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 Classification2. 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 Considerations3. 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 Methods4. 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 Distributions5. 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-Delay6. Priority 6.1. Non-Pre-Emptive Priority 6.2. Pre-Emptive Priority; Breakdown of Machines7. 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 Traffic8. 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 TransformsReferencesAuthor IndexSubject IndexOther Titles in Series