Realization probabilities: the dynamics of queuing systems
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London u.a.
Springer
1994
|
| Schriftenreihe: | Lecture notes in control and information sciences
194 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005874801&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 320 S. |
| ISBN: | 3540198725 0387198725 |
Internformat
MARC
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| 245 | 1 | 0 | |a Realization probabilities |b the dynamics of queuing systems |c Xi-Ren Cao |
| 264 | 1 | |a London u.a. |b Springer |c 1994 | |
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| 650 | 7 | |a système événement discret |2 inriac | |
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Datensatz im Suchindex
| _version_ | 1819300976775921664 |
|---|---|
| adam_text | Contents
1 Introduction 1
1.1 An Overview 1
1.2 Dynamics of Queuing Systems 8
1.3 A Two Server Cyclic Queuing Network 12
2 Mathematical Background 21
2.1 Probability Theory 21
2.1.1 The Elementary Concepts 21
2.1.2 Some Facts and Theorems 31
2.2 Stochastic Processes 39
2.2.1 Markov Chains 39
2.2.2 Markov Processes 45
2.2.3 Semi Markov Processes 50
2.2.4 Regenerative Processes 51
2.2.5 Point Processes 53
2.3 Queuing Systems 59
2.3.1 The Single Station Queue 59
2.3.2 Queuing Networks 64
2.4 Linear Differential Equations 71
S Realization Probabilities in Closed Jackson Networks 75
3.1 The Markov Process Model 75
3.2 Realization Probabilities 79
3.2.1 The Evolution of a Perturbation on a Sample Path . 79
3.2.2 Realization Probabilities 83
3.3 Sample Sensitivities 88
3.3.1 Sample Performance Functions and Their Derivatives 88
viii
3.3.2 Perturbations Due to Parameter Changes 89
3.3.3 Calculation of Sample Derivatives of Throughputs . 93
3.4 Sensitivities of Steady State Throughputs to Mean Service
Times 101
3.4.1 The Sample Performance Function TL(sv,Z) 101
3.4.2 Formulas for Steady State Throughput Sensitivities 103
3.5 Other Sensitivities 109
3.5.1 Service Rates Change in a Set of States 109
3.5.2 Sensitivities to the Number of Customers 110
3.5.3 Sensitivities to Any Changes in Service Time Distri¬
butions Ill
4 Realization Factors in State Dependent Networks 117
4.1 Realization Factors and Their Equations 118
4.1.1 Perturbation Evolution in State Dependent Networks 118
4.1.2 General Performance Measures and Realization Factorsl21
4.1.3 Equations for Realization Factors 124
4.1.4 The Uniqueness of the Solutions 129
4.2 Sensitivity Formulas for Closed Networks 133
4.2.1 The Convergence of Sample Sensitivities 133
4.2.2 Sensitivities of Steady State Performance 137
4.3 Linear Formulation of Performance Sensitivities 141
4.3.1 System Dynamics Revisited 141
4.3.2 The Sensitivity Matrix 142
4.3.3 Reducing the Dimension 148
4.4 Sensitivity Formulas for Open Networks 153
4.4.1 Realization Factors for Open Networks 153
4.4.2 Sensitivity Formulas 155
4.4.3 The Sensitivities of an M/M/l Queue 160
4.4.4 The Quasi Lipschitz Condition 163
5 Systems with General Distributions 169
5.1 Closed Networks 169
5.1.1 The Network and Its Steady State Probabilities ... 169
5.1.2 Differential Equations for Realization Factors .... 173
5.1.3 The Perturbation Generation Function 177
5.1.4 Sample Derivatives 180
5.1.5 Steady State Sensitivity Formulas 183
5.2 Open Networks 189
ix
6 Multiclass Networks and Networks with Blocking 193
6.1 Multiclass Networks 194
6.1.1 Irreducible Multiclass Networks 194
6.1.2 The Sensitivity Analysis 205
6.2 Networks With Blocking 211
6.2.1 Perturbation Propagation Through Blocking Periods 211
6.2.2 Perturbation Realization 214
6.2.3 The Sensitivity Analysis 219
6.3 The Interchangeably 225
6.3.1 The Continuity of the Sample Functions 227
6.3.2 A Necessary Condition for Multiclass Networks . . . 230
6.3.3 A Sufficient Condition for Networks With Blocking . 235
6.4 A Summary 237
7 Sensitivity Analysis of Generalized Semi Markov Processes241
7.1 The Generalized Semi Markov Processes 242
7.2 Event Coupling in a GSMP 244
7.2.1 The Classification of Event Coupling 244
7.2.2 The Event Coupling Tree 248
7.3 Sensitivity Analysis Based on Realization 252
7.3.1 Realization Factors 253
7.3.2 Sample Sensitivities 255
7.3.3 Sensitivity of Steady State Performance 256
8 Operational Sensitivity Analysis 259
8.1 Operational Variables and Operational Assumptions .... 260
8.2 Operational Sensitivity Analysis 264
8.2.1 Realization Ratios 264
8.2.2 Operational Sensitivity Formulas 270
9 Explicit Formulas, Algorithms, and Applications to Opti¬
mization 275
9.1 A Two Server Cyclic Network 277
9.2 Explicit Formulas for Load Dependent Closed Jackson Net¬
works 282
9.2.1 Norton s Aggregation for Sensitivities 282
9.2.2 The Explicit Sensitivity formulas 286
9.3 The Convolution Algorithm for the Sensitivities 291
9.4 Decentralized Optimization of A Closed Jackson Network . 294
9.4.1 The Problem and the Solution 294
X
9.4.2 The Proof of the Lemma 297
Bibliography 303
Selected Notations 313
Index 317
|
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| discipline | Informatik Mathematik |
| format | Book |
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| indexdate | 2024-12-20T09:28:39Z |
| institution | BVB |
| isbn | 3540198725 0387198725 |
| language | English |
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| physical | X, 320 S. |
| publishDate | 1994 |
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| publisher | Springer |
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| series | Lecture notes in control and information sciences |
| series2 | Lecture notes in control and information sciences |
| spellingShingle | Cao, Xi-Ren Realization probabilities the dynamics of queuing systems Lecture notes in control and information sciences Files d'attente, théorie des ram Probabilités ram Wachttijdproblemen gtt dynamique système inriac système file attente inriac système événement discret inriac Probabilities Queuing theory Wartesystem (DE-588)4251734-5 gnd Sensitivitätsanalyse (DE-588)4129730-1 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| subject_GND | (DE-588)4251734-5 (DE-588)4129730-1 (DE-588)4121894-2 |
| title | Realization probabilities the dynamics of queuing systems |
| title_auth | Realization probabilities the dynamics of queuing systems |
| title_exact_search | Realization probabilities the dynamics of queuing systems |
| title_full | Realization probabilities the dynamics of queuing systems Xi-Ren Cao |
| title_fullStr | Realization probabilities the dynamics of queuing systems Xi-Ren Cao |
| title_full_unstemmed | Realization probabilities the dynamics of queuing systems Xi-Ren Cao |
| title_short | Realization probabilities |
| title_sort | realization probabilities the dynamics of queuing systems |
| title_sub | the dynamics of queuing systems |
| topic | Files d'attente, théorie des ram Probabilités ram Wachttijdproblemen gtt dynamique système inriac système file attente inriac système événement discret inriac Probabilities Queuing theory Wartesystem (DE-588)4251734-5 gnd Sensitivitätsanalyse (DE-588)4129730-1 gnd Wahrscheinlichkeitsverteilung (DE-588)4121894-2 gnd |
| topic_facet | Files d'attente, théorie des Probabilités Wachttijdproblemen dynamique système système file attente système événement discret Probabilities Queuing theory Wartesystem Sensitivitätsanalyse Wahrscheinlichkeitsverteilung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005874801&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005848579 |
| work_keys_str_mv | AT caoxiren realizationprobabilitiesthedynamicsofqueuingsystems |