Stochastic Theory of Service Systems
- 1st Edition - February 17, 2016
- Imprint: Pergamon
- Author: L. Kosten
- Editors: I. N. Sneddon, M. Stark
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 1 8 1 6 - 1
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 5 0 5 8 - 1
International Series of Monographs in Pure and Applied Mathematics, Volume 103: Stochastic Theory of Service Systems focuses on the principles, methodologies, and approaches… Read more
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International Series of Monographs in Pure and Applied Mathematics, Volume 103: Stochastic Theory of Service Systems focuses on the principles, methodologies, and approaches involved in the stochastic theory of service systems. The publication first examines the general description of service systems, characteristics of the arrival process, standard cases, and the distribution of waiting-times in the system M/M/c-delay. Discussions focus on "random" condition, probability of delay and average waiting-time for the system M/M/c-delay, Engset formula, and probability of blocking for the system M/M/c-blocking. The text then examines general holding-time assumption, non-stationary behavior, and priority. Topics include pre-emptive priority, transient behavior of the system M/G/1-delay, Markov process with a finite number of states, and hyperexponential distributions. The manuscript takes a look at simulation, arrival and service in batches, and restricted availability, including approximate determination of probabilities of blocking, "unscheduled ferry problem", principles of roulette simulation, and implementation of randomness. The publication is a dependable source material for researchers interested in the stochastic theory of service systems.
1. Introduction
1.1. General Description of Service Systems
1.1.1. Characteristics of Holding-Times
1.1.2. Characteristics of the Flow of Demands
1.1.3. the Queue-Discipline
1.1.4. The Time-Dependence of the System's Behaviour; Steady-State Conditions
1.1.5. What are the Questions that are Normally Asked?
1.1.6. Situations not Covered by the Described Model
1.1.7. Analysis Versus Simulation
1.2. Characteristics of Holding-Times; Continuation
1.3. Characteristics of the Arrival Process
1.3.1. the Poisson Arrival Process
1.3.2. Virtual and Actual Demands; Time- and Demand-Averages
1.3.3. A Simple Birth-Process; The Poisson Distribution
1.3.4. The Distribution of Interarrival-Times for the Poisson Arrival Process
1.3.5. Other Distributions of Interarrival-Times
1.4. Kendall's Classification
2. The Standard Cases 26
2.1. Probability of Blocking for the System M/M/c-Blocking
2.2. the Engset Formula
2.3. Probability of Delay and Average Waiting-Time for the System M/M/c-Delay
2.4. Econometric Considerations
3. The Distribution of Waiting-Times in the System M/M/c-Delay
3.1. First-Come-First-Served
3.2. Last-Come-First-Served
3.3. "Random"-Condition
3.4. Comparison of the Cases "First-Come-First-Served", "Last-Come-Firstserved" and "Random"
3.5. A Note on Analytical Methods
4. General Holding-Time Assumption (CM-Class)
4.1. The Case M/G/c-Blocking
4.2. The Case M/G/1-Delay
4.3. A Note on the System M/G/c-Delay
4.4. Use of Erlang-k Distributions
4.5. Hyperexponential Distributions
5. Non-Stationary Behaviour
5.1. Markov Process with a Finite Number of States
5.2. The Case M/M/c-Blocking; Transient Behaviour
5.3. Transient Behaviour of the System M/G/1-Delay
6. Priority
6.1. Non-Pre-Emptive Priority
6.2. Pre-Emptive Priority; Breakdown of Machines
7. Restricted Availability
7.1. Introduction
7.2. Restricted Availability; Exact Evaluation of Probabilities of Blocking
7.3. Approximate Determination of Probabilities of Blocking; Characteristics of Overflow Traffic
8. Arrival and Service in Batches
8.1. Introduction
8.2. Arrivals in Batches; Individual Service (Exponential Holding-Time)
8.3. Service in Batches of Capacity c; Constant Holding-Time
8.4. The "Custodian'S Problem"
8.5. The "Unscheduled Ferry Problem"
9. Simulation
9.1. Introduction; Non-Analytical Methods
9.2. Principles of Time-True Simulation
9.3. Principles of Roulette Simulation
9.4. the Implementation of Randomness
9.5. Accuracy of Simulation Results
9.6. the "Cluster Effect"
Appendix: Generating Functions and Laplace Transforms
References
Author Index
Subject Index
Other Titles in Series
- Edition: 1
- Published: February 17, 2016
- Imprint: Pergamon
- Language: English