Holdings: Stochastic models in queueing theory

Stochastic models in queueing theory:

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Bibliographic Details
Main Author:	Medhi, Jyotiprasad (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Academic Press 2003
Edition:	2. ed.
Subjects:	Queuing theory Stochastic processes Wartesystem Stochastischer Prozess Stochastisches Modell Warteschlangentheorie
Online Access:	Publisher description Table of contents Inhaltsverzeichnis
Physical Description:	XVIII, 482 S. graph. Darst.
ISBN:	0124874622

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Record in the Search Index

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adam_text	J. MEDHI STOCHASTIC MODELS IN QUEUEINGTHEORY S F I C I N D E D I T I O N ACADEMIC PRESS V Y AN IMPRINTOF ELSEVIER SCIENCE AMSTERDAM SOSTON LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO CONTENTS PREFACE XV CHAPTER L STOCHASTIC PROCESSES 1 1.1 INTRODUCTION 1 1.2 MARKOV CHAINS 2 1.2.1 BASIC IDEAS 2 1.2.2 CLASSIFICATION OF STATES AND CHAINS 4 1.3 CONTINUOUS-TIME MARKOV CHAINS 14 1.3.1 SOJOURNTIME 14 1.3.2 TRANSITION DENSITY MATRIX OR INFINITESIMAL GENERATOR 15 1.3.3 LIMITING BEHAVIOR: ERGODICITY 16 1.3.4 TRANSIENT SOLUTION 18 1.3.5 ALTERNATIVE DEFINITION 19 1.4 BIRTH-AND-DEATH PROCESSES 23 1.4.1 SPECIAL CASE: M/M/L QUEUE 25 1.4.1 PURE BIRTH PROCESS: YULE-FURRY PROCESS 25 1.5 POISSON PROCESS 25 1.5.1 PROPERTIES OFTHE POISSON PROCESS 28 1.5.2 GENERALIZATION OFTHE POISSON PROCESS 29 1.5.3 ROLE OFTHE POISSON PROCESS IN PROBABILITY MODEIS 31 1.6 RANDOMIZATION: DERIVED MARKOV CHAINS 32 1.6.1 MARKOV CHAIN ON AN UNDERLYING POISSON PROCESS (OR SUBORDINATED TO A POISSON PROCESS) 33 VII VIII CONTENTS 1.6.2 EQUIVALENCE OF THE TWO LIMITINGFORMS 33 1.6.3 NUMERICAL METHOD 34 1.7 RENEWAL PROCESSES 35 1.7.1 INTRODUCTION 35 1.7.2 RESIDUAL AND EXCESS LIFETIMES 36 1.8 REGENERATIVE PROCESSES 37 1.8.1 APPLICATION IN QUEUEING THEORY 38 1.9 MARKOV RENEWAL PROCESSES AND SEMI-MARKOV PROCESSES 39 PROBLEMS 41 REFERENCES AND FURTHER READING 46 CHAPTER2 QUEUEING SYSTEMS: GENERAL CONCEPTS 47 2.1 INTRODUCTION 47 2.1.1 BASIC CHARACTERISTICS 48 2.1.2 THE INPUT OR ARRIVAL PATTERN OFCUSTOMERS 48 2.1.3 THE PATTERN OF SERVICE 49 2.1.4 THE NUMBER OF SERVERS 49 2.1.5 THE CAPACITY OF THE SYSTEM 49 2.1.6 THE QUEUE DISCIPLINE 49 2.2 QUEUEING PROCESSES 50 2.3 NOTATION 51 2.4 TRANSIENT AND STEADY-STATE BEHAVIOR 52 2.5 LIMITATIONS OF THE STEADY-STATE DISTRIBUTION 53 2.6 SOME GENERAL RELATIONSHIPS IN QUEUEING THEORY 54 2.7 POISSON ARRIVAL PROCESS AND ITS CHARACTERISTICS 59 2.7.1 PASTA: POISSON ARRIVALS SEE TIME AVERAGES 59 2.7.2 ASTA: ARRIVALS SEE TIME AVERAGES 62 REFERENCES AND FURTHER READING 62 CHAPTER3 BIRTH-AND-DEATH QUEUEING SYSTEMS: EXPONENTIAL MODELS 65 3.1 INTRODUCTION 65 3.2 THE SIMPLE AF/AF/1 QUEUE 65 3.2.1 STEADY-STATE SOLUTION OFAF/M/1 66 3.2.2 WAITING-TIME DISTRIBUTIONS 68 3.2.3 THE OUTPUT PROCESS 72 3.2.4 SEMI-MARKOV PROCESS ANALYSIS 75 3.3 SYSTEM WITH LIMITED WAITING SPACE: THE M/M/L/K MODEL 77 3.3.1 STEADY-STATE SOLUTION 77 3.3.2 EXPECTED NUMBER IN THE SYSTEM L 78 3.3.3 EQUIVALENCE OF ANM/AF/L/KMODEL WITH A TWO-STAGE CYCLIC MODEL 80 CONTENTS IX 3.4 BIRTH-AND-DEATH PROCESSES: EXPONENTIAL MODELS 81 3.5 THE M/M/CO MODEL: EXPONENTIAJ MODEL WITH AN INFINITE NUMBEROF SERVERS 83 3.6 THE MODEL M/M/E 84 3.6.1 STEADY-STATE DISTRIBUTION 84 3.6.2 EXPECTED NUMBER OF BUSY AND IDLE SERVERS 87 3.6.3 WAITING-TIME DISTRIBUTIONS 89 3.6.4 THE OUTPUT PROCESS 93 3.7 THE M/M/C/C SYSTEM: ERLANG LOSS MODEL 95 3.7.1 ERLANG LOSS (BLOCKING) FORMULA: RECURSIVE ALGORITHM 99 3.7.2 RELATION BETWEENERLANG SSS ANDCFORMUIAS 100 3.8 MODEL WITH FINITE INPUTSOURCE 101 3.8.1 STEADY-STATE DISTRIBUTION: M /M/CJ JM (M C). ENGSET DELAY MODEL 101 3.8.2 ENGSET LOSS MODEL M/M/C//M/{M C) 106 3.8.3 THE MODEL M/M/C//M (M C) 109 3.9 TRANSIENT BEHAVIOR 110 3.9.1 INTRODUCTION 110 3.9.2 DIFFERENCE-EQUATION TECHNIQUE 112 3.9.3 METHOD OF GENERATINGFUNCTION 117 3.9.4 BUSY-PERIOD ANALYSIS 119 3.9.5 WAITING-TIME PROCESS: VIRTUAL WAITINGTIME 125 3.10 TRANSIENT-STATE DISTRIBUTION OFTHE M/M/C MODEL 127 3.10.1 SOLUTION OFTHE DIFFERENTIAL-DIFFERENCE EQUATIONS 127 3.10.2 BUSY PERIOD OF AN M/M/C QUEUE 133 3.10.3 TRANSIENT-STATE DISTRIBUTION OFTHE OUTPUT OF AN M/M/C QUEUE 136 3.11 MULTICHANNEL QUEUE WITH ORDEREDENTRY 138 3.11.1 TWO-CHANNEL MODEL WITH ORDERED ENTRY (WITH FINITE CAPACITY) 139 3.11.2 THECASEM = L,/V = A/ 140 3.11.3 PARTICULARCO.SE:/W = N = 1 (OVERFLOW SYSTEM) 142 3.11.4 OUTPUT PROCESS 144 PROBLEMS AND COMPLEMENTS 145 REFERENCES AND FURTHER READING 159 CHAPTER4 NON-BIRTH-AND-DEATH QUEUEING SYSTEMS: MARKOVIAN MODELS 165 4.1 INTRODUCTION 165 4.1.1 THE SYSTEM M/EJ 165 4.1.2 THE SYSTEM E K /M/ 170 X CONTENTS 4.2 BULK QUEUES 174 4.2.1 MARKOVIAN BULK-ARRIVAL SYSTEM: M X /M/L IIA 4.2.2 EQUIVALENCEOFAF//W/LAND/M/E R /L SYSTEMS 178 4.2.3 WAITING-TIME DISTRIBUTION IN AN M X /M/L QUEUE 178 4.2.4 TRANSIENT-STATE BEHAVIOR 179 4.2.5 THE SYSTEM M X /M/OO 181 4.3 QUEUEING MODELS WITH BULK (BATCH) SERVICE 185 4.3.1 THE SYSTEM M/M{A, O)/L 186 4.3.2 DISTRIBUTION OF THE WAITING-TIME FOR THE SYSTEM M/M(A,B)/L 190 4.3.3 SERVICE BATCH-SIZE DISTRIBUTION 195 4.4 M/M(A,I»)/L:TRANSIENT-STATE DISTRIBUTION 196 4.4.1 STEADY-STATE SOLUTION 198 4.4.2 BUSY-PERIOD DISTRIBUTION 198 4.5 TWO-SERVER MODEL :M/M(A,D)/2 202 4.5.1 PARTICULARCASE: M/M(L,B)/2 204 4.6 THE AF/AF(L,O)/C MODEL 205 4.6.1 STEADY-STATE RESULTS M/M(L ; B)/C 208 PROBLEMS AND COMPLEMENTS 210 REFERENCES AND FURTHER READING 217 CHAPTER5 NETWORK OF QUEUES 221 5.1 NETWORK OF MARKOVIAN QUEUES 221 5.2 CHANNELS IN SERIES OR TANDEM QUEUES 222 5.2.1 QUEUES IN SERIES WITH MULTIPLE CHANNELS AT EACH PHASE 224 5.3 JACKSON NETWORK 226 5.4 CLOSED MARKOVIAN NETWORK (GORDON AND NEWELL NETWORK) 233 5.5 CYCLIC QUEUE 236 5.6 BCMP NETWORKS 238 5.7 CONCLUDING REMARKS 240 5.7.1 LOSS NETWORKS 241 PROBLEMS AND COMPLEMENTS 242 REFERENCES AND FURTHER READING 249 CHARTER 6 NON-MARKOVIAN QUEUEING SYSTEMS 255 6.1 INTRODUCTION 255 6.2 EMBEDDED-MARKOV-CHAIN TECHNIQUE FOR THE SYSTEM WITH POISSON INPUT 256 CONTENTS 6.3 THE M/G/L MODE!: POLLACZEK-KHINCHIN FORMULA 259 6.3.1 STEADY-STATE CFISTRIBUTION OF DEPARTURE EPOCH SYSTEM SIZE 259 6.3.2 WAITING-TIME DISTRIBUETION 261 6.3.3 GENERAL TIME SYSTEM SIZE DISTRIBUETION OF ANM/G/1 QUEUE: SUPPLEMENTARY VARIABLE TECHNIQUE 267 6.3.4 SEMI-MARKOV PRACESS APPROACH 274 6.3.5 APPROACH VIA MARTINGALE 274 6.4 BUS/PERIOD 276 6.4.1 INTRODUCTION 276 6.4.2 BUSY-PERIOD DISTRIBUETION: TAKACS INTEGRAL EQUATION 277 6.4.3 FURTHER DISCUSSION OFTHE BUSY PERIOD 279 6.4.4 DELAY BUSY PERIOD 284 6.4.5 DELAY BUSY PERIOD UNDER N-POLICY 28B 6.5 QUEUES WITH FINITE INPUT SOURCE: M/G/ 1//N SYSTEM 289 6.6 SYSTEM WITH LIMITED WAITING SPACE: M/G/L/K SYSTEM 292 6.7 THEAF/G/1 MODEL WITH BULK ARRIVAL 295 6.7.1 THE NUMBER IN THE SYSTEM AT DEPARTURE EPOCHS IN STEADY STATE (POLLACZEK-KHINCHIN FORMULA) 295 6.7.2 WAITING-TIME DISTRIBUETION 295 6.7.3 FEEDBACKQUEUES 302 6.8 THE M/G(A, O)/L MODEL WITH GENERAL BULK SERVICE 304 6.9 THE G/M/L MODEL 306 6.9.1 STEADY-STATE ARRIVAL EPOCH SYSTEM SIZE 306 6.9.2 GENERAL TIME SYSTEM SIZE IN STEADY STATE 309 6.9.3 WAITING-TIME DISTRIBUETION 311 6.9.4 EXPECTED DURATION OF BUSY PERIOD AND IDLE PERIOD 313 6.10 MULTISERVER MODEL 314 6.10.1 THE M/G/OO MODEL: TRANSIENT-STATE DISTRIBUETION 314 6.10.2 THE MODEL G/M/C 319 6.10.3 THEMODELM/G/C 322 6.11 QUEUES WITH MARKOVIAN ARRIVAL PROCESS 324 PROBLEMS AND COMPLEMENTS 326 REFERENCES AND FURTHER READING 334 XUE CONTENTS CHAPTER7 QUEUES WITH GENERAL ARRIVAL TIME AND SERVICE-TIME DISTRIBUTIONS 339 7.1 THE G/G/L QUEUE WITH GENERAL ARRIVAL TIME AND SERVICE-TIME DISTRIBUTIONS 339 7.1.1 LINDLEY S INTEGRAL EQUATION 341 7.1.2 LAPLACE TRANSFORM OF IV 343 7.1.3 GENERALIZATION OF THE POLLACZEK-KHINCHIN TRANSFORM FORMULA 346 7.2 MEAN AND VARIANCEOF WAITINGTIMEW 348 7.2.1 MEAN OF IV (SINGLE-SERVER QUEUE) 348 7.2.2 VARIANCEOF W 351 7.2.3 MULTISERVER QUEUES: APPROXIMATION OF MEAN WAITINGTIME 353 7.3 UUEUES WITH BATCH ARRIVALS G (X) /G/L 356 7.4 THE OUTPUT PROCESSOFA G/G/L SYSTEM 358 7.4.1 PARTICULAR CASE 359 7.4.2 OUTPUT PROCESS OF A G/G/C SYSTEM 360 7.5 SOME BOUNDS FOR THE G/G/L SYSTEM 360 7.5.1 BOUNDFORF{/) 360 7.5.2 BOUNDS FOR E(W) 360 PROBLEMS AND COMPLEMENTS 368 REFERENCES AND FURTHER READING 371 CHAPTER8 MISCELLANEOUSTOPICS 375 8.1 HEAVY-TRAFFIC APPROXIMATION FOR WAITING-TIME DISTRIBUTION 375 8.1.1 KINGMAN S HEAVY-TRAFFIC APPROXIMATION FOR A G/G/L QUEUE 375 8.1.2 EMPIRICAL EXTENSION OF THEM/G/1 HEAVY-TRAFFIC APPROXIMATION 379 8.1.3 G/M/C QUEUE IN HEAVYTRAFFIC 381 8.2 BROWNIAN MOTION PROCESS 383 8.2.1 INTRODUCTION 383 8.2.2 ASYMPTOTIC QUEUE-LENGTH DISTRIBATION 386 8.2.3 DIFFUSION APPROXIMATION FOR A G/G/L QUEU E 389 8.2.4 VIRTUAL DELAY FOR THE G/G/L SYSTEM 391 8.2.5 APPROACH THROUGH AN ABSORBING BARRIER WITH INSTANTANEOUS RETURN 394 8.2.6 DIFFUSION APPROXIMATION FOR A G/G/C QUEUE: STATE-DEPENDENT DIFFUSION EQUATION 395 CONTENTS XIII 8.2.7 DIFFUSION APPROXIMATIONFORANM/G/C MODEL 396 8.2.8 CONCLUDING REMARKS 397 8.3 QUEUEING SYSTEMS WITH VACATIONS 398 8.3.1 INTRODUCTION 398 8.3.2 STOCHASTIC DECOMPOSITION 399 8.3.3 POISSON INPUT QUEUE WITH VACATIONS: [EXHAUSTIVE-SERVICE] QUEUE-LENGTH DISTRIBUTION 399 8.3.4 POISSON INPUT QUEUE WITH VACATIONS: WAITING-TIME DISTRIBUTION 404 8.3.5 M/G/L SYSTEM WITH VACATIONS: NANEXHAUSTIVE SERVICE 406 8.3.6 LIMITED SERVICE SYSTEM: M/G/L* V, MODEL 407 8.3.7 GATED SERVICE SYSTEM: M/G/1 1/P, MODEL 408 8.3.8 M/G/L/K QUEUE WITH MULTIPLE VACATIONS 412 8.3.9 MEAN VALUE ANALYSIS THROUGH HEURISTIC TREATMENT 416 8.4 DESIGN AND CONTROL OF QUEUES 423 8.5 RETRIAL QUEUEING SYSTEM 427 8.5.1 RETRIAL QUEUES: MODEL DESCRIPTION 427 8.5.2 SINGLE-SERVER MODEL: M/M/L RETRIAL QUEUE 429 8.5.3 M/G/L RETRIAL QUEUE 432 8.5.4 MULTISERVER MODEIS 436 8.5.5 MODEL WITH FINITE ORBIT SIZE 439 8.5.6 OTHER RETRIAL QUEUE MODELS 440 8.6 EMERGENCE OFA NEW TREND IN TELETRAFFICTHEORY 441 8.6.1 INTRODUCTION 441 8.6.2 HEAVY-TAIL DISTRIBUTIONS 442 8.6.3 M/G/L WITH HEAVY-TAILED SERVICE TIME 445 8.6.4 PARETO MIXTURE OF EXPONENTIAL (PME) DISTRIBUTION 445 8.6.5 GAMMA MIXTURE OF PARETO (GMP) DISTRIBUTION 447 8.6.6 BETA MIXTURE OF EXPONENTIAL (BME) DISTRIBUTION 450 8.6.7 A CLASS OF HEAVY-TAIL DISTRIBUTIONS 452 8.6.8 LONG-RANGE DEPENDENCE 454 PROBLEMS AND COMPLEMENTS 455 REFERENCES AND FURTHER READING 461 APPENDIX 469 INDEX 477
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publisher	Academic Press
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spelling	Medhi, Jyotiprasad Verfasser (DE-588)12875298X aut Stochastic models in queueing theory J. Medhi 2. ed. Amsterdam [u.a.] Academic Press 2003 XVIII, 482 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Queuing theory Stochastic processes Wartesystem (DE-588)4251734-5 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 Wartesystem (DE-588)4251734-5 s Stochastisches Modell (DE-588)4057633-4 s 1\p DE-604 http://www.loc.gov/catdir/description/els031/2002110814.html Publisher description http://www.loc.gov/catdir/toc/els031/2002110814.html Table of contents GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010102831&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Medhi, Jyotiprasad Stochastic models in queueing theory Queuing theory Stochastic processes Wartesystem (DE-588)4251734-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangentheorie (DE-588)4255044-0 gnd
subject_GND	(DE-588)4251734-5 (DE-588)4057630-9 (DE-588)4057633-4 (DE-588)4255044-0
title	Stochastic models in queueing theory
title_auth	Stochastic models in queueing theory
title_exact_search	Stochastic models in queueing theory
title_full	Stochastic models in queueing theory J. Medhi
title_fullStr	Stochastic models in queueing theory J. Medhi
title_full_unstemmed	Stochastic models in queueing theory J. Medhi
title_short	Stochastic models in queueing theory
title_sort	stochastic models in queueing theory
topic	Queuing theory Stochastic processes Wartesystem (DE-588)4251734-5 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Stochastisches Modell (DE-588)4057633-4 gnd Warteschlangentheorie (DE-588)4255044-0 gnd
topic_facet	Queuing theory Stochastic processes Wartesystem Stochastischer Prozess Stochastisches Modell Warteschlangentheorie
url	http://www.loc.gov/catdir/description/els031/2002110814.html http://www.loc.gov/catdir/toc/els031/2002110814.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010102831&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT medhijyotiprasad stochasticmodelsinqueueingtheory

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