Stochastic theory of service systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Pergamon Press
1973
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | International series of monographs in pure and applied mathematics
103 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 168 S. Ill. |
| ISBN: | 0080169481 |
Internformat
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Datensatz im Suchindex
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| adam_text | Titel: Stochastic theory of service systems
Autor: Kosten, Leendert
Jahr: 1973
CONTENTS Preface ix 1. Introduction 1 1.1. General description of service systems 1 1.1.1. Characteristics of holding-times 4 1.1.2. Characteristics of the flow of demands 4 1.1.3. The queue-discipline 5 1.1.4. The time-dependence of the system’s behaviour; steady-state conditions 6 1.1.5. What are the questions that are normally asked? 7 1.1.6. Situations not covered by the described model 8 1.1.7. Analysis versus simulation 9 1.2. Characteristics of holding-times; continuation 10 1.3. Characteristics of the arrival process 17 1.3.1. The Poisson arrival process 18 1.3.2. Virtual and actual demands; time- and demand-averages 19 1.3.3. A simple birth-process; the Poisson distribution 20 1.3.4. The distribution of interarrival-times for the Poisson arrival process 22 1.3.5. Other distributions of interarrival-times 23 1.4. Kendall’s classification 24 2. The Standard Cases 26 2.1. Probability of blocking for the system M/Af/c-blocking 26 2.2. The Engset formula 31 2.3. Probability of delay and average waiting-time for the system M/M/c- delay 33 2.4. Econometric considerations 37 3. The Distribution of Waiting-times in the System Af/Af/c- delay 41 3.1. First-come-first-served 41 3.2. Last-come-first-served 42 3.3. “Random”-condition 45 3.4. Comparison of the cases “first-come-first-served”, “last-come-first- served” and “random” 47 3.5. A note on analytical methods 48 vii
vm CONTENTS 4. General Holding-time Assumption (CAf-cIass) SO 4.1. The case M/G/c-blocking 51 4.2. The case M/G/ 1-delay 55 4.3. A note on the system Af/G/c-delay 60 4.4. Use of Erlang-^ distributions 62 4.5. Hyperexponential distributions 67 5. Non-stationary Behaviour 71 5.1. Markov process with a finite number of states 71 5.2. The case M/M/c-blocking; transient behaviour 75 5.3. Transient behaviour of the system Af/G/l-delay 79 6. Priority 86 6.1. Non-pre-emptive priority 87 6.2. Pre-emptive priority; breakdown of machines 92 7. Restricted Availability 101 7.1. Introduction 101 7.2. Restricted availability; exact evaluation of probabilities of blocking 104 7.3. Approximate determination of probabilities of blocking; characteristics of overflow traffic 107 8. Arrival and Service in Batches 112 8.1. Introduction 112 8.2. Arrivals in batches; individual service (exponential holding-time) 113 8.3. Service in batches of capacity c; constant holding-time 115 8.4. The “custodian’s problem” 119 8.5. The “unscheduled ferry problem” 123 9. Simulation 127 9.1. Introduction; non-analytical methods 127 9.2. Principles of time-true simulation 130 9.3. Principles of roulette simulation 131 9.4. The implementation of randomness 135 9.5. Accuracy of simulation results 139 9.6. The “cluster effect” 142 Appendix: Generating Functions and Laplace Transforms 148 References 155 Author Index 159 Subject Index 161 Other titles in series 166
|
| adam_txt |
Titel: Stochastic theory of service systems
Autor: Kosten, Leendert
Jahr: 1973
CONTENTS Preface ix 1. Introduction 1 1.1. General description of service systems 1 1.1.1. Characteristics of holding-times 4 1.1.2. Characteristics of the flow of demands 4 1.1.3. The queue-discipline 5 1.1.4. The time-dependence of the system’s behaviour; steady-state conditions 6 1.1.5. What are the questions that are normally asked? 7 1.1.6. Situations not covered by the described model 8 1.1.7. Analysis versus simulation 9 1.2. Characteristics of holding-times; continuation 10 1.3. Characteristics of the arrival process 17 1.3.1. The Poisson arrival process 18 1.3.2. Virtual and actual demands; time- and demand-averages 19 1.3.3. A simple birth-process; the Poisson distribution 20 1.3.4. The distribution of interarrival-times for the Poisson arrival process 22 1.3.5. Other distributions of interarrival-times 23 1.4. Kendall’s classification 24 2. The Standard Cases 26 2.1. Probability of blocking for the system M/Af/c-blocking 26 2.2. The Engset formula 31 2.3. Probability of delay and average waiting-time for the system M/M/c- delay 33 2.4. Econometric considerations 37 3. The Distribution of Waiting-times in the System Af/Af/c- delay 41 3.1. First-come-first-served 41 3.2. Last-come-first-served 42 3.3. “Random”-condition 45 3.4. Comparison of the cases “first-come-first-served”, “last-come-first- served” and “random” 47 3.5. A note on analytical methods 48 vii
vm CONTENTS 4. General Holding-time Assumption (CAf-cIass) SO 4.1. The case M/G/c-blocking 51 4.2. The case M/G/ 1-delay 55 4.3. A note on the system Af/G/c-delay 60 4.4. Use of Erlang-^ distributions 62 4.5. Hyperexponential distributions 67 5. Non-stationary Behaviour 71 5.1. Markov process with a finite number of states 71 5.2. The case M/M/c-blocking; transient behaviour 75 5.3. Transient behaviour of the system Af/G/l-delay 79 6. Priority 86 6.1. Non-pre-emptive priority 87 6.2. Pre-emptive priority; breakdown of machines 92 7. Restricted Availability 101 7.1. Introduction 101 7.2. Restricted availability; exact evaluation of probabilities of blocking 104 7.3. Approximate determination of probabilities of blocking; characteristics of overflow traffic 107 8. Arrival and Service in Batches 112 8.1. Introduction 112 8.2. Arrivals in batches; individual service (exponential holding-time) 113 8.3. Service in batches of capacity c; constant holding-time 115 8.4. The “custodian’s problem” 119 8.5. The “unscheduled ferry problem” 123 9. Simulation 127 9.1. Introduction; non-analytical methods 127 9.2. Principles of time-true simulation 130 9.3. Principles of roulette simulation 131 9.4. The implementation of randomness 135 9.5. Accuracy of simulation results 139 9.6. The “cluster effect” 142 Appendix: Generating Functions and Laplace Transforms 148 References 155 Author Index 159 Subject Index 161 Other titles in series 166 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| index_date | 2024-07-02T16:11:51Z |
| indexdate | 2024-07-09T20:49:13Z |
| institution | BVB |
| isbn | 0080169481 |
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| spelling | Kosten, Leendert Verfasser (DE-588)127783709 aut Stochastic theory of service systems by L. Kosten 1. ed. Oxford [u.a.] Pergamon Press 1973 XII, 168 S. Ill. txt rdacontent n rdamedia nc rdacarrier International series of monographs in pure and applied mathematics 103 Files d'attente, Théorie des Processus stochastiques Queuing theory Stochastic processes Systemtheorie (DE-588)4058812-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Wartesystem (DE-588)4251734-5 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Systemtheorie (DE-588)4058812-9 s Warteschlangentheorie (DE-588)4255044-0 s 1\p DE-604 Wartesystem (DE-588)4251734-5 s 2\p DE-604 International series of monographs in pure and applied mathematics 103 (DE-604)BV001888024 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015226386&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kosten, Leendert Stochastic theory of service systems International series of monographs in pure and applied mathematics Files d'attente, Théorie des Processus stochastiques Queuing theory Stochastic processes Systemtheorie (DE-588)4058812-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wartesystem (DE-588)4251734-5 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| subject_GND | (DE-588)4058812-9 (DE-588)4057630-9 (DE-588)4251734-5 (DE-588)4255044-0 |
| title | Stochastic theory of service systems |
| title_auth | Stochastic theory of service systems |
| title_exact_search | Stochastic theory of service systems |
| title_exact_search_txtP | Stochastic theory of service systems |
| title_full | Stochastic theory of service systems by L. Kosten |
| title_fullStr | Stochastic theory of service systems by L. Kosten |
| title_full_unstemmed | Stochastic theory of service systems by L. Kosten |
| title_short | Stochastic theory of service systems |
| title_sort | stochastic theory of service systems |
| topic | Files d'attente, Théorie des Processus stochastiques Queuing theory Stochastic processes Systemtheorie (DE-588)4058812-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Wartesystem (DE-588)4251734-5 gnd Warteschlangentheorie (DE-588)4255044-0 gnd |
| topic_facet | Files d'attente, Théorie des Processus stochastiques Queuing theory Stochastic processes Systemtheorie Stochastischer Prozess Wartesystem Warteschlangentheorie |
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