Performance analysis of queuing and computer networks:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press
2008
|
| Schriftenreihe: | Chapman & Hall/CRC computer and information science series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. XXI |
| Beschreibung: | XXI, 449 S. graph. Darst. |
| ISBN: | 9781584889861 |
Internformat
MARC
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| 245 | 1 | 0 | |a Performance analysis of queuing and computer networks |c G. R. Dattatreya |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2008 | |
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| 650 | 4 | |a Computer networks |x Evaluation | |
| 650 | 4 | |a Network performance (Telecommunication) | |
| 650 | 4 | |a Queuing theory | |
| 650 | 4 | |a Telecommunication |x Traffic | |
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IMAGE 1
PERFORMANCE ANALYSIS OF
QUEUING AND COMPUTER NETWORKS
G. R. DATTATREYA UNIVERSITY OF TEXAS AT DALLAS U.S.A.
CRC PRESS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC PRESS IS
AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS A C H A P
M AN & HALL BOOK
IMAGE 2
CONTENTS
1 INTRODUCTION 1
1.1 BACKGROUND 1
1.2 QUEUES IN COMPUTERS AND COMPUTER NETWORKS 2
1.2.1 SINGLE PROCESSOR SYSTEMS 2
1.2.2 SYNCHRONOUS MULTI-PROCESSOR SYSTEMS 3
1.2.3 DISTRIBUTED OPERATING SYSTEM 3
1.2.4 DATA COMMUNICATION NETWORKS 3
1.2.4.1 DATA TRANSFER IN COMMUNICATION NETWORKS 3
1.2.4.2 ORGANIZATION OF A COMPUTER NETWORK 4
1.2.5 QUEUES IN DATA COMMUNICATION NETWORKS 5
1.3 QUEUING MODELS 6
1.4 CONCLUSION 9
2 CHARACTERIZATION OF DATA TRAFFIC 13
2.1 INTRODUCTION 13
2.2 THE PARETO RANDOM VARIABLE 15
2.3 THE POISSON RANDOM VARIABLE 22
2.3.1 DERIVATION OF THE POISSON PMF 23
2.3.2 INTERARRIVAL TIMES IN A POISSON SEQUENCE OF ARRIVALS 25
2.3.3 PROPERTIES OF POISSON STREAMS OF ARRIVALS 26
2.3.3.1 MEAN OF EXPONENTIAL RANDOM VARIABLE 26
2.3.3.2 MEAN OF THE POISSON RANDOM VARIABLE 27
2.3.3.3 VARIANCE OF THE EXPONENTIAL RANDOM VARIABLE . . 28 2.3.3.4
VARIANCE OF POISSON RANDOM VARIABLE 29
2.3.3.5 THE Z TRANSFORM OF A POISSON RANDOM VARIABLE . . 29 2.3.3.6
MEMORYLESS PROPERTY OF THE EXPONENTIAL RANDOM VARIABLE 30
2.3.3.7 TIME FOR THE NEXT ARRIVAL 31
2.3.3.8 NONNEGATIVE, CONTINUOUS, MEMORYLESS RANDOM VARIABLES 31
2.3.3.9 SUCCESSION OF IID EXPONENTIAL INTERARRIVAL TIMES . . 31 2.3.3.10
MERGING TWO INDEPENDENT POISSON STREAMS . . . 32 2.3.3.11 IID
PROBABILISTIC ROUTING INTO A FORK 35
2.4 SIMULATION 37
2.4.1 TECHNIQUE FOR SIMULATION 37
2.4.2 GENERALIZED BERNOULLI RANDOM NUMBER 37
2.4.3 GEOMETRIC AND MODIFIED GEOMETRIC RANDOM NUMBERS . . . 39
VU
IMAGE 3
VIII
2.4.4 EXPONENTIAL RANDOM NUMBER 39
2.4.5 PARETO RANDOM NUMBER 40
2.5 ELEMENTS OF PARAMETER ESTIMATION 42
2.5.1 PARAMETERS OF PARETO RANDOM VARIABLE 43
2.5.2 PROPERTIES OF ESTIMATORS 46
2.6 SEQUENCES OF RANDOM VARIABLES 47
2.6.1 CERTAIN AND ALMOST CERTAIN EVENTS 49
2.7 ELEMENTS OF DIGITAL COMMUNICATION AND DATA LINK PERFORMANCE . . 52
2.7.1 THE GAUSSIAN NOISE MODEL 52
2.7.2 BIT ERROR RATE EVALUATION 54
2.7.3 FRAME ERROR RATE EVALUATION 56
2.7.4 DATA RATE OPTIMIZATION 57
2.8 EXERCISES 59
3 THE M/M/L/OO QUEUE 63
3.1 INTRODUCTION 63
3.2 DERIVATION OF EQUILIBRIUM STATE PROBABILITIES 64
3.2.1 OPERATION IN EQUILIBRIUM 70
3.2.2 SETTING THE SYSTEM TO START IN EQUILIBRIUM 71
3.3 SIMPLE PERFORMANCE FIGURES 72
3.4 RESPONSE TIME AND ITS DISTRIBUTION 76
3.5 MORE PERFORMANCE FIGURES FOR M/M/L/OO SYSTEM 77
3.6 WAITING TIME DISTRIBUTION 80
3.7 DEPARTURES FROM EQUILIBRIUM M/M/L/OO SYSTEM . . . 81
3.8 ANALYSIS OF ON-OFF MODEL OF PACKET DEPARTURES 86
3.9 ROUND ROBIN OPERATING SYSTEM 88
3.10 EXAMPLES 94
3.11 ANALYSIS OF BUSY TIMES 96
3.11.1 COMBINATIONS OF ARRIVALS AND DEPARTURES DURING A BUSY TIME PERIOD
98
3.11.2 DENSITY FUNCTION OF BUSY TIMES 99
3.11.3 LAPLACE TRANSFORM OF THE BUSY TIME 101
3.12 FORWARD DATA LINK PERFORMANCE AND OPTIMIZATION 104
3.12.1 RELIABLE COMMUNICATION OVER UNRELIABLE DATA LINKS 104
3.12.2 PROBLEM FORMULATION AND SOLUTION 105
3.13 EXERCISES 109
4 STATE DEPENDENT MARKOVIAN QUEUES 115
4.1 INTRODUCTION 115
4.2 STOCHASTIC PROCESSES 115
4.2.1 MARKOV PROCESS 117
4.3 CONTINUOUS PARAMETER MARKOV CHAMS 118
4.3.1 TIME INTERVALS BETWEEN STATE TRANSITIONS 118
4.3.2 STATE TRANSITION DIAGRAMS 118
4.3.3 DEVELOPMENT OF BALANCE EQUATIONS 119
IMAGE 4
IX
4.3.4 GRAPHICAL METHOD TO WRITE BALANCE EQUATIONS 123
4.4 MARKOV CHAINS FOR STATE DEPENDENT QUEUES 124
4.4.1 STATE DEPENDENT RATES AND EQUILIBRIUM PROBABILITIES 124
4.4.2 GENERAL PERFORMANCE FIGURES 127
4.4.2.1 THROUGHPUT 127
4.4.2.2 BLOCKING PROBABILITY 127
4.4.2.3 EXPECTED FRACTION OF LOST JOBS 127
4.4.2.4 EXPECTED NUMBER OF CUSTOMERS IN THE SYSTEM . . 128 4.4.2.5
EXPECTED RESPONSE TIME 128
4.5 INTUITIVE APPROACH FOR TIME AVERAGES 129
4.6 STATISTICAL ANALYSIS OF MARKOV CHAINS'SAMPLE FUNCTIONS 132
4.7 LITTLE'S RESULT 141
4.7.1 FIFOCASE 141
4.7.2 NON-FIFOCASE 142
4.8 APPLICATION SYSTEMS 143
4.8.1 CONSTANT RATE FINITE BUFFER M/M/L/FE SYSTEM 143
4.8.2 FORWARD DATA LINK WITH A FINITE BUFFER 146
4.8.3 M/M/OO OR IMMEDIATE SERVICE 147
4.8.4 PARALLEL SERVERS 148
4.8.5 CLIENT-SERVER MODEL 152
4.9 MEDIUM ACCESS IN LOCAL AREA NETWORKS 160
4.9.1 HEAVILY LOADED CHANNEL WITH A CONTENTION BASED TRANSMISSION
PROTOCOL 160
4.9.1.1 CONSEQUENCES OF MODELING APPROXIMATIONS . . . 161 4.9.1.2
ANALYSIS STEPS 162
4.9.2 A SIMPLE CONTENTION-FREE LAN PROTOCOL 163
4.10 EXERCISES 170
5 THE M/G/L QUEUE 179
5.1 INTRODUCTION 179
5.2 IMBEDDED PROCESSES 180
5.3 EQUILIBRIUM AND LONG TERM OPERATION OFM/G/1/OO QUEUE . . . 181
5.3.1 RECURRENCE EQUATIONS FOR STATE SEQUENCE 181
5.3.2 ANALYSIS OF EQUILIBRIUM OPERATION 183
5.3.3 STATISTICAL BEHAVIOR OF THE DISCRETE PARAMETER SAMPLE FUNCTION 185
5.3.4 STATISTICAL BEHAVIOR OF THE CONTINUOUS TIME STOCHASTIC PROCESS 189
5.3.5 POISSON ARRIVALS SEE TIME AVERAGES 190
5.4 DERIVATION OF THE POLLACZEK-KHINCHIN MEAN VALUE FORMULA 193
5.4.1 PERFORMANCE FIGURES 198
5.5 APPLICATION EXAMPLES 198
5.5.1 M/D/L/OO: CONSTANT SERVICE TIME 198
5.5.2 M/U/1/OO: UNIFORMLY DISTRIBUTED SERVICE TIME 198
5.5.3 HYPOEXPONENTIAL SERVICE TIME 199
5.5.4 HYPEREXPONENTIAL SERVICE TIME 199
IMAGE 5
X
5.6 SPECIAL CASES 200
5.6.1 PARETO SERVICE TIMES WITH INFINITE VARIANCE 200
5.6.2 FINITEBUFFERM/G/1 SYSTEM 200
5.7 EXERCISES 202
6 DISCRETE TIME QUEUES 209
6.1 INTRODUCTION 209
6.2 TUNING AND SYNCHRONIZATION 209
6.3 STATE TRANSITIONS AND THEIR PROBABILITIES 211
6.4 DISCRETE PARAMETER MARKOV CHAINS 216
6.4.1 HOMOGENEOUS MARKOV CHAINS 218
6.4.2 CHAPMAN-KOLMOGOROV EQUATIONS 220
6.4.3 IRREDUCIBLE MARKOV CHAINS 220
6.5 CLASSIFICATION OF STATES 223
6.5.1 APERIODIC STATES 223
6.5.2 TRANSIENT AND RECURRENT STATES 226
6.6 ANALYSIS OF EQUILIBRIUM MARKOV CHAINS 231
6.6.1 BALANCE EQUATIONS 232
6.6.2 TIME AVERAGES 239
6.6.3 LONG TERM BEHAVIOR OF APERIODIC CHAINS 240
6.6.4 CONTINUOUS PARAMETER MARKOV CHAINS 244
6.7 PERFORMANCE EVALUATION OF DISCRETE TIME QUEUES 245
6.7.1 THROUGHPUT 245
6.7.2 BUFFER OCCUPANCY 246
6.7.3 RESPONSE TIME 247
6.7.4 RELATIONSHIP BETWEEN TZ C AND 7R E 248
6.8 APPLICATIONS 249
6.8.1 THE GENERAL GEOM/GEOM/M/FC QUEUE 253
6.8.1.1 TRANSITION PROBABILITIES 253
6.8.1.2 EQUILIBRIUM STATE PROBABILITIES 254
6.8.2 SLOTTED CROSSBAR 256
6.8.3 LATE ARRIVAL SYSTEMS 258
6.9 CONCLUSION 259
6.10 EXERCISES 259
7 CONTINUOUS TIME QUEUING NETWORKS 267
7.1 INTRODUCTION 267
7.2 MODEL AND NOTATION FOR OPEN NETWORKS 268
7.3 GLOBAL BALANCE EQUATIONS 270
7.4 TRAFFIC EQUATIONS 273
7.5 THE PRODUCT FORM SOLUTION 276
7.6 VALIDITYOF PRODUCT FORM SOLUTION 278
7.7 DEVELOPMENT OF PRODUCT FORM SOLUTION FOR CLOSED NETWORKS . . . 282
7.8 CONVOLUTION ALGORITHM 286
7.9 PERFORMANCE FIGURES FROM THE G(N, M) MATRIX 288
IMAGE 6
XI
7.9.1 MARGINAL STATE PROBABILITIES 288
7.9.2 AVERAGE NUMBER IN A STATION 289
7.9.3 THROUGHPUT IN A STATION 289
7.9.4 UTILIZATION IN A STATION 289
7.9.5 EXPECTED RESPONSE TIME IN A STATION 290
7.10 MEAN VALUE ANALYSIS 293
7.10.1 ARRIVAL THEOREM 294
7.10.2 CYCLIC NETWORK 295
7.10.2.1 MVA FOR CYCLIC QUEUES 295
7.10.3 NONCYCLIC CLOSED NETWORKS 296
7.10.3.1 MVA FOR NONCYCLIC NETWORKS 298
7.11 CONCLUSION 301
7.12 EXERCISES 301
8 THE G/M/L QUEUE 307
8.1 INTRODUCTION 307
8.2 THE IMBEDDED MARKOV CHAIN FOR G/M/L/OO QUEUE 307
8.3 ANALYSIS OF THE PARAMETER A 313
8.3.1 STABILITY CRITERION IN TERMS OF THE PARAMETERS OF THE QUEUE . .
317 8.3.2 DETERMINATION OF A 319
8.4 PERFORMANCE FIGURES IN G/M/L/OO QUEUE 321
8.4.1 EXPECTED RESPONSE TIME 321
8.4.2 EXPECTED NUMBER IN THE SYSTEM 321
8.5 FINITE BUFFER G/M/L/FC QUEUE 322
8.6 PARETO ARRIVALS IN A G/M/L/OO QUEUE 323
8.7 EXERCISES 326
9 QUEUES WITH BURSTY, MMPP, AND SELF-SIMILAR TRAFFIC 329
9.1 INTRODUCTION 329
9.2 DISTINCTION BETWEEN SMOOTH AND BURSTY TRAFFIC 331
9.3 SELF-SIMILAR PROCESSES 334
9.3.1 FRACTIONAL BROWNIAN MOTION 335
9.3.2 DISCRETE TIME FRACTIONAL GAUSSIAN NOISE AND ITS PROPERTIES . 336
9.3.3 PROBLEMS IN GENERATION OF PURE FBM 337
9.4 HYPEREXPONENTIAL APPROXIMATION TO SHIFTED PARETO INTERARRIVAL TIMES
337
9.5 CHARACTERIZATION OF MERGED PACKET SOURCES 339
9.6 PRODUCT FORM SOLUTION FOR THE TRAFFIC SOURCE MARKOV CHAIN . . . 340
9.6.1 EVALUATION OF H, THE CONSTANT IN THE PRODUCT FORM SOLUTION . 343
9.7 JOINT MARKOV CHAIN FOR THE TRAFFIC SOURCE AND QUEUE LENGTH . . .
344 9.8 EVALUATION OF EQUILIBRIUM STATE PROBABILITIES 348
9.8.1 ANALYSIS OF THE SEQUENCE SS ( N ) 351
9.9 QUEUES WITH MMPP TRAFFIC AND THEIR PERFORMANCE 355
9.10 PERFORMANCE FIGURES 357
9.11 CONCLUSION 357
IMAGE 7
9.12 EXERCISES 358
10 ANALYSISOF FLUID FLOW MODELS 363
10.1 INTRODUCTION 363
10.2 LEAKY BUECKET WITH TWO STATE ON-OFF INPUT 364
10.2.1 DEVELOPMENT OF DIFFERENTIAL EQUATIONS FOR BUFFER CONTENT . . 365
10.2.2 STABILITY CONDITION 376
10.3 LITTLE'S RESULT FOR FLUID FLOW SYSTEMS 377
10.4 OUTPUT PROCESSOF BUFFER FEDBY TWO STATE ON-OFF CHAIN 382
10.5 GENERAL FLUID FLOW MODEL AND ITS ANALYSIS 384
10.6 LEAKY BUECKET FED BY M/M/L/OO QUEUE OUTPUT 387
10.7 EXERCISES 394
A REVIEW OF PROBABILITY THEORY 397
A.L RANDOM EXPERIMENT 397
A.2 AXIOMS OF PROBABILITY 397
A.2.1 SOME USEFUL RESULTS 398
A.2.2 CONDITIONAL PROBABILITY AND STATISTICAL INDEPENDENCE . . . 399
A.3 RANDOM VARIABLE 400
A.3.1 CUMULATIVE DISTRIBUTION FUNCTION 401
A.3.2 DISCRETE RANDOM VARIABLES AND THE PROBABILITY MASS FUNCTION 402
A.3.3 CONTINUOUS RANDOM VARIABLES AND THE PROBABILITY DENSITY FUNCTION
403
A.3.4 MIXED RANDOM VARIABLES 404
A.4 CONDITIONAL PMF AND CONDITIONAL PDF 405
A.5 EXPECTATION, VARIANCE, AND MOMENTS 407
A.5.1 CONDITIONAL EXPECTATION 411
A.6 THEOREMS CONNECTING CONDITIONAL AND MARGINAL FUNCTIONS 412
A.7 SUMS OF RANDOM VARIABLES 415
A.7.1 SUM OF TWO DISCRETE RANDOM VARIABLES 415
A.7.2 SUM OF TWO CONTINUOUS RANDOM VARIABLES 416
A.8 BAYES' THEOREM 417
A.9 FUNCTION OF A RANDOM VARIABLE 421
A.9.1 DISCRETE FUNCTION OF A RANDOM VARIABLE 421
A.9.1.1 DISCRETE FUNCTION OF A DISCRETE RANDOM VARIABLE . . 421 A.9.1.2
DISCRETE FUNCTION OF A CONTINUOUS RANDOM VARIABLE 422 A.9.2 STRICTLY
MONOTONICALLY INCREASING FUNCTION 422
A.9.3 STRICTLY MONOTONICALLY DECREASING FUNCTION 423
A.9.4 THE GENERAL CASE OF A FUNCTION OF A RANDOM VARIABLE 423
A.10 THE LAPLACE TRANSFORM C 428
A.LL THE Z TRANSFORM 430
A.12 EXERCISES 434 |
| adam_txt |
IMAGE 1
PERFORMANCE ANALYSIS OF
QUEUING AND COMPUTER NETWORKS
G. R. DATTATREYA UNIVERSITY OF TEXAS AT DALLAS U.S.A.
CRC PRESS TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC PRESS IS
AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS A C H A P
M AN & HALL BOOK
IMAGE 2
CONTENTS
1 INTRODUCTION 1
1.1 BACKGROUND 1
1.2 QUEUES IN COMPUTERS AND COMPUTER NETWORKS 2
1.2.1 SINGLE PROCESSOR SYSTEMS 2
1.2.2 SYNCHRONOUS MULTI-PROCESSOR SYSTEMS 3
1.2.3 DISTRIBUTED OPERATING SYSTEM 3
1.2.4 DATA COMMUNICATION NETWORKS 3
1.2.4.1 DATA TRANSFER IN COMMUNICATION NETWORKS 3
1.2.4.2 ORGANIZATION OF A COMPUTER NETWORK 4
1.2.5 QUEUES IN DATA COMMUNICATION NETWORKS 5
1.3 QUEUING MODELS 6
1.4 CONCLUSION 9
2 CHARACTERIZATION OF DATA TRAFFIC 13
2.1 INTRODUCTION 13
2.2 THE PARETO RANDOM VARIABLE 15
2.3 THE POISSON RANDOM VARIABLE 22
2.3.1 DERIVATION OF THE POISSON PMF 23
2.3.2 INTERARRIVAL TIMES IN A POISSON SEQUENCE OF ARRIVALS 25
2.3.3 PROPERTIES OF POISSON STREAMS OF ARRIVALS 26
2.3.3.1 MEAN OF EXPONENTIAL RANDOM VARIABLE 26
2.3.3.2 MEAN OF THE POISSON RANDOM VARIABLE 27
2.3.3.3 VARIANCE OF THE EXPONENTIAL RANDOM VARIABLE . . 28 2.3.3.4
VARIANCE OF POISSON RANDOM VARIABLE 29
2.3.3.5 THE Z TRANSFORM OF A POISSON RANDOM VARIABLE . . 29 2.3.3.6
MEMORYLESS PROPERTY OF THE EXPONENTIAL RANDOM VARIABLE 30
2.3.3.7 TIME FOR THE NEXT ARRIVAL 31
2.3.3.8 NONNEGATIVE, CONTINUOUS, MEMORYLESS RANDOM VARIABLES 31
2.3.3.9 SUCCESSION OF IID EXPONENTIAL INTERARRIVAL TIMES . . 31 2.3.3.10
MERGING TWO INDEPENDENT POISSON STREAMS . . . 32 2.3.3.11 IID
PROBABILISTIC ROUTING INTO A FORK 35
2.4 SIMULATION 37
2.4.1 TECHNIQUE FOR SIMULATION 37
2.4.2 GENERALIZED BERNOULLI RANDOM NUMBER 37
2.4.3 GEOMETRIC AND MODIFIED GEOMETRIC RANDOM NUMBERS . . . 39
VU
IMAGE 3
VIII
2.4.4 EXPONENTIAL RANDOM NUMBER 39
2.4.5 PARETO RANDOM NUMBER 40
2.5 ELEMENTS OF PARAMETER ESTIMATION 42
2.5.1 PARAMETERS OF PARETO RANDOM VARIABLE 43
2.5.2 PROPERTIES OF ESTIMATORS 46
2.6 SEQUENCES OF RANDOM VARIABLES 47
2.6.1 CERTAIN AND ALMOST CERTAIN EVENTS 49
2.7 ELEMENTS OF DIGITAL COMMUNICATION AND DATA LINK PERFORMANCE . . 52
2.7.1 THE GAUSSIAN NOISE MODEL 52
2.7.2 BIT ERROR RATE EVALUATION 54
2.7.3 FRAME ERROR RATE EVALUATION 56
2.7.4 DATA RATE OPTIMIZATION 57
2.8 EXERCISES 59
3 THE M/M/L/OO QUEUE 63
3.1 INTRODUCTION 63
3.2 DERIVATION OF EQUILIBRIUM STATE PROBABILITIES 64
3.2.1 OPERATION IN EQUILIBRIUM 70
3.2.2 SETTING THE SYSTEM TO START IN EQUILIBRIUM 71
3.3 SIMPLE PERFORMANCE FIGURES 72
3.4 RESPONSE TIME AND ITS DISTRIBUTION 76
3.5 MORE PERFORMANCE FIGURES FOR M/M/L/OO SYSTEM 77
3.6 WAITING TIME DISTRIBUTION 80
3.7 DEPARTURES FROM EQUILIBRIUM M/M/L/OO SYSTEM . . . 81
3.8 ANALYSIS OF ON-OFF MODEL OF PACKET DEPARTURES 86
3.9 ROUND ROBIN OPERATING SYSTEM 88
3.10 EXAMPLES 94
3.11 ANALYSIS OF BUSY TIMES 96
3.11.1 COMBINATIONS OF ARRIVALS AND DEPARTURES DURING A BUSY TIME PERIOD
98
3.11.2 DENSITY FUNCTION OF BUSY TIMES 99
3.11.3 LAPLACE TRANSFORM OF THE BUSY TIME 101
3.12 FORWARD DATA LINK PERFORMANCE AND OPTIMIZATION 104
3.12.1 RELIABLE COMMUNICATION OVER UNRELIABLE DATA LINKS 104
3.12.2 PROBLEM FORMULATION AND SOLUTION 105
3.13 EXERCISES 109
4 STATE DEPENDENT MARKOVIAN QUEUES 115
4.1 INTRODUCTION 115
4.2 STOCHASTIC PROCESSES 115
4.2.1 MARKOV PROCESS 117
4.3 CONTINUOUS PARAMETER MARKOV CHAMS 118
4.3.1 TIME INTERVALS BETWEEN STATE TRANSITIONS 118
4.3.2 STATE TRANSITION DIAGRAMS 118
4.3.3 DEVELOPMENT OF BALANCE EQUATIONS 119
IMAGE 4
IX
4.3.4 GRAPHICAL METHOD TO WRITE BALANCE EQUATIONS 123
4.4 MARKOV CHAINS FOR STATE DEPENDENT QUEUES 124
4.4.1 STATE DEPENDENT RATES AND EQUILIBRIUM PROBABILITIES 124
4.4.2 GENERAL PERFORMANCE FIGURES 127
4.4.2.1 THROUGHPUT 127
4.4.2.2 BLOCKING PROBABILITY 127
4.4.2.3 EXPECTED FRACTION OF LOST JOBS 127
4.4.2.4 EXPECTED NUMBER OF CUSTOMERS IN THE SYSTEM . . 128 4.4.2.5
EXPECTED RESPONSE TIME 128
4.5 INTUITIVE APPROACH FOR TIME AVERAGES 129
4.6 STATISTICAL ANALYSIS OF MARKOV CHAINS'SAMPLE FUNCTIONS 132
4.7 LITTLE'S RESULT 141
4.7.1 FIFOCASE 141
4.7.2 NON-FIFOCASE 142
4.8 APPLICATION SYSTEMS 143
4.8.1 CONSTANT RATE FINITE BUFFER M/M/L/FE SYSTEM 143
4.8.2 FORWARD DATA LINK WITH A FINITE BUFFER 146
4.8.3 M/M/OO OR IMMEDIATE SERVICE 147
4.8.4 PARALLEL SERVERS 148
4.8.5 CLIENT-SERVER MODEL 152
4.9 MEDIUM ACCESS IN LOCAL AREA NETWORKS 160
4.9.1 HEAVILY LOADED CHANNEL WITH A CONTENTION BASED TRANSMISSION
PROTOCOL 160
4.9.1.1 CONSEQUENCES OF MODELING APPROXIMATIONS . . . 161 4.9.1.2
ANALYSIS STEPS 162
4.9.2 A SIMPLE CONTENTION-FREE LAN PROTOCOL 163
4.10 EXERCISES 170
5 THE M/G/L QUEUE 179
5.1 INTRODUCTION 179
5.2 IMBEDDED PROCESSES 180
5.3 EQUILIBRIUM AND LONG TERM OPERATION OFM/G/1/OO QUEUE . . . 181
5.3.1 RECURRENCE EQUATIONS FOR STATE SEQUENCE 181
5.3.2 ANALYSIS OF EQUILIBRIUM OPERATION 183
5.3.3 STATISTICAL BEHAVIOR OF THE DISCRETE PARAMETER SAMPLE FUNCTION 185
5.3.4 STATISTICAL BEHAVIOR OF THE CONTINUOUS TIME STOCHASTIC PROCESS 189
5.3.5 POISSON ARRIVALS SEE TIME AVERAGES 190
5.4 DERIVATION OF THE POLLACZEK-KHINCHIN MEAN VALUE FORMULA 193
5.4.1 PERFORMANCE FIGURES 198
5.5 APPLICATION EXAMPLES 198
5.5.1 M/D/L/OO: CONSTANT SERVICE TIME 198
5.5.2 M/U/1/OO: UNIFORMLY DISTRIBUTED SERVICE TIME 198
5.5.3 HYPOEXPONENTIAL SERVICE TIME 199
5.5.4 HYPEREXPONENTIAL SERVICE TIME 199
IMAGE 5
X
5.6 SPECIAL CASES 200
5.6.1 PARETO SERVICE TIMES WITH INFINITE VARIANCE 200
5.6.2 FINITEBUFFERM/G/1 SYSTEM 200
5.7 EXERCISES 202
6 DISCRETE TIME QUEUES 209
6.1 INTRODUCTION 209
6.2 TUNING AND SYNCHRONIZATION 209
6.3 STATE TRANSITIONS AND THEIR PROBABILITIES 211
6.4 DISCRETE PARAMETER MARKOV CHAINS 216
6.4.1 HOMOGENEOUS MARKOV CHAINS 218
6.4.2 CHAPMAN-KOLMOGOROV EQUATIONS 220
6.4.3 IRREDUCIBLE MARKOV CHAINS 220
6.5 CLASSIFICATION OF STATES 223
6.5.1 APERIODIC STATES 223
6.5.2 TRANSIENT AND RECURRENT STATES 226
6.6 ANALYSIS OF EQUILIBRIUM MARKOV CHAINS 231
6.6.1 BALANCE EQUATIONS 232
6.6.2 TIME AVERAGES 239
6.6.3 LONG TERM BEHAVIOR OF APERIODIC CHAINS 240
6.6.4 CONTINUOUS PARAMETER MARKOV CHAINS 244
6.7 PERFORMANCE EVALUATION OF DISCRETE TIME QUEUES 245
6.7.1 THROUGHPUT 245
6.7.2 BUFFER OCCUPANCY 246
6.7.3 RESPONSE TIME 247
6.7.4 RELATIONSHIP BETWEEN TZ C AND 7R E 248
6.8 APPLICATIONS 249
6.8.1 THE GENERAL GEOM/GEOM/M/FC QUEUE 253
6.8.1.1 TRANSITION PROBABILITIES 253
6.8.1.2 EQUILIBRIUM STATE PROBABILITIES 254
6.8.2 SLOTTED CROSSBAR 256
6.8.3 LATE ARRIVAL SYSTEMS 258
6.9 CONCLUSION 259
6.10 EXERCISES 259
7 CONTINUOUS TIME QUEUING NETWORKS 267
7.1 INTRODUCTION 267
7.2 MODEL AND NOTATION FOR OPEN NETWORKS 268
7.3 GLOBAL BALANCE EQUATIONS 270
7.4 TRAFFIC EQUATIONS 273
7.5 THE PRODUCT FORM SOLUTION 276
7.6 VALIDITYOF PRODUCT FORM SOLUTION 278
7.7 DEVELOPMENT OF PRODUCT FORM SOLUTION FOR CLOSED NETWORKS . . . 282
7.8 CONVOLUTION ALGORITHM 286
7.9 PERFORMANCE FIGURES FROM THE G(N, M) MATRIX 288
IMAGE 6
XI
7.9.1 MARGINAL STATE PROBABILITIES 288
7.9.2 AVERAGE NUMBER IN A STATION 289
7.9.3 THROUGHPUT IN A STATION 289
7.9.4 UTILIZATION IN A STATION 289
7.9.5 EXPECTED RESPONSE TIME IN A STATION 290
7.10 MEAN VALUE ANALYSIS 293
7.10.1 ARRIVAL THEOREM 294
7.10.2 CYCLIC NETWORK 295
7.10.2.1 MVA FOR CYCLIC QUEUES 295
7.10.3 NONCYCLIC CLOSED NETWORKS 296
7.10.3.1 MVA FOR NONCYCLIC NETWORKS 298
7.11 CONCLUSION 301
7.12 EXERCISES 301
8 THE G/M/L QUEUE 307
8.1 INTRODUCTION 307
8.2 THE IMBEDDED MARKOV CHAIN FOR G/M/L/OO QUEUE 307
8.3 ANALYSIS OF THE PARAMETER A 313
8.3.1 STABILITY CRITERION IN TERMS OF THE PARAMETERS OF THE QUEUE . .
317 8.3.2 DETERMINATION OF A 319
8.4 PERFORMANCE FIGURES IN G/M/L/OO QUEUE 321
8.4.1 EXPECTED RESPONSE TIME 321
8.4.2 EXPECTED NUMBER IN THE SYSTEM 321
8.5 FINITE BUFFER G/M/L/FC QUEUE 322
8.6 PARETO ARRIVALS IN A G/M/L/OO QUEUE 323
8.7 EXERCISES 326
9 QUEUES WITH BURSTY, MMPP, AND SELF-SIMILAR TRAFFIC 329
9.1 INTRODUCTION 329
9.2 DISTINCTION BETWEEN SMOOTH AND BURSTY TRAFFIC 331
9.3 SELF-SIMILAR PROCESSES 334
9.3.1 FRACTIONAL BROWNIAN MOTION 335
9.3.2 DISCRETE TIME FRACTIONAL GAUSSIAN NOISE AND ITS PROPERTIES . 336
9.3.3 PROBLEMS IN GENERATION OF PURE FBM 337
9.4 HYPEREXPONENTIAL APPROXIMATION TO SHIFTED PARETO INTERARRIVAL TIMES
337
9.5 CHARACTERIZATION OF MERGED PACKET SOURCES 339
9.6 PRODUCT FORM SOLUTION FOR THE TRAFFIC SOURCE MARKOV CHAIN . . . 340
9.6.1 EVALUATION OF H, THE CONSTANT IN THE PRODUCT FORM SOLUTION . 343
9.7 JOINT MARKOV CHAIN FOR THE TRAFFIC SOURCE AND QUEUE LENGTH . . .
344 9.8 EVALUATION OF EQUILIBRIUM STATE PROBABILITIES 348
9.8.1 ANALYSIS OF THE SEQUENCE SS ( N ) 351
9.9 QUEUES WITH MMPP TRAFFIC AND THEIR PERFORMANCE 355
9.10 PERFORMANCE FIGURES 357
9.11 CONCLUSION 357
IMAGE 7
9.12 EXERCISES 358
10 ANALYSISOF FLUID FLOW MODELS 363
10.1 INTRODUCTION 363
10.2 LEAKY BUECKET WITH TWO STATE ON-OFF INPUT 364
10.2.1 DEVELOPMENT OF DIFFERENTIAL EQUATIONS FOR BUFFER CONTENT . . 365
10.2.2 STABILITY CONDITION 376
10.3 LITTLE'S RESULT FOR FLUID FLOW SYSTEMS 377
10.4 OUTPUT PROCESSOF BUFFER FEDBY TWO STATE ON-OFF CHAIN 382
10.5 GENERAL FLUID FLOW MODEL AND ITS ANALYSIS 384
10.6 LEAKY BUECKET FED BY M/M/L/OO QUEUE OUTPUT 387
10.7 EXERCISES 394
A REVIEW OF PROBABILITY THEORY 397
A.L RANDOM EXPERIMENT 397
A.2 AXIOMS OF PROBABILITY 397
A.2.1 SOME USEFUL RESULTS 398
A.2.2 CONDITIONAL PROBABILITY AND STATISTICAL INDEPENDENCE . . . 399
A.3 RANDOM VARIABLE 400
A.3.1 CUMULATIVE DISTRIBUTION FUNCTION 401
A.3.2 DISCRETE RANDOM VARIABLES AND THE PROBABILITY MASS FUNCTION 402
A.3.3 CONTINUOUS RANDOM VARIABLES AND THE PROBABILITY DENSITY FUNCTION
403
A.3.4 MIXED RANDOM VARIABLES 404
A.4 CONDITIONAL PMF AND CONDITIONAL PDF 405
A.5 EXPECTATION, VARIANCE, AND MOMENTS 407
A.5.1 CONDITIONAL EXPECTATION 411
A.6 THEOREMS CONNECTING CONDITIONAL AND MARGINAL FUNCTIONS 412
A.7 SUMS OF RANDOM VARIABLES 415
A.7.1 SUM OF TWO DISCRETE RANDOM VARIABLES 415
A.7.2 SUM OF TWO CONTINUOUS RANDOM VARIABLES 416
A.8 BAYES' THEOREM 417
A.9 FUNCTION OF A RANDOM VARIABLE 421
A.9.1 DISCRETE FUNCTION OF A RANDOM VARIABLE 421
A.9.1.1 DISCRETE FUNCTION OF A DISCRETE RANDOM VARIABLE . . 421 A.9.1.2
DISCRETE FUNCTION OF A CONTINUOUS RANDOM VARIABLE 422 A.9.2 STRICTLY
MONOTONICALLY INCREASING FUNCTION 422
A.9.3 STRICTLY MONOTONICALLY DECREASING FUNCTION 423
A.9.4 THE GENERAL CASE OF A FUNCTION OF A RANDOM VARIABLE 423
A.10 THE LAPLACE TRANSFORM C 428
A.LL THE Z TRANSFORM 430
A.12 EXERCISES 434 |
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| id | DE-604.BV023425531 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:32:40Z |
| indexdate | 2024-08-01T00:28:03Z |
| institution | BVB |
| isbn | 9781584889861 |
| language | English |
| lccn | 2008011866 |
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| physical | XXI, 449 S. graph. Darst. |
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| series2 | Chapman & Hall/CRC computer and information science series |
| spelling | Dattatreya, Galigekere R. Verfasser aut Performance analysis of queuing and computer networks G. R. Dattatreya Boca Raton, Fla. [u.a.] CRC Press 2008 XXI, 449 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC computer and information science series Literaturverz. S. XXI Computer networks Evaluation Network performance (Telecommunication) Queuing theory Telecommunication Traffic Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Rechnernetz (DE-588)4070085-9 gnd rswk-swf Dienstgüte (DE-588)4496068-2 gnd rswk-swf Rechnernetz (DE-588)4070085-9 s Warteschlangentheorie (DE-588)4255044-0 s Dienstgüte (DE-588)4496068-2 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016607894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dattatreya, Galigekere R. Performance analysis of queuing and computer networks Computer networks Evaluation Network performance (Telecommunication) Queuing theory Telecommunication Traffic Warteschlangentheorie (DE-588)4255044-0 gnd Rechnernetz (DE-588)4070085-9 gnd Dienstgüte (DE-588)4496068-2 gnd |
| subject_GND | (DE-588)4255044-0 (DE-588)4070085-9 (DE-588)4496068-2 |
| title | Performance analysis of queuing and computer networks |
| title_auth | Performance analysis of queuing and computer networks |
| title_exact_search | Performance analysis of queuing and computer networks |
| title_exact_search_txtP | Performance analysis of queuing and computer networks |
| title_full | Performance analysis of queuing and computer networks G. R. Dattatreya |
| title_fullStr | Performance analysis of queuing and computer networks G. R. Dattatreya |
| title_full_unstemmed | Performance analysis of queuing and computer networks G. R. Dattatreya |
| title_short | Performance analysis of queuing and computer networks |
| title_sort | performance analysis of queuing and computer networks |
| topic | Computer networks Evaluation Network performance (Telecommunication) Queuing theory Telecommunication Traffic Warteschlangentheorie (DE-588)4255044-0 gnd Rechnernetz (DE-588)4070085-9 gnd Dienstgüte (DE-588)4496068-2 gnd |
| topic_facet | Computer networks Evaluation Network performance (Telecommunication) Queuing theory Telecommunication Traffic Warteschlangentheorie Rechnernetz Dienstgüte |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016607894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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