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A Variety of Queueing Models for Mobile Communication Systems A VARIETY OF QUEUEING MODELS FOR MOBILE COMMUNICATION SYSTEMS William Wing Pong Kwok A thesis submitted in conforrnity with the requirements for the degree of Master of Applied Science Department of Mechanical and Industrial Engineering University of Toronto O Copyright by William Wing Pong Kwok (1999) 1 National Library Bibliotheque nationale du Canada Acquisitions and Acquisitions et Bibiiographic Services services bibliographiques 395 Weilingtm Street 395. n# Wdiington Ottawa ON KIA ON4 OaawaON K1AW Canada canada The author has granted a non- L'auteur a accordé une licence non exclusive licence ailowing the exclusive permettant à la National Library of Canada to Bibliothèque nationale du Canada de reproduce, loan, distniute or seil reproduire, @ter, distribuer ou copies of this thesis in microfom., vendre des copies de cette thèse sous paper or electronic formats. la forme de microfiche/film, de reproduction sur papier ou sur format électronique. The author retains ownership of the L'auteur conserve la propriété du copyright in this thesis. Neither the droit d'auteur qui protège cette thèse. thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be printed or othewise de celle-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation. A VARiETY OF QUEUEING MODELS FOR MOBILE COMMUNICATION SYSTEMS William Wlng Pong Kwok Degree of Master of Applied Science, 1999 Department of Mechanical & Industrial Engineering University of Toronto ABSTRACT The impact of customer behavior plays an important dein the planning of multi-media cellular mobile communication networks. In fact, the quality of service (QoS), such as waiting time and accessibility, that is experienced by each individual customer is the main factor in the evaluation of system performance. In this thesis, we are going to uivestigate the wai~gtime/delay of a broad class of mobile communication system-oriented queueing models. Both exact analytic and approximation algorithm techniques are employed in order to obtain the exact and approximate waiting/delay distribution of those models. We concentrate on probability disnibution instead of mean value because an one-point esthate is not -tient to provide a good performance evaluation, We propose different queueing models in order to describe different cbaracteristics of mobile systerns. in general, mobile customers cm be divided into two main categories, kshcustomer arrivals and handover customers. A fksh customer amival is a customer who initiates a new cal1 and a handover custorner is a customer who moves from an adjacent cell. Each category can be fierdivided into voice and data and each sub-category can be classified according to its moving speed- Because the handover customers have a significant impact on the quality of service, a set of channels is reserved for them at each base station and they are called gudchannels. AIso, different server control mechanisms are implemented in order to optimize channel (or semer) utilization. ACKNOWLEDGEMENT It is very hard to express the importance of a person in a few words. Prof. MJ-M. Posner has fiilfilied ail the quafiaes as a supervisor with excellence. 1wish to express my deep appreciation and sinccre grasitude to him, for his constant encouragement, infinite patience and guidance throughout my entire graduate study and thesis writing. As a scienfic advisor, he aiways encouraged me to elaborate actual ideas and, in particular, to bring up aew ideas. His generosity in suppiying material support is also sincerely appreciated CONTENTS 1 INTRODUCTION............................................................................................ 1 1.1 Cntroduction and ovewiew..................................................................................... 1 1 -2 Literature review on mobile telecommunication systems-............................................... -5 2 LEVEL CROSSING GND DECOMPOSITION METBODOLOGIES...................... .... 10 2.1 Level crossing methodology .................................................................................. 10 2.2 Surnrnary of the notation used in level crossing anaiysis................................................. 15 2.3 Decomposition rnethodology ................................................................................. 16 3 SINGLE SERVER QUEüEING MODELS ........................ .... .............................. 18 3.1 Introduction.................................................................................................... -18 3.2 Relationships between vacation type queuehg systerns and mobile communication systerns....... 18 3.3 Single semer queues with multipIe vacation policy ....................................................... 18 3.4 Single semer queues with single vacation policy .......................................................... 23 3.5 Queues with variable number of servers.................................................................... 28 3.6 Single server queues with only one vacation afier each busy period .................................... 34 4 PERFORMANCE MEASURES AND NUMERICAL EXAMPLES.............................. 41 4.1 General perfomance masures ............................................................................. -41 4.2 Specific performance measures and stationacy conditions. .............................................. 43 4.3 Numencal examples of the models .......................................................................... 49 5 TWO SERVER QUEUEING SYSTEMS............................................................... 62 5.1 Introduction ..................................................................................................... 62 5 -2 Mobile communication systerns with guard channel ...................................................... 62 5.3 Tandem queues with intermediate arrivals.................................................................. 69 5.4 Extensions of the models and Merdevelopment ....................................................... 76 6 RETRIAL QUEUES .........................................................................................78 6 .I Introducton ...................................................................................................... 78 6.2 Retrial queues with two types of customer anïvals ...................................................... -79 6.3 Retrial queues with fmite input buffer capacity and single vacation policy ........................... 81 6.4 Retrial queues with feedback............ .. ................................................................. 86 6.4.1 M/M/l retrial queues with feedback ..........................................................-........... -86 6.4.2 Retrial queues wîth feedback and single vacation policy .............................................. -91 6.5 Limitation of andytic methods ............................................................................. -95 7 MUL'MPLE PHASE TRANSMISSION SYSTEMS WITE RS BLOCKING................... 96 7.1 Introduction. .................................................................................................... 96 7.2 Review of the literature ....................................................................................... 97 7.3 lnsensitivity property of tandem queues with RS blocking ..............................................98 7.4 Decornposition analyses of tandem queues with infmite buffers at the fust node ................... 102 7.5 Analyses of simulation results for tandem queues with infinite buffers at the fmt node ........... 106 7.5.1 RS blocking with no intermediate bar................................................................ 106 7.5.2 RS blocking with one intermediate baer............................................................... 109 7-53 RS blocking with two intediatebuEers ............................................................ -111 7.6 Decornposition analyses of tandem queues with finite buffers at the first node .................... -114 7.6.1 Throughput capacity of fmite tandem queues with RS blocking policy ........................... -114 7.6.2 Decomposihon algorithm for the finite tandem queues (RS) ......................................... 116 7.7 Analyses of simulation results for tandem queues with finite buffers at the first node ............. 119 7.7. i RS blocking with no intermediate buffer ................................................................ 119 7.7.2 RS blocking with one or two intermediate buffers .................................................... -121 7.8 Extension to split and merge configuration. ............................................................. -124 7.8.1 Split configurations...................................................................................... 124 7.8.2 Merge configurations....................................................................................... 125 8 MULTIPLE PEJASE TRANSMISSION SYSTEMS WITH BAS BLOCKING................ 126 8.1 Introduction .................................................................................................. -126 8.2 Insensitivity property of tandem queues witb blocking ................................................. 126 8.3 Decomposition analyses of tandem queues with infimite buffers at the first node ................... 127 8.4 Analyses of simulations results for tandem queues with inhite buffers at the fmt node. ....... -129 8.4.1 BAS blocking witb zem, one or two intermediate
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