Queueing Modelling Fundamentals: With Applications in Communication Networks , 2nd Edition

List of Illustrations.

Preface.

1. Preliminaries.

1.1. Probability Theory.

1.2. z-Transforms - Generating Functions.

1.3. Laplace Transforms.

1.4. Matrix Operations.

Problems.

2. Introduction to Queueing Systems.

2.1. Nomenclature of a Queueing System.

2.2. Random Variables and their Relationships.

2.3. Kendall Notation.

2.4 Little's Theorem.

2.5 Resource Utilization and Traffic Intensity.

2.6 Flow Conservation Law.

2.7 Poisson Process.

2.8 Properties of Poisson Process.

Problems.

3. Discrete and Continuous Markov Processes.

3.1. Stochastic Processes.

3.2. Discrete-time Markov Chains.

3.3. Continuous-time Markov Chains.

3.4. Birth-Death Processes.

Problems.

4. Single-Queue Markovian Systems.

4.1. Classical M/M/1 Queue.

4.2. PASTA - Poisson Arrivals See Time Averages.

4.3. M/M/1/S Queueing Systems.

4.5. Multi-server Systems - M/M/m

4.6. Erlang's Loss Queueing Systems - M/M/m/m Systems.

4.7. Engset's Loss Systems.

4.8. Considerations for Applications of Queueing Models

Problems.

5. Semi-Markovian Queueing Systems.

5.1. The M/G/1 Queueing System.

5.2 The Residual Service Time Approach.

5.3 M/G/1 Non-preemptive Priority Queueing.

5.4 Priority Queueing Systems.

5.5 The G/M/1  Queueing System.

6. Open Queueing Networks.

6.1. Markovian Queries in Tandem.

6.2. Applications of Tandem Queues in Data Networks.

6.3. Jackson Queueing Networks.

Problems.

7. Closed Queueing Networks.

7.1. Jackson Closed Queueing Networks.

7.2. Steady-state Probability Distribution.

7.3. Convolution Algorithm.

7.4. Performance Measures.

7.5. Mean Value Analysis.

7.6. Application of Closed Queueing Networks.

Problems.

8. Markov-Modulated Arrival Process.

8.1. Markov-modulated Poisson Process (MMPP).

8.2. Markov-modulated Bernoulli Process.

8.3. Markov-modulated Fluid Flow.

8.4. Network Calculus.

9. Flow and Congestion Control.

9.1. Introduction.

9.2. Quality of Service.

9.3. Analysis of Sliding Window Flow Control Mechanisms.

9.4. Rate Based Adaptive Congestion Control.

References.

Index.