A Queueing Theory Analysis of Wireless Radio Systems Applied to HS-DSCH
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2004:139 CIV MASTER’S THESIS A Queueing Theory Analysis of Wireless Radio Systems Applied to HS-DSCH NIKLAS BRÄNNSTRÖM MASTER OF SCIENCE PROGRAMME Department of Mathematics 2004:139 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 04/139 - - SE A Queueing Theory analysis of wireless radio systems –Applied to HS-DSCH Niklas Br¨annstr¨om May 2004 Examiner: Supervisor: Thomas Gunnarsson Arne Simonsson Department of Mathematics Ericsson Research Lule˚aUniversity of Technology Ericsson AB Lule˚a Abstract This report is a theoretical approach, using queuing systems, to describe delay characteristics of wireless telecommunication systems. In the report we derive the waiting time and total time distributions for two classes of queuing systems, namely G/M/1andM/G/1. We give examples of particular queues belonging to each of these classes and analyse them. We find that the distributions are independent of packet size if the queuing discipline is first come first served, and that the total time distribution of the G/M/1 system is exponentially distributed regardless of the inter arrival process. We also apply the theories to a wireless radio system, HS-DSCH, and compare the theoretical results to simulation results. The M/E2/1 queue (with a constant delay added) is shown to be a good model of HS-DSCH. It also contains an example of how to use the calculated distributions to, given a certain delay tolerance, predict the behaviour of a new service in an existing system. The intended reader of this thesis is assumed to have some background in stochastic processes. Sammanfattning Idenh¨ar rapporten f¨ors¨oker vi beskriva egenskaper hos f¨ordr¨ojningar itr˚adl¨osa radion¨at utg˚aende fr˚an k¨oteoretiska resonemang. I rapporten h¨arleds v¨antetidsf¨ordelning och totaltidsf¨ordelning f¨or tv˚a klasser av k¨oer, n¨amnligen M/G/1ochG/M/1. Det ges flera exempel p˚ak¨oer, och anal- yser av dessa, ur de b¨agge klasserna. De mest intressanta resultatenar ¨ att f¨ordelningarnaar ¨ oberoende av paketstorleken om k¨odisciplinenar ¨ f¨orst in f¨orst ut, och att totaltidsf¨ordelningen av G/M/1 systemetar ¨ exponen- tialf¨ordelad oavsett hur ankomstprocessen ser ut. Teorierna till¨ampas p˚a ett specifikt radion¨at, HS-DSCH. De teoretiska re- sultaten f¨or detta system j¨amf¨ors med simuleringsresultat, och vi visar att M/E2/1 k¨on (med en konstant f¨ordr¨ojning inkluderad)ar ¨ en bra modell av HS-DSCH. Vi visar ocks˚a, givet ett f¨ordr¨ojningskrav, hur de ber¨aknade f¨ordelningarna kan anv¨andas f¨or att ber¨akna egenskaperna hos en ny tj¨anst i ett befintligt system. Det f¨oruts¨atts att l¨asaren har viss kunskap om stokastiska processer. Prologue This thesis constitutes the final part of my Master of Science program, Teknisk Fysik (Engineering Physics), at Lule˚a university of technology. The assigner of this thesis is Ericsson Research in Lule˚a, a part of Ericsson AB. I want to thank my supervisor Arne Simonsson for his great help with this thesis. His ”hands-on” knowledge of these systems is profound. He has also guided me through the jungle of three and four letter abbreviations of digerent radio standards, protocols and systems, helping me to get to the core of what I needed. I also wish to thank the rest of the stag at EAB/TBF for their occasional remarks, thoughts and encouragements. I would like to thank my examiner Thomas Gunnarsson, head of the mathematics department, for his useful remarks along the way. However busy, when needed, he has always managed to find gaps in his calendar. A I also appreciate the L TEX hints I have received from my fellow student Erik Astr¨˚ om. I am also very thankful for the hours Petri Juuso, at TietoEnator, spent restoring the contents of this thesis after my computer had broken down. Contents 1Introduction 5 1.1Theradioenvironment...................... 7 1.1.1 HS-DSCH (High Speed Downlink Shared CHannel) . 8 1.2OutlineoftheReport....................... 8 2 Setting of the Problem 10 2.1GeneralProblem......................... 10 2.2TheProblemstudied....................... 11 3 Theory of Queues 13 3.1Notation.............................. 14 3.2KendallNotation......................... 15 3.3M/G/1FCFS........................... 17 3.3.1 M/M/1FCFS....................... 19 3.3.2 M/Eq/1FCFS....................... 20 3.3.3 M/Hq/1 .......................... 23 3.3.4 M/D/1........................... 26 3.4G/M/1............................... 27 3.4.1 M/M/1FCFS....................... 28 3.4.2 Eq/M/1FCFS....................... 28 3.4.3 U/M/1FCFS....................... 29 3.4.4 Hq/M/1FCFS...................... 29 3.4.5 D/M/1FCFS....................... 30 3.5M/M/1Round-Robin....................... 30 3.6Queuingdisciplines........................ 31 3.7ConstantDelay.......................... 31 4Analysis 32 4.1M/G/1FCFS........................... 32 4.1.1 M/M/1FCFS....................... 33 4.1.2 M/E2/1FCFS....................... 38 4.1.3 The M/Eq/1familyofQueues.............. 38 4.1.4 M/Hq/1 .......................... 42 4.2G/M/1FCFS........................... 45 3 4.2.1 Eq/M/1.......................... 45 4.3M/M/1Round-Robin....................... 47 5 Application: HS-DSCH (High Speed Downlink Shared CHan- nel) 49 5.1Modelverification......................... 49 5.2GeneralResults.......................... 51 5.3Streaming............................. 53 5.4PushToTalk(PTT)....................... 55 5.5Otherradioprotocols....................... 57 6 Summary 59 6.1Conclusions............................ 59 6.2Furtherstudies.......................... 60 6.3Epilogue.............................. 61 AAppendix 62 A.1 Classification of Markov Chains ................. 62 A.2PoissonProcesses......................... 64 A.3 Derivation of total time distribution of the M/M/1 System . 65 A.4 Derivation of total time distribution of the G/M/1 System . 68 A.5 Derivation of total time distribution of the M/G/1 System . 73 4 Chapter 1 Introduction Mankind has always communicated with each other. This communication has taken various forms; ordinary conversations, drumbeating, smoke signals, telephone calls, e-mails etc. Common for all of them is that they use a media. Is this media shareable? Or rather, to which extent is the media shareable? For example, it is not possible to send two analogue radio programs on the same frequency (or it would be dicult to listen to them), so in this case the frequency is not shareable. But consider conversations around a dinner table, here multiple conversations may take place at the same time, they share the air. The issue of this report is to find to what extent a radio channel is share- able between the users, with respect to the quality of service they expect. The question at hand is to study how the throughput varies with the toler- able delay on the service. A major part of the radio networks of today are packet switched, like WLAN, GPRS, EDGE, which lends them well to radio channel sharing in order to increase the total capacity in the net. However, each specific service has a certain demand on maximum delay. For example an ordinary telephone call is very sensitive to delay, you do not want to have parts of the call getting stuck in a ”radio trac jam”. Other services though, like ftp downloading on the Internet is not sensitive to delay. In the latter case we can get more capacity from the channel. Compare with a transportation problem: Consider an airplane taking 10 passengers per flight, making 5 flights from A to B daily. Suppose the army wants to send 50 soldiers from A to B and wants them there by the end of the day, then the airplane can fly back and forth moving the soldiers from A to B. Now the capacity of the airline is fully used. Instead suppose that one day 50 businessmen want to fly into B for breakfast meetings. Now the airline can only service 10 of the businessmen. The remaining 40 businessmen, who did not get a seat on the first plane, will stay in A, because they cannot accept arriving several hours later in B. Now the throughput in the airline is only 20%. And the reason is that the businessmen cannot accept delays at the same extent as the soldiers can. What if the businessmen arrive at random 5 occasions at the airport, wanting a seat on the next plane, what would then be the capacity of the airline? To highlight a digerent aspect of a similar problem, consider a store sell- ing5digerent types of items: Item A, B, C, D, E priced 5, 4, 3, 2 and 1 respectively. There is no digerence in the time it takes to sell any of the items. If the customers entering the store can tolerate to wait (for a long time if necessary), and if the store is able to serve all customers before closing time, then the customers can be served in any order (in the natural order most likely). The flow of money into the cashmachine will be maximal any- way. Now suppose the customers cannot wait for more than a quarter of an hour before leaving the store, then the store manager has to rethink. If she wants to maximize her cashflow, then the customers wanting to buy item A should be served first, and then customers wanting to buy item B and so forth, always serving the customer with the most expensive item. Then her cashflow will be maximal, but at the risk of being considered unfair by many of her lost customers. This example shows another dimension of the problems with delay constraints, namely that order of service is important. The main reason for studying the relationship between throughput and delay is to be able to build systems of the right dimensions. If we want to introduce a service that tolerates a maximum delay of d seconds, then with the aid of the relationship we can tell how much capacity is needed in the system.