16), we have, after some manipulations, {Wi.)2 - fiWt + -y = 0 (2.17) where = X2m\ X3ml _ 1 CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 27 1 / A 2 m 2 A 3 m 3 A 7 = A T r + ^ r + — j- + \2m\ + A 3 m | 1 - e - A i m x A i ( l - e - A i m 2 ) A i ( l - e - A i m 3 ) (2.19) F r o m (2.17), we have Wi = (2.20) Class 2 We have, by expectation, that the mean wait ing time of class 2 packets is given by (see e.g. [26]) W2 = mean remaining transmission time seen by the class 2 arr ival + mean transmission time for the packets i n peer and higher pr ior i ty classes, which have already been in the queues at the class 2 arr ival + mean transmission time for the packets i n higher pr ior i ty class, which arrive during the wai t ing time of the class 2 packet . (2-21) This implies ^ psms ^ X1Wimt 2 2 2 ^ * ' 1 + A i W i V ' where iVt- represents the mean number of class i packets in queue i for i=l, 2 or 3. B y Li t t le ' s Formula , we have CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 28 Note that the term XiW2rrii/(l + ^1^1) m (2.22) is an approximation for the th i rd component of W2 i n (2.21), since the arr ival d is t r ibut ion of class 1 packets (those which get into queue 1 successfully) is not Poisson because of the blocking. To simplify the analysis, we assume the arr ival is Poisson wi th mean A i / ( 1 + Ait-V^) here. F r o m (2.22), we have (1 + A 1 ^ 1 ) ( l - A 2 m 2 ) - Air rn V ; where Class 3 Simi lar to class 2, the mean wait ing t ime of class 3 packets is given by m pxmi p2m2 p3m3 J^— XiW^rm — W3 = —^— + -j- + — ^ — + 2^ Nirrii + i + ^— + X2W3m2 (2.26) where by Li t t le ' s Formula , N3 = X3W3 . (2.27) After some manipulations, we have, from (2.26), W3 = $ + + ™0 + X2m2W2{i + XiWj) 2g^ (1 + A 1 W 1 ) ( 1 - A 2 m 2 - A 3 m 3 ) - A i m i Reca l l that W3 denotes the mean wai t ing time of data packets for the M S T D M protocol. T o be specific for modeling the performance measure, we have to incor-porate the system characteristics into the equations we have obtained above. For M S T D M , the length of data packets cannot be longer than that of voice packets. In CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 29 our model, as data packets represent a mixture of actual data packets and first voice packets, the assumption of constant packet length, which is made at the beginning of this section, has impl ic i t ly set the length of data packets to be equal to that of voice packets because first voice packets and voice packets are of the same fixed length. Here we denote their length by m which is assumed to be a mult iple of the end-to-end channel propagation delay r . Define Pd \3rr1, the data throughput pv = A x m A x r a Pv = Pv , the voice throughput (2.29) (2.30) (2.31) 1 + X1W1 1 + pvWln where Wln is the normalized value of Wi w.r.t . ra; and V F 2 n and WSn have the similar meaning i n the following. Using the same assumptions and symbols we have made for C S M A / C D i n section 2.1.3, we have (2.32) where Pn = Pd Jfc 2a 2(i/-1) + (1 + a) 2 1 _ e-kapv 1 _ e-(l+a)pv — {1 + pd[l + a + ka{v - 1)}} (2.33) Pv In = ^ \ l + a + ^[l + a + ka{u-l)] Pv I Pv (1 + tt)2 Pd 1 - e-( 1 + 0 [)^ pv k2a2{v-l) + (1 + a) 2 -kapv 1 _ e-(l+a)h (2.34) W 2n $n + PvWln{l + a + $n) (1 + pvWln)[l - ka{u - l)pd] - pv{l + a) (2.35) CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 30 where 1 \ pv(l + a)> 2 \ l + faWln + pd[(l + a)2 + k2a2(is-l)} (2.36) W = ®n + PvW^jl + a + $n) + koi{u - l)PdW2n{l + p „ ^ l n ) 3 n (1 + PvWln){l - pd[l + a + ka{u - 1)]} - Pv(l + a) (2.37) We have mentioned before that because the channel is slotted, a packet has an addit ional wai t ing t ime of half a slot on the average. We neglected this factor in our analysis. Thus , we have to add the term r / 2 to the mean wai t ing t ime of data packets i n (2.37). Therefore, the normalized mean delay of data packets is, after some manipulat ions, given by We notice that i n (2.38), the normalized mean data delay Dn is expressed in terms of pd and pv. To compute the voice throughput pv from given values of pd and p„, we first use (2.32) to find Win. T h e n we can take (2.31) and the value of W i n just obtained to calculate the voice throughput pv to which the given pair of pd and pv corresponds. 2.2.4 Numerical Results Dn = 1 + WSn + | (2.38) In the following numerical results, we assume that retransmission of data packets is opt imized by means of a suitable adaptive retransmission scheduling scheme so that the probabi l i ty of success in contending for an empty slot among data sources CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 31 is l / e , i.e. v = e. In Figure 2.10 and Figure 2.11, we plot the data delay-throughput characteristics at various values of pv using numerical results as well as s imulat ion results. The values of the system parameters used i n Figure 2.10 are a=0.0125 and k=S whereas they are respectively 0.05 and 2 i n Figure 2.11. F r o m the figures, we observe that the data delay-throughput characteristic for M S T D M displays the same trend as that for C S M A / C D . Al so , the delay perfor-mance declines apparently when the voice throughput pv i n the channel increases. Th i s is obvious because voice packets occupy part of the channel capacity for trans-mission. W i t h a higher voice throughput, the max imum of the data throughput that can be achieved is reduced relatively. W h e n voice throughput decreases, the data delay curve approaches that of C S M A / C D as expected. In our s imulat ion model for the slotted M S T D M protocol, we assume there is an infinite populat ion of data sources which collectively form an independent Poisson source. The number of voice sources is, on the other hand, finite and we assume al l of them are active. B y varying the number of voice sources, we can change the level of voice throughput i n our system. A s we have done for the analysis, the first voice packets are considered as part of the data packets i n the simulation. The actual data packets have the same length as the packets generated by voice sources. Moreover, it takes the time of one end-to-end channel propagation delay to have the effects of signal propagation removed from the channel after a packet transmission. The adaptive retransmission scheduling algori thm used is binary exponential backoff which is applied to both data packets and first voice packets. A more detailed description of the simulation model is given i n the next chapter. The 95% confidence intervals for the M S T D M simulat ion results shown i n Figure 2.10 CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 32 0.4 0.S 0.6 Data throughput Figure 2.10: D a t a delay-throughput characteristics for M S T D M (a = k = 3). 0.0125, CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 33 I 1 1 1 I I L analysis simulation >> a T J C 2 0.000 0.045 0.146 0.292 0.439 0.586 i o.o 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Data throughput T—" 0.7 0.8 1.0 Figure 2.11: D a t a delay-throughput characteristics for M S T D M (a = 0.05, k = 2). CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 34 and Figure 2.11 are listed i n Append ix B . 2 , together w i th the analyt ical results for easy comparisons. F ina l ly , we see from the figures that the curves obtained from the analysis and the s imulat ion match very well w i t h each other. Th i s shows that our analysis gives very good approximate results for the data delay performance of the M S T D M protocol. P u t t i n g the delay-throughput characteristics (from the numerical results) i n F i g -ure 2.10 and Figure 2.11 in another form, we have Figure 2.12 and Figure 2.13. They show the data delay versus the fraction of data load at constant channel throughput (sum of the throughputs of voice and data) for the two sets of parame-ters. There are some interesting points noted on these curves. We see from Figure 2.12 that the data delay is reduced as the fraction of data load increases. Th i s is because i f the fraction of the load generated by voice sources decreases (or the fraction of data load increases), the number of sources which have a higher pr ior i ty of transmission than data sources decreases. A s a result, the delay experienced by data sources decreases. In Figure 2.13, the data delay also shows the same charac-teristic at low channel throughput, but the decrease is comparatively smaller. A s the channel throughput becomes rather high, it changes from decrease to increase. The reason for this is that when the load of channel traffic is heavy and collisions of data packets waste a significant port ion of the channel capacity (the collision recovery t ime is 1/10 of the packet transmission t ime i n Figure 2.13 whereas i t is only 3/80 i n Figure 2.12), the increase i n the number of data collisions counteracts the effect of having fewer number of voice sources as the fraction of data load in -creases. Therefore, the increase in the data delay is a result of the increased-channel contention. CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 35 Figure 2.12: Data delay versus fraction of data load for M STDM (a = fc = 3). 0.0125, CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM Figure 2.13: D a t a delay versus fraction of data load for M S T D M (a = 0.05, A; = CHAPTER 2. PERFORMANCE ANALYSIS OF CSMA/CD AND MSTDM 37 2.3 Summary We have proposed a non-preemptive pr ior i ty queueing model for evaluating the mean delay-throughput performance of the slotted non-persistent C S M A / C D pro-tocol. This analyt ical approach has also served as a stepping stone for formulating a s imilar approximate model for the M S T D M protocol. The analysis here is the first piece of work done on the data delay performance of M S T D M and yields explicit results for the mean data delay-throughput characteristics. For each analysis of the two protocols, numerical results have been presented and discussed. A s compar-isons w i t h s imulat ion results show, the accuracy of the analysis is h igh although it is based on a simple approximate model. Chapter 3 Simulation of MSTDM The analysis in the previous chapter provides a method for evaluating the mean delay-throughput performance of data packets for M S T D M . However, it does not give the higher moments of data delay as well as any information on voice delay characteristics. To gain a deeper understanding on the characteristics of M S T D M , simulation was done extensively to evaluate the delay performance of voice and data for this protocol. In this chapter, we first present the simulation model for the M S T D M protocol which is described in Section 2.2.1. Then we show the simula-tion results and discuss the delay characteristics of both voice and data. Moreover, we find that if we give the first voice packet generated at the beginning of a talk-spurt a shorter retransmission delay than data packet, we can considerably reduce the channel-acquisition delay for voice sources without sacrificing the data delay performance significantly. 38 CHAPTER 3. SIMULATION OF MSTDM 39 3.1 Description of the Simulation Model In our s imulat ion model for the M S T D M protocol, we assume there is an infinite populat ion of data sources which collectively form an independent Poisson source. The number of voice sources is, on the other hand, finite and we assume all of them are engaged i n ta lking activities. B y varying the number of voice sources in the M S T D M simulator, we can change the level of the throughput of voice packets 1 . The durations of the talkspurt and the silent period are assumed to be expo-nentially distributed [27] w i th means 1 sec and 1.4 sec respectively. The period of transmission for voice sources is 28 msec. Therefore, first voice packets contribute to 2.8% of the total number of packets generated by voice sources. The coding rate for speech is 64 Kbps . Thus , the number of voice bits which arrive i n 28 msec is 1792. Th i s is the size of the data area of voice packet. Including the space required for preempt area, packet header and overflow area, we let the voice packet length be 2000 bits. The channel transmission rate i n our system is assumed to be 10 M b p s and so the transmission time of a voice packet is 200 /zsec. The number of voice bits which arrive i n the interval of one voice packet transmission time is 12.8 bits. The size of the overflow area is, therefore, 13 bits. In this s imulat ion, we assume data packets have a fixed length which is the same as that of first voice packets and voice packets. A s the slotted M S T D M protocol is considered here, we assume the t ime axis is divided into slots. T h e size of a slot is equal to the end-to-end channel propagation 1If we set the number of voice sources to be zero, the MSTDM simulator will become a CSMA/CD one. We do this to run simulation for the CSMA/CD protocol. The results obtained are used for verifying the analytical results in Section 2.1.4 CHAPTER 3. SIMULATION OF MSTDM 40 delay. Since transmission can only be started at the beginning of a slot, the packet transmission t ime is assumed to be a mult iple number of slots in our M S T D M simulator. Because of the effect of signal propagation, the channel w i l l not be sensed idle right after a packet has been completely transmitted. We assume it takes the t ime of one slot to have this effect removed from the channel for each packet transmission. Moreover, when data packets and/or first voice packets have a coll ision, the t ime that i t takes for the channel to recover from busy state to idle state is a mult iple number of slots. There are two parameters that specify the simulated system. The first is the nor-malized end-to-end channel propagation delay (a) which is defined as the quotient of the end-to-end channel propagation delay divided by the packet transmission time. Another parameter is the normalized collision recovery time which is given by kct, where A; is the number of slots required to recover from a collision. A s data packets and first voice packets may experience collision i n the vulnerable interval, they have to be retransmitted according to a retry scheme. In our s imulat ion stud-ies, we have attempted to apply the same as well as different retry schemes to data packets and first voice packets. In the first case, we use the binary exponential backoff ( B E B ) algori thm to schedule retransmission for both of them. In our B E B , if a packet has just experi-enced its C t h collision, it w i l l be transmitted at the point R slots from the time the source senses the channel idle, where R is picked up uniformly from the interval {0, 2' — 1} slots and i=rmn{C, 8 } . If the channel is busy at the t ime of retransmis-sion, the rescheduling procedure above wi l l be repeated at the same interval for the selection of retransmission time. Note that i f a packet has suffered eight collisions or CHAPTER 3. SIMULATION OF MSTDM 41 more, the retransmission interval w i l l s t i l l remain at 255 slots un t i l i t is successfully transmitted. In the second case, we use the B E B algori thm for data packets and the linear incremental backoff (LIB) algori thm [28] for first voice packets. L I B implies that the retransmission t ime is picked up uniformly from the interval {0, C} slots, where C is the number of collisions a packet has suffered. For other details, L I B is the same as B E B . B u t we do not put an upper l imi t on the retransmission interval for L I B . We notice that the retransmission delay i n L I B should be much shorter than that i n B E B on the average. The M S T D M simulator is implemented i n the high-level language ' C . O u r prime objective of running the simulator is to evaluate the delay performances of the three types of packets. We have run the simulator for two pairs of system parameters. The first pair are a = 0.0125 and k = 3 whereas another pair are a = 0.05 and k = 2. If the speed of signal propagation i n the channel is assumed to be two-third of that of l ight, the first a implies a slot size of 2.5 jusec which corresponds to a channel length of 500 m and the other is 10 fisec, a channel length of 2 K m . For each of the two simulated systems, we have applied the same as well as different retry schemes to data packets and first voice packets as described above. B y comparing these two cases of retransmission scheduling, we can find out the effects on the delays of first voice packets and data packets i f the former is given a shorter retransmission delay than the latter. A t ime span of about five minutes i n the real M S T D M system is simulated for each run. We believe that this is sufficient for obtaining reasonable statistical results CHAPTER 3. SIMULATION OF MSTDM 42 for our performance evaluation. The simulation results obtained verify this c la im as they show definite trends consistently. 3.2 Simulation Results and Discussions In the following, when data packets and first voice packets adopt the B E B algori thm for retransmission, the word 'data ' is used to include both of them. Th i s is because if the former and the latter have the same retransmission delay dis tr ibut ion, they w i l l behave without any difference from each other i n the system. However, when data packets use B E B and first voice packets use L I B , we have to mention them distinctly. In the simulat ion, the delay performances of the three types of packets were respectively obtained i n terms of the mean and the standard deviat ion of their delay. The packet delay i n the following figures is i n the unit of packet transmission t ime and the throughput is i n the unit of packet per packet transmission time. Figure 3.1 through Figure 3.4 show the simulat ion results for the two sets of system parameters when bo th data packets and first voice packets use the B E B algori thm. The mean and the standard deviation of packet delay versus the data throughput are plotted at constant voice throughput (pv) for data packets and voice packets i n each simulated system 2 . F r o m Figure 3.1 and Figure 3.3, we see that the data delay performance declines apparently when the voice throughput pv i n the channel increases. Th i s is obvious because voice packets occupy part of the channel capacity for transmission and 2The mean data delay of the simulation results obtained in this case has been used to verify the analysis on the performance of MSTDM in Chapter 2. CHAPTER 3. SIMULATION OF MSTDM 43 1 1 1 1 ' TJ s a •a c • = p- 0.000 o = p- 0.044 " = p- 0.147 • = p - 0.293 x =p- 0.437 o = p- 0.585 » = £ - 0.738 0.4 0.9 0.8 Data throughput (a) M e a n data delay 0 4 0.5 o.e Data throughput (b) Standard deviat ion of data delay Figure 3.1: Delay characteristics of data packets when both first voice packets and data packets use B E B for retransmission (a = 0.0125, k = 3) CHAPTER 3. SIMULATION OF MSTDM 44 0.4 0.5 00 Data throughput (a) M e a n voice delay So > 2 •O rt •O 2 2 tn a = p - 0.044 o = p - 0.147 A = p - 0.293 • = p - 0.437 x = p - 0.585 o = p - 0.738 0.4 05 0.6 Data throughput (b) Standard deviation of voice delay Figure 3.2: Delay characteristics of voice packets when bo th first voice packets and data packets use B E B for retransmission (a = 0.0125, k = 3) CHAPTER 3. SIMULATION OF MSTDM 45 0.4 0.5 0.6 Data throughput (a) M e a n data delay 4) T3„ •o C D = p- 0.000 ° = p- 0.045 a = p - 0.146 * = p - 0.293 « =p- 0.439 • = p - 0.586 0.4 0.3 0.6 Data throughput (b) Standard deviation of data delay Figure 3.3: Delay characteristics of data packets when both first voice packets and data packets use B E B for retransmission (a = 0.05, k = 2) CHAPTER 3. SIMULATION OF MSTDM 46 o = p - 0.045 o = p - 0.146 A = p - 0.292 • = p - 0.439 * = p - 0.586 0.3 0.4 0.5 0.6 0.7 Data throughput (a) M e a n voice delay •a 6 a •a • • = p- 0.045 o = p - 0.146 4 = p - 0.292 * =p- 0.439 » = p - 0.586 0.4 0 5 0.8 Data throughput (b) Standard deviation of voice delay Figure 3.4: Delay characteristics of voice packets when bo th first voice packets and data packets use B E B for retransmission (a = 0.05, k = 2) CHAPTER 3. SIMULATION OF MSTDM 47 have a higher pr ior i ty of transmission than data packets. W i t h a higher voice throughput, the m a x i m u m of the data throughput that can be achieved is reduced relatively. F r o m light to medium load of data traffic (relative to the m a x i m u m data throughput achievable), the mean and the standard deviation of data delay are quite small except at heavy load of voice traffic. However, they increases rapidly when the data throughput is high. This is a well-known characteristic for the performance of data packets using random access protocol for transmission. Compar ing the curves i n Figure 3.1 and Figure 3.3, we find that the delay performance is better for a = 0.0125 and k = 3 than for a = 0.05 and k = 2. Th i s is because collisions of data packets and removals of signal propagation after packet transmissions waste a more significant port ion of the channel capacity in the latter case. Note that when the voice throughput is zero, the curves i n Figure 3.1 and Figure 3.3 show the data delay performance of the slotted non-persistent C S M A / C D protocol. In Figure 3.2 and Figure 3.4, we show the voice delay performance. We see that the mean delay of voice packets increases almost linearly w i th the data throughput when we keep the voice throughput constant. A t the same channel throughput (sum of the throughputs of voice and data), the voice delay is much smaller when the channel is dominated by voice load than by data load. The reason is that voice packet transmissions do not interfere w i th each other as they are periodic and separable. O n the other hand, data packet transmissions are bursty and so they may interfere w i th the periodic transmissions of voice sources. Therefore, the overflow area i n voice packets is more ut i l ized when the data throughput becomes higher. Yet we observe from the results that the mean wai t ing time of voice packets CHAPTER 3. SIMULATION OF MSTDM 48 is well below one packet transmission time i n al l cases of our simulat ion. For the standard deviation of voice delay, we find that it increases rapidly w i th the data throughput at the beginning, but its characteristics become leveled or even dropping slightly at high data throughput. Th i s is i n sharp contrast to the standard deviation characteristics of data delay. It is because data delay is unbounded while there is an upper l imi t of one packet transmission time on voice packet wai t ing time. W h e n B E B is used for data packets and L I B for first voice packets, the simulat ion results for the two sets of system parameters are shown from Figure 3.5 to Figure 3.10. In this case, we have separate figures for data packets, first voice packets and voice packets. The characteristics of the packet delay versus the throughput of data plus first voice packets are plotted. Compar ing the curves i n Figure 3.5 and Figure 3.8 w i t h the ones i n Figure 3.1 and Figure 3.3, we see that the data delay performance is nearly unaffected when first voice packets are given a shorter retransmission delay than data packets, except at very high voice throughput. The reason for this is that the load of first voice packets is light in the channel as there is only one first voice packet i n each talkspurt . They represent 2.8% of the total number of packets generated by voice sources i n the simulat ion. Therefore, as comparison w i t h the previous case shows, giving first voice packets a faster retransmission does not deteriorate the data delay performance significantly unless the channel is highly ut i l ized by voice sources, i.e. the s i tuat ion where the channel is congested and the load of first voice packets is larger than or comparable to that of data packets. However, by doing so, we can improve the delay performance of first voice pack-CHAPTER 3. SIMULATION OF MSTDM 49 -fcs. •e e D = p- 0.000 o = p- 0.045 o = p - 0.147 • = p- 0.293 * = p- 0.439 o = p- 0.583 " = p- 0.734 0 2 0.3 0.4 0 5 0.6 0.7 Throughput of data plus first voice packets (a) M e a n delay of data packets a 5 •o >*3. •a •o u «B TJ C 5 - 0.000 - 0.045 - 0.147 - 0.293 - 0.439 - 0.583 p- 0.734 0 3 0.4 0 5 0.S 0 7 Throughput of data plus first voice packets (b) Standard deviation of data packet delay Figure 3.5: Delay characteristics of data packets when first voice packets use L I B and data packets use B E B for retransmission ( a = 0.0125, k = 3) CHAPTER 3. SIMULATION OF MSTDM 50 (b) Standard deviation of first voice packet delay Figure 3.6: Delay characteristics of first voice packets when first voice packets use L I B and data packets use B E B for retransmission (a = 0.0125, k = 3) CHAPTER 3. SIMULATION OF MSTDM 51 > o = p - 0.045 o =p- 0.147 a = p- 0.293 • = p - 0.439 « = p- 0.583 o = p- 0.734 2 0.3 0.4 0.3 0.6 0 7 Throughput of data plus first voice packets (a) Mean delay of voice packets •v T3 c • = p- 0.045 o =p- 0.147 « = p - 0.293 * = p - 0.439 x =p- 0.583 « = p - 0.734 oo 0.3 0.4 0.3 0.6 0.7 Throughput of data plus first voice packets (b) Standard deviation of voice packet delay Figure 3.7: Delay characteristics of voice packets when first voice packets use LIB and data packets use B E B for retransmission (a = 0.0125, k = 3) CHAPTER 3. SIMULATION OF MSTDM 52 • •o e • = p- o.ooo o = p- 0.044 4 =p- 0.147 * = p- 0.292 « = p- 0.444 o = p- 0.586 2 0.3 0.4 0.3 0.8 0 7 Throughput of data plus first voice packets (a) M e a n delay of data packets o c o *3 (d Pb. T) TJ fc. <B •o c S tn = p- 0.000 = p- 0.044 = p- 0.147 = p- 0.292 • p- 0.444 = p- 0.586 0 3 0.4 0.3 0.8 0.7 Throughput of data plus first voice packets (b) Standard deviation of data packet delay Figure 3.8: Delay characteristics of data packets when first voice packets use L I B and data packets use B E B for retransmission ( a = 0.05, A; = 2) CHAPTER 3. SIMULATION OF MSTDM 53 Figure 3.9: Delay characteristics of first voice packets when first voice packets use L I B and data packets use B E B for retransmission (a = 0.05, k = 2) CHAPTER 3. SIMULATION OF MSTDM 54 a = p- 0.044 o = p- 0.147 4 = p- 0.292 • = p- 0.444 * = p- 0.586 0.3 0.4 0.5 0.8 0 7 Throughput of data plus first voice packets (a) M e a n delay of voice packets a> •O Us-•v c S tn a a = p- 0.044 o = p- 0.147 » = p- 0.292 • = p- 0.444 x = p- 0.586 0.3 0.4 O S 0.8 0.7 Throughput of data plus first voice packets (b) Standard deviation of voice packet delay Figure 3.10: Delay characteristics of voice packets when first voice packets use L I B and data packets use B E B for retransmission ( a = 0.05, k = 2) CHAPTER 3. SIMULATION OF MSTDM 55 ets considerably. Th i s can be seen by comparing Figure 3.6 and Figure 3.9 wi th Figure 3.1 and Figure 3.3. Note that the data delay i n Figure 3.1 and Figure 3.3 also refers to the delay of first voice packets as mentioned at the beginning of this section. The comparisons show that the delay of first voice packets grows more slowly and more steadily w i th the increase of data load i n the channel when they have a shorter retransmission delay than data packets. Therefore, although both first voice packets and data packets use C S M A / C D , the former can be transmitted i n a shorter t ime than the latter on the average. Th i s gain is more remarkable when data load occupies a considerable por t ion of the channel capacity. We know from the protocol description that the first voice packet needs to be t ransmit ted w i th in one period of voice transmission if the speech at the beginning of a talkspurt is not to be cl ipped. In our M S T D M simulator, the packet transmission t ime is 200 /^sec (at a channel transmission rate of 10 Mbps) and the period of voice transmission is 28 msec. F r o m the simulation results, we see that the first voice packet delay is just i n the order of millisecond even at h igh channel throughput when both data packets and first voice packets adopt the B E B algor i thm for re-transmission. Th i s delay should be well below 28 msec most of the t ime. Therefore, it may not be needed to give a faster retransmission for first voice packets although it can s t i l l help minimize the chance of voice bits being discarded without affecting the data delay performance significantly. However, i f the channel transmission rate is lowered to 1 M b p s , the packet trans-mission t ime w i l l become 2 msec. Then the first voice packet delay just mentioned above w i l l correspondingly increase by 10 times going from the order of millisecond to ten milliseconds. B u t it can be considerably decreased if first voice packets use CHAPTER 3. SIMULATION OF MSTDM 56 L I B and data packets use B E B . In this case, it is, therefore, very favourable to have a shorter retransmission delay for first voice packets i n order to reduce the channel-acquisition time for voice sources. Th i s can prevent the speech from being clipped w i th only l i t t le adverse effect on the data delay performance. F ina l ly , we notice that the delay characteristics of voice packets i n F igure 3.7 and Figure 3.10 are almost identical to the ones i n Figure 3.2 and Figure 3.4. Th i s shows that their performance remains unchanged no matter first voice packets and data packets have the same or different retry schemes. 3.3 Summary We have presented the performance evaluation of the M S T D M protocol using s im-ulat ion. The effects of this protocol on the delay performances of data packets, first voice packets and subsequent voice packets have been shown and discussed respec-t ively i n terms of the mean and the standard deviation of their delay. Moreover, we find that i f first voice packets are given a shorter retransmission delay than data packets, the channel-acquisition delay for voice sources can be considerably reduced without sacrificing the data delay performance significantly. Chapter 4 M S T D M Network for a Metropolitan Area T h e M S T D M protocol supports both voice and data traffic i n a local area net-work. However, its efficiency decreases inversely w i t h the transmission rate and the channel length because of its bus contention nature. In this chapter, a scheme which alleviates the distance and transmission rate constraints associated w i t h this protocol is introduced [16]. The approach is to divide a network spanning a large area into a number of sub-networks called homenets, for improving the M S T D M protocol efficiency. Then we propose an access protocol for the interconnection of homenets. It facilitates the communications between stations i n different homenets for both voice and data services. F ina l ly , we find the op t imum number of homenets, into which a large area should be parti t ioned, to minimize the mean delay of data packets w i th in homenet. 57 CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 58 4.1 Homenet Network A s we see i n the previous two chapters, the performance of the M S T D M protocol deteriorates w i t h the increase of a which is defined as the ratio of the end-to-end channel propagation delay to the packet transmission time. The protocol does not even work i f cc is greater than one. These characteristics are, i n general, va l id for any bus contention protocol w i th carrier sensing property [13]. In an M S T D M system, the preempt area of voice packets does not carry any information. Its length depends on the m a x i m u m time that it takes for data sources and voice sources t ransmit t ing first voice packets to recover from a collision. Since the m a x i m u m collision recovery t ime increases w i t h the end-to-end propagation delay, the fraction of the voice packet, which carries useful data, is small when a is large. A s a result, the efficiency of the M S T D M protocol w i l l be low if i t is directly applied to a network which spans a large area and has a high transmission rate. In order to solve this problem, we have to alleviate the distance and transmission rate constraints associated w i th the M S T D M protocol. The homenet approach pre-sented here is to divide the stations in a network covering a large area, for example a metropoli tan area, into regional groups so that the end-to-end channel propagation delay applied to each region is reduced [16] [29] [30]. The communications channel w i t h a high total bi t rate is also divided, and a fraction of the capacity is assigned to each regional group. Stations i n a region only transmit in the fraction of the ca-pacity assigned to their group. Th i s decreases the transmission rate of the stations, compared w i t h the case when the total channel capacity is available to them. The overall effect is that the ratio of the end-to-end channel propagation delay i n each CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 59 region to the packet transmission time is considerably decreased. E a c h group forms a local area network called homenet, using the M S T D M proto-col . The physical medium can be a conventional subsplit cable system, for example a C A T V network which can be found under the ground of many metropoli tan areas [31]. The transmission of signal is uni-directional in broadband. Figure 4.1 shows a network w i t h three homenets on a subsplit cable system. The stations i n each homenet transmit i n frequency band / 0 i n upstream. There is a local reflection point i n each homenet. A t the reflection point, the upstream frequency band / 0 is prevented from propagating to adjacent homenet by means of notch filter. It is also translated into the downstream frequency band / „ i n homenet n, where n is an index for one of the homenets i n the network. E a c h station has one frequency agile receiver (or more). The stations in homenet n receive packets for communications w i th in homenet by listening to / „ , which is their homenet frequency. Usual ly, a sta-t ion listens to its homenet frequency al l the time unless it is informed to switch to another frequency. Moreover, the upstream frequency band fo is translated into fre-quency band / # „ at the reflection point of homenet n, and fDn propagates towards the head end of the whole network, which is the root of a subsplit cable system. A t the head end 1 , / p n is converted to fn which is carried throughout the network, 1 Besides the frequency translation operations, a variety of user services can be incorporated in the head end. Analog video can be broadcasted from the head end to every station in the network in a different frequency band like a C A T V system. A head-end station identical to the ones used at the user nodes can be implemented to perform the functions of an interactive data base providing different kinds of information to its customers. Another head-end station can act as a switching processor for establishing voice links with sources outside the network. A user sends a data packet to this processor giving the number to be called. It then processes the call and connects the user's voice path to the outside line. Similarly, a station at the head end can function as a gate-way which is responsible for data communications with the outside networks. If necessary, the stations providing services at the head end can have receivers listening to all homenet frequencies at the same time and can form a homenet of their own. C H A P T E R 4. M S T D M N E T W O R K F O R A M E T R O P O L I T A N A R E A 60 two No tch filter bands / o and f$ O local reflection point ^ head end Figure 4.1: Homenet network on a subsplit cable system. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 61 except homenet n where the fn transmitted from the head end is notch filtered at the reflection point to prevent collision with the /„ localized within homenet n. Through this configuration, the connectivity between stations in the network is complete. Once a packet has been successfully transmitted in a homenet, it can be received anywhere in the whole network. In this way, a station in homenet k, for example, can receive packets sent from homenet / by listening to frequency band fi, instead of its homenet frequency. Therefore, the link for inter-homenet packet transfer is set up. This homenet approach restricts the contention for channel acqui-sition to be localized among stations within homenet, no matter the transmission is for intra- or inter-homenet packet transfer. The result is a significant improvement in protocol efficiency. 4.2 Description of the Access Protocol A station has to know to which frequency it should listen for getting an inter-homenet packet addressd to it. In this section, we propose an access protocol for inter-homenet communications. This access protocol makes use of a monitor which is implemented in each homenet and basically performs the function of a store-and-forward node. 4.2.1 Interconnection The monitor in each homenet has receivers listening to all homenet frequencies at the same time. It accepts those packets which are sent from other homenets to the CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 62 stat ion A\ homenet 1 monitor M2 station B2 homenet 2 Figure 4.2: Inter-homenet packet transfer of bursty data. stations i n its homenet. It keeps the packets unchanged and delivers them to their destinations as a store-and-forward node. For example, station A\ in homenet 1 wants to send a data packet to station B2 i n homenet 2. W h e n the transmission is successful, the monitor (M2) i n homenet 2 detects this packet in frequency band fy. Recognizing the destination address be-longs to one of the stations wi th in its homenet, M2 receives the packet and stores it i n the buffer. T h e n M2 transmits the packet to B2 following the M S T D M protocol i n the same way as other stations i n homenet 2. F ina l l y B2 receives the packet in frequency band / 2 , its homenet frequency. The operation of this packet transfer is depicted in Figure 4.2. Th i s access protocol is suitable for handling bursty data traffic for inter-homenet communications. Yet , for voice packet transmission, we can eliminate the monitor CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 63 from being involved after the in i t ia l set-up as shown in Figure 4.3. We use the communications between Ai and B2 as an example again. N o w A\ wants to have a conversation w i th B2. So A\ sends a call-connection request packet to B2. This packet is carried through the network to B2 by the method just mentioned. Assum-ing B2 accepts the connection, it sends a call-confirmation packet back to Ai and its receiver is switched to listen to fi. After receiving the confirmation, Ai switches to listen to f2. Now Ai and B2 receive voice packets i n another's homenet frequency as if they were resided i n another's homenet 2 . Through the setting of an indicat ion bi t i n the packet header, the monitors in both homenet 1 and homenet 2 know that the packets sending between Ai and B2 are received by them directly. Therefore, the monitors do not accept these packets. The connection remains throughout the conversation un t i l one side disconnects the l ink by a clear-connection request. T h e n Ai and B2 return to their homenet frequencies. In this way, no addit ional delay is created on top of that due to the M S T D M protocol for voice packet transmission. Thus , M S T D M works well even for inter-homenet voice traffic. Th i s k ind of connection between stations i n different homenets is also suitable for long file transfer, which can avoid the extra data delay caused when the monitor is involved for every single packet transfer. However, the connection is l ikely to be one-way i n this case. If a station wants to have addit ional connections simultaneously, it has to be equipped w i t h more than one receiver. 2If Ai wants to talk to somebody outside the network, B2 will be one of the functional units of the head-end switching processor described before. These functional units are switching nodes which process the calls and connect the users' voice paths to the outside lines. In this example, the .outgoing signal from Ai is carried in frequency band fi to the switching node B2, and the incoming signal from the outside world is transmitted from B2 to Ai in frequency band f2- At the initial set-up, the number to be called is included in .Ai's call-connection request packet. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 64 fi homenet 1 homenet 2 (a) Call-connection request M i <6 B2 homenet 1 | homenet 2 (b) C a l l confirmation A i h homenet 1 homenet 2 (c) Conversation in session Figure 4.3: L i n k set-up for conversation between two stations i n different homenets. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 65 4.2.2 Other Related Issues Inter-homenet packets resulted from bursty data traffic pass through the monitors before reaching their destinations. We may assign priorities to different types of inter-homenet data packets so that the one with highest priority is served by the monitor sooner than the others, instead of being first-come-first-serve. Priority can be made according to the need of a packet for faster response or a toll scheme. This can make the network more adaptable to the users' need. As a monitor listens to all homenet frequencies, it can observe all of the chan-nel's traffic, construct traffic matrices and perform load analysis to measure the utilization of each homenet. It can then determine which homenet can support additional connections under certain constraint of performance measure. If a con-nection cannot be made, for example between homenet 1 and homenet 2, because of an overload of input traffic in the former, the monitor in homenet 2 will transmit a clear-connection request stating the reason for rejection to the sending station in homenet 1, after receiving its call-connection request packet. Addressing is also an important issue in denning the access protocol [1]. We need an efficient way of managing station addresses as machines move and new homenets join in the network. The use of absolute station addresses, each of which is unique over the whole network, in this way, is better than homenet specific station addresses. Two problems arise when the latter addressing method is adopted. The first is that when a station is moved from one homenet to another, it may have to change its address if another station there is using the same one. Moreover, a homenet specific address has to be combined with a unique network address so CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 66 that the whole address is unambiguous over the network space for inter-homenet communications. However, the absolute addressing method solves these problems, provided that the address space used is large enough to ensure uniqueness and give adequate room for growth. To support mult icasting communications, we require another addressing mode which makes use of logical station addresses. A logical address can be shared by a group of stations which may be located i n more than one homenet. A packet sent w i t h a logical address can, therefore, be received by more than one station. A l so , a station w i th more than one logical address can receive packets from different logical groups of stations. Th i s k ind of service is very useful i n many distributed applications, such as tele-conferencing and the access and update of distr ibuted data bases. In order to distinguish whether the address is absolute or logical, a specific indicat ion bi t has to be included i n the packet header. To support the above two types of addressing mode for inter-homenet communications, a monitor has to mainta in two lists of addresses for the stations i n its homenet, one for absolute addressing and another for logical addressing. 4.3 Optimum Number of Homenets 4.3.1 Analysis Suppose we have a subsplit cable system wi th certain channel capacity. If we divide it into a number of homenets and each homenet occupies part of the total channel capacity, the efficiency of the M S T D M protocol increases because (i) the end-to-CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 67 end propagation delay within homenet decreases, and (ii) the packet transmission time increases. The result is that we reduce the mean delay of data packets for transmission within homenet, which is normalized w.r.t. the packet transmission time. However, as the system is divided, it takes longer actual time to transmit a packet because only part of the total channel capacity is available to each homenet. Therefore, there is an optimum number of homenets the system should be divided into for networking, in order to minimize the mean data delay within homenet. Here we assume the stations are uniformly distributed and they are equally divided into N homenets. The area of the resultant homenets is inversely pro-portional to N. It is assumed that the resultant homenets are roughly circles or squares so that the distance between the two ends of the transmission media in a homenet is inversely proportional to AT 1 / 2 . Thus, the end-to-end propagation delay within homenet is reduced by 1/iV 1 / 2 , compared with an undivided system. But the division increases the packet transmission time by N. We assume the packet lengths for voice and data are constant and equal in the following. Let a^j be the normalized end-to-end propagation delay w.r.t. the packet transmission time in a homenet. Then CK^ = a/N3/2 where a is the propagation delay between the two ends of the undivided system, normalized w.r.t. the packet transmission time in that system. In Chapter 2, we obtain analytically the mean delay (Dn) of data packets for the slotted M S T D M protocol with non-persistent data packet transmission. Applying the results in Section 2.2.3, we find the mean data delay for transmission within homenet, which is normalized w.r.t the packet CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 68 transmission time in the undivided system. It is given by (4.1) where Wln (4.2) Pn = Pd k2a2{u - 1) {l + a/N3/2)2 -—\l + Pd Pv I OL ic OL 1 + N ^ + NT^^~1) (4.3) _ 1 J 1 a Pd a ka . . 1 + T T o T T + T7?iz\y ~ 1) ( l + a / 7 V 3 / 2 ) 2 P d 1 _ e-(l+a/N^)P„ + p v jy-3/2fc2a2(i/-l) + (1 + a/N3/2)2 w2n = $n + PvWln{l + a/N3/2 + $n) (1 + pvWln)[l - Pdkct{v - l)/N3/2] - pv{l + a/N3/2) (4.4) (4.5) _ 1 f p u ( l + «/NV2)2  n 2\ l + PvWln + P d OL O? (4.6) W = $n + PvWm{l + a/N3/2 + $w) + Pdka{u - l)W2n{l + pvWln)/Ns/2  3 n (1 + pvWln){l - pd[l + a/N3/2 + ka{u - l)/N3/2}} - pv(l + a/N3/2) (4.7) Recall that in the equations above, a. pd is the data utilization in a homenet; b. pv/(l + pvWln) is the voice utilization (pv) in the same homenet; CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 69 c. k is the number of the end-to-end propagation delay wi th in the homenet, which is required to recover from a collision of data packets and/or first voice packets; and d. 1/u is the probabil i ty of successful transmission for data packets and first voice packets. 4 . 3 . 2 Numerical Results Using (4.1), we plot Dn versus N. Figure 4.4 through Figure 4.6 show this rela-tionship at different data util izations pd, but we keep the voice ut i l iza t ion pv to be constant at 0, 0.2 and 0.4 of the channel capacity of the homenet i n the figures re-spectively. The values of a, k and v used are, respectively, 0.9, 2 and e. Note that when pv is zero, there is only data traffic i n the homenet network and the M S T D M protocol degenerates to C S M A / C D . We see from the figures that as the number of homenets increases, the mean data delay decreases because of the improvement i n protocol efficiency. T h e n it reaches a m i n i m u m and starts to increase. The increase occurs because the t ime it actually takes to transmit a packet increases w i t h the number of homenets. Therefore, there is an op t imum number of partitions the sys-t em should be divided into for min imiz ing the mean delay of data packets wi th in homenet. In an actual system, the op t imum number of homenets depends on the geometry of the system and the designed util izations of bo th voice and data i n the homenets. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 70 Number of homenets Figure 4.4: Mean data delay for transmission within homenet as a function of the number of homenets at pv = 0. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 71 Number of homenets Figure 4.5: Mean data delay for transmission within homenet as a function of the number of homenets at pv = 0.2. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 72 1x10° _, L 8 10 12 14 16 Number of homenets 18 20 22 Figure 4.6: Mean data delay for transmission within homenet as a function of the number of homenets at pv = 0.4. CHAPTER 4. MSTDM NETWORK FOR A METROPOLITAN AREA 73 4 . 4 Summary We have introduced the homenet approach for networking in a metropoli tan area, using the M S T D M protocol. Also we have proposed an access protocol for the interconnection of homenets and have discussed some of the related issues. Based on the analyt ical results obtained for the performance of M S T D M i n Chapter 2, we find the op t imum number of homenets for interconnection, which minimizes the mean delay of data packets wi th in homenet. Chapter 5 Conclusions This thesis mainly contains the research work in two areas: performance evaluation of the M S T D M protocol and its application in metropoli tan area networks. A minor part is given to the performance analysis of the C S M A / C D protocol. T w o methods are taken for the performance evaluation. They are mathemat-ical analysis and simulation. F i rs t , we propose the M / G / l model w i t h two non-preemptive priorities for the slotted non-persistent C S M A / C D protocol. This ana-ly t ica l approach presents a simpler way of performance evaluation than the previous works in the literature, and yields explicit results for the mean delay-throughput characteristics. Because M S T D M is a variat ion on C S M A / C D , we are able to formulate a similar analyt ical model for the former by extending the previous M / G / l system to three non-preemptive priorities. One point , which makes the extended model differ from ordinary priori ty queueing systems, is that the highest pr ior i ty queue has only one buffer. We solve the model and obtain explicit results for the mean data delay-74 CHAPTER 5. CONCLUSIONS 75 throughput performance of the slotted non-persistent M S T D M protocol. This is the first piece of work done on the data delay performance of M S T D M i n the literature. For each analysis of the two protocols, numerical examples are shown, and their delay characteristics are discussed and compared w i t h s imulat ion results. A s the comparisons show, the analysis yields very good approximate results. The short-coming of this analysis is that it is only good for the mean of data delay. T o find the general characteristics of the data delay and voice delay of the M S T D M protocol and its stability, further research needs to be performed. Simulat ion provides a promising way of performance evaluation when the tracta-b i l i ty of the mathematical analysis cannot be reached. We ran simulations for M S T D M , and the delay characteristics of data packets, first voice packets and sub-sequent voice packets are obtained in terms of the mean and the standard deviation of their delay. These s imulat ion results enrich our understanding on the perfor-mance of this protocol, and they are described and discussed i n detail i n the thesis. In the s imulat ion, the same as well as different retransmission scheduling algo-r i thms are applied for data packets and first voice packets. In the first case, both of them use the binary exponential backoff a lgori thm for retransmission; and in the second case, the former uses this a lgori thm while the latter uses the linear incre-mental backoff algori thm. Compar ing the s imulat ion results from these two cases, we find that i f first voice packets are given a shorter retransmission delay than data packets, the channel-acquisition delay for voice sources can be considerably reduced without sacrificing the data delay performance significantly. CHAPTER 5. CONCLUSIONS 76 Because of its contention nature, the performance of the M S T D M protocol i n a network deteriorates when the channel length and transmission rate of the network increase. In order to make this protocol applicable to metropol i tan area networks, we have to find a suitable configuration which can alleviate the distance and trans-mission rate constraints associated. In the thesis, the homenet approach is introduced for solving this problem. A n access protocol for the interconnection of homenets is proposed, which facilitates the communications between stations in different homenets for bo th voice and data services. The issues about traffic control and addressing are also mentioned. G i v e n the cri terion to minimize the mean data delay for transmission w i t h i n homenet, we perform an analysis and find the op t imum number of homenets for interconnection. Appendix A In this appendix, we show the analysis that derives (2.1) for the non-preemptive pr ior i ty queueing model shown in Figure 2.2. The analysis makes use of a two-dimensional M a r k o v chain [32]. A more simplified approach based on expectation can be found, for example, in [26]. A M a r k o v chain is imbedded at transmission completion epoch. Since there are 2 distinct classes of packets, we have to distinguish among the imbedded points as to which class completed service. This is indicated by the term k class epoch, where k = 1 or 2. Let n,-fc be the number of class k packets in the system at the i t h departure epoch and a3k be the number of class j packets arr iving during the transmission of a class k packet. The (i + l ) s t departure epoch is class 1 for nn > 0, and rci+U = nn — 1 + an Ki+1,2 = ni2 + a2i • ( A . l ) The (i + l ) s t departure epoch is class 2 for rc,-2 > 0 when the i th departure leaves 77 APPENDIX A. 78 the system devoid of class 1 packet. Then ».-+i,2 = ni2 - 1 + o 2 2 • (A.2) When the ith departure leaves the system empty, with probability Ai /A, ^.+1,2 = « 2 1 ( A - 3 ) where A = Ai + A 2 , and with probability A 2 / A , rc.-+i,2 = « 2 2 • (A.4) Define p = Aim"i + A 2 m 2 . (A-5) Then for the following 3 disjoint events in the queue dynamics, we have Prob [na = 0 and ni2 = 0] = 1 — "p = P 0 Prob [n a > 0] = A ^ / A = P x Prob [n t l = 0 and ni2 > 0] = A 2 ^ / A = P2 . (A.6) Conditioning on the 3 events to calculate the two-dimensional probability generating functions of and n,+i | 2, we have E[Z1n,'+1'1Z2"''+1'2] = P 0 { ( A 1 / A ) E [ Z 1 a i l Z 2 ° 2 1 | n t l = ni2 = 0] + (A 2 /A)E [Z?*Z?*\nix = n,-2 = 0] } + APPENDIX A. 79 P 1 E [ Z 1 n ' 1 _ 1 + a i l Z 2 " ' 2 + a 2 1 | n a > 0] + P 2 E [Z^ Z?i2~1+a22\na = 0, ni2 > 0] . (A.7) Solving (A.7) by differentiating w.r.t . Z\ and Z2i and after some manipulations, we obtain — , X2[\im\ + A2m22] 2 p ( l — Aimi)(l — Aimi — A2m2) where n 2 2 is the mean number of class 2 packets in the system given that one of them is beginning transmission. The average number of class 2 packets which arrive during the wai t ing time of the one being transmitted is n 2 2 — 1. Since packets arr iving to an empty system suffer no queueing delay, the mean wai t ing time (W2) of class 2 packets is given by W2 = (p/A2)(n22 - 1) by Lit t le 's Formula . (A.9) Subst i tut ing (A.8) into (A.9) , we obtain W2 = _AimT+A2mf ^ _ 2(1 — A 1m 1)(l — Ximi — A2m2) which is (2.1). Appendix B B . l Tables of the C S M A / C D Simulation Results Table B . l : 95% Confidence intervals for the C S M A / C D simulat ion results shown i n Figure 2.3 (k = 2). (a) a = 0.001 (b) a = 0.01 (c) a = 0.05 (d) a = 0.1 (e) a = 0.2 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.010 1.005 (1.004, 1.007) 1.006 0.101 1.059 (1.057, 1.061) 1.057 0.201 1.128 (1.124, 1.131) 1.127 0.300 1.214 (1.210, 1.218) 1.216 0.401 1.340 (1.331, 1.349) 1.337 0.500 1.496 (1.480, 1.512) 1.505 0.603 1.767 (1.746, 1.788) 1.768 0.702 2.195 (2.149, 2.241) 2.197 0.801 3.067 (3.021, 3.112) 3.062 0.851 3.896 (3.742, 4.049) 3.934 0.900 5.588 (5.388, 5.789) 5.719 0.911 6.314 (5.901, 6.727) 6.410 0.921 7.259 (6.868, 7.650) 7.206 0.928 7.872 (7.249, 8.495) 7.896 B . l (a) 80 APPENDIX B. 81 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i ca l mean 0.010 1.009 (1.009, 1.010) 1.010 0.100 1.064 (1.062, 1.066) 1.062 0.301 1.231 (1.226, 1.237) 1.231 0.501 1.553 (1.545, 1.561) 1.551 0.702 2.404 (2.367, 2.442) 2.381 0.801 3.620 (3.547, 3.692) 3.574 0.840 4.714 (4.392, 5.036) 4.588 0.862 5.575 (5.316, 5.834) 5.552 0.877 6.505 (6.172, 6.837) 6.512 0.899 9.158 (8.643, 9.673) 8.800 B . l (b) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.010 1.030 (1.029, 1.030) 1.031 0.100 1.093 (1.091, 1.096) 1.090 0.300 1.313 (1.303, 1.322) 1.305 0.400 1.512 (1.507, 1.518) 1.495 0.501 1.838 (1.816, 1.860) 1.817 0.599 2.477 (2.428, 2.526) 2.420 0.701 4.214 (4.024, 4.403) 4.136 0.757 7.512 (7.155, 7.870) 7.493 B . l (c) APPENDIX B. 82 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.010 1.055 (1.053, 1.057) 1.057 0.100 1.133 (1.130, 1.137) 1.128 0.300 1.445 (1.431, 1.459) 1.428 0.400 1.799 (1.776, 1.823) 1.753 0.502 2.503 (2.451, 2.556) 2.461 0.550 3.303 (3.196, 3.410) 3.150 0.570 3.682 (3.544, 3.821) 3.612 0.580 4.104 (3.937, 4.271) 3.908 0.601 4.828 (4.700, 4.956) 4.706 0.605 5.139 (4.804, 5.473) 4.904 0.614 5.589 (5.394, 5.785) 5.424 0.626 6.460 (6.012, 6.908) 6.358 B . l (d) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.010 1.108 (1.105, 1.110) 1.109 0.100 1.227 (1.221, 1.233) 1.214 0.198 1.442 (1.430, 1.455) 1.415 0.300 1.877 (1.855, 1.900) 1.850 0.400 3.061 (3.000, 3.123) 3.030 0.421 3.592 (3.491, 3.694) 3.574 0.440 4.369 (4.185, 4.553) 4.300 0.461 5.800 (5.346, 6.253) 5.531 0.470 6.577 (6.250, 6.903) 6.361 0.480 7.735 (7.347, 8.123) 7.620 B . l (e) APPENDIX B. 83 B .2 Tables of the M S T D M Simulation Results Table B.2: 95% Confidence intervals for the M S T D M simulat ion results shown i n Figure 2.10 (a = 0.0125, k = 3). (a) pv=0 (b) pv = 0.044 (c) pv = 0.147 (d) p„ = 0.293 (e) pv = 0.437 (f) p„ = 0.585 (g) Pv = 0.738 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.010 1.011 (1.010, 1.011) 1.011 0.100 1.066 (1.064, 1.068) 1.064 0.301 1.238 (1.233, 1.244) 1.239 0.501 1.586 (1.579, 1.593) 1.584 0.698 2.534 (2.480, 2.588) 2.518 0.801 4.160 (4.017, 4.302) 4.157 0.850 6.034 (5.799, 6.270) 6.439 0.867 7.578 (7.334, 7.822) 8.135 0.878 9.300 (8.367, 10.234) 9.855 B.2 (a) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i ca l mean 0.011 1.039 (1.036, 1.041) 1.038 0.101 1.101 (1.099, 1.102) 1.100 0.301 1.308 (1.303, 1.314) 1.306 0.501 1.738 (1.730, 1.746) 1.739 0.701 3.055 (2.999, 3.112) 3.100 0.801 5.785 (5.676, 5.893) 6.049 0.821 7.617 (7.376, 7.859) 8.045 0.831 8.861 (8.345, 9.377) 9.279 B.2 (b) APPENDIX B. 84 Data throughput Mean data delay 9 5 % Confidence interval Analytical mean 0.014 1.121 (1.116, 1.126) 1.119 0.104 1.218 (1.214, 1.222) 1.210 0.205 1.353 (1.349, 1.357) 1.343 0.305 1.537 (1.531, 1.542) 1.529 0.405 1.829 (1.813, 1.844) 1.827 0.505 2.292 (2.267, 2.316) 2.309 0.603 3.236 (3.200, 3.271) 3.313 0.705 6.395 (6.079, 6.711) 6.742 0.724 8.574 (7.906, 9.243) 8.760 0.733 9.184 (8.734, 9.634) 9.781 B.2 ( C) Data throughput Mean data delay 95% Confidence interval Analytical mean 0.019 1.309 (1.301, 1.317) 1.316 0.108 1.486 (1.470, 1.502) 1.467 0.209 1.762 (1.740, 1.784) 1.740 0.309 2.156 (2.101, 2.211) 2.143 0.409 2.772 (2.750, 2.794) 2.829 0.507 4.445 (4.294, 4.595) 4.662 0.567 7.160 (6.811, 7.510) 7.372 0.579 8.693 (7.653, 9.733) 8.538 B.2 (d) APPENDIX B. 85 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.023 1.681 (1.641, 1.721) 1.658 0.112 2.039 (2.013, 2.065) 1.985 0.213 2.524 (2.486, 2.562) 2.528 0.313 3.637 (3.546, 3.727) 3.713 0.412 6.988 (6.379, 7.597) 6.956 0.422 8.414 (7.214, 9.614) 7.931 B.2 (e) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.027 2.530 (2.489, 2.571) 2.404 0.117 3.211 (3.135, 3.285) 3.126 0.217 5.116 (4.882, 5.349) 5.229 0.266 7.357 (6.503, 8.210) 7.151 0.277 8.553 (7.601, 9.506) 8.102 B.2 (f) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.031 4.937 (4.845, 5.029) 4.503 0.071 5.647 (5.601, 6.023) 5.367 0.091 7.209 (6.474, 7.944) 6.303 B-2 (g) APPENDIX B. 86 Table B.3: 95% Confidence intervals for the M S T D M simulat ion results shown in Figure 2.11 (a = 0.05, k = 2). (a) pv = 0 (b) pu = 0.045 (c) P v = 0.146 (d) pv = 0.292 (e) pv = 0.439 (f) pv = 0.586 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.010 1.030 (1.029, 1.030) 1.031 0.100 1.093 (1.091, 1.096) 1.090 0.300 1.313 (1.303, 1.322) 1.305 0.400 1.512 (1.507, 1.518) 1.495 0.501 1.838 (1.816, 1.860) 1.817 0.599 2.477 (2.428, 2.526) 2.420 0.701 4.214 (4.024, 4.403) 4.136 0.757 7.512 (7.155, 7.870) 7.493 B.3 (a) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i ca l mean 0.011 1.062 (1.058, 1.066) 1.059 0.102 1.132 (1.131, 1.132) 1.129 0.302 1.403 (1.399, 1.407) 1.391 0.402 1.652 (1.645, 1.659) 1.633 0.501 2.083 (2.069, 2.097) 2.053 0.600 2.977 (2.967, 2.988) 2.930 0.702 6.576 (6.390, 6.761) 6.317 0.720 8.589 (8.197, 8.982) 8.219 B.3 (b) APPENDIX B. 87 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.014 1.155 (1.147, 1.162) 1.149 0.104 1.269 (1.260, 1.278) 1.252 0.204 1.433 (1.426, 1.439) 1.415 0.305 1.699 (1.681, 1.717) 1.673 0.404 2.152 (2.131, 2.174) 2.137 0.505 3.054 (3.007, 3.101) 3.030 0.603 6.206 (5.979, 6.432) 6.234 0.624 8.171 (7.965, 8.378) 8.030 B.3 (c) D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.018 1.395 (1.371, 1.420) 1.373 0.108 1.602 (1.574, 1.631) 1.559 0.208 1.956 (1.930, 1.982) 1.912 0.308 2.513 (2.479, 2.546) 2.529 0.408 3.863 (3.748, 3.978) 3.912 0.458 5.836 (5.435, 6.237) 5.738 0.478 6.640 (6.198, 7.081) 6.884 0.499 8.952 (8.233, 9.670) 9.064 B.3 (d) APPENDIX B. 88 D a t a throughput M e a n data delay 95% Confidence interval Ana ly t i ca l mean 0.022 1.824 (1.786, 1.863) 1.747 0.113 2.304 (2.263, 2.346) 2.193 0.213 3.123 (3.027, 3.218) 3.085 0.312 5.336 (5.195, 5.478) 5.571 0.332 6.447 (6.182, 6.712) 6.589 0.353 7.957 (7.458, 8.456) 7.922 B.3 (e) Da ta throughput M e a n data delay 95% Confidence interval Ana ly t i c a l mean 0.027 2.897 (2.848, 2.945) 2.678 0.067 3.353 (3.242, 3.464) 3.133 0.117 4.102 (3.957, 4.248) 3.922 0.166 5.231 (4.897, 5.565) 5.118 0.187 6.368 (6.110, 6.625) 6.072 0.207 7.247 (6.962, 7.533) 7.155 B.3 (f) 89 References [1] J . 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