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

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