Modeling and Analysis of Infocommunication Systems

János Sztrik

New Szechenyi Plan logo

University of Debrecen

Lektor 1

Dr. József Bíró

Doctor of the Hungarian Academy of Sciences, Full Professor, Budapest University of Technology and Economics

Lektor 2

Dr. Zalán Heszberger

PhD, Associate Professor, Budapest University of Technology and Economics

The curriculum granted / supported by the project Nr. TÁMOP-4.1.2.A/1-11/1-2011-0103.


Table of Contents

Preface
I. Modeling and Analysis of Information Technology Systems
1. Basic Concepts from Probability Theory
1.1. 1.1. Brief Summary
1.2. 1.2. Some Important Discrete Probability Distributions
1.3. 1.3. Some Important Continuous Probability Distributions
2. Fundamentals of Stochastic Modeling
2.1. 2.1. Distributions Related to the Exponential Distribution
2.2. 2.2. Basics of Reliability Theory
2.3. 2.3. Generation of Random Numbers
2.4. 2.4. Random Sums
3. Analytic Tools, Transforms
3.1. 3.1. Generating Function
3.2. 3.2. Laplace-Transform
4. Stochastic Systems
4.1. 4.1. Poisson Process
4.2. 4.2. Performance Analysis of Some Simple Systems
5. Continuous-Time Markov Chains
5.1. 5.1. Birth-Death Processes
II. Exercises
6. Basic Concepts from Probability Theory
6.1. 6.1. Discrete Probability Distributions
6.2. 6.2. Continuous Probability Distributions
7. Fundamentals of Stochastic Modeling
7.1. 7.1. Exponential Distribution and Related Distributions
7.2. 7.2. Basics of Reliability Theory
7.3. 7.3. Random Sums
8. Analytic Tools
8.1. 8.1. Generating Function
8.2. 8.2. Laplace-Transform
9. Stochastic Systems
9.1. 9.1. Poisson Process
9.2. 9.2. Some Simple Systems
III. Basic Queueing Theory
10. Fundamental Concepts of Queueing Theory
10.1. 10.1. Performance Measures of Queueing Systems
10.2. 10.2. Kendall's Notation
10.3. 10.3. Basic Relations for Birth-Death Processes
10.4. 10.4. Queueing Softwares
11. Infinite-Source Queueing Systems
11.1. 11.1. The Queue
11.2. 11.2. The Queue with Balking Customers
11.3. 11.3. Priority Queues
11.4. 11.4. The Queue, Systems with Finite Capacity
11.5. 11.5. The Queue
11.6. 11.6. The Queue, Erlang-Loss System
11.7. 11.7. The Queue
11.8. 11.8. The Queue - Multiserver, Finite-Capacity Systems
11.9. 11.9. The Queue
12. Finite-Source Systems
12.1. 12.1. The Queue, Engset-Loss System
12.2. 12.2. The Queue
12.3. 12.3. Heterogeneous Queues
12.3.1. 12.3.1. The Queue
12.3.2. 12.3.2. Performance Measures
12.4. 12.4. The Queue
12.4.1. 12.4.1. Distribution Function of the Waiting and Response Time
12.4.2. 12.4.2. Laplace-transform of the Waiting and Response Times
12.5. 12.5. The Queue
12.6. 12.6. The Queue
12.7. 12.7. The Queue
12.7.1. 12.7.1. Determination of the steady-state distribution
IV. Exercises
13. Infinite-Source Systems
14. Finite-Source Systems
V. Queueing Theory Formulas
15. Relationships
15.1. 15.1. Notations and Definitions
15.2. 15.2. Relationships between random variables
16. Basic Queueing Theory Formulas
16.1. 16.1. M/M/1 Formulas
16.2. 16.2. M/M/1/K Formulas
16.3. 16.3. M/M/c Formulas
16.4. 16.4. M/M/2 Formulas
16.5. 16.5. M/M/c/c Formulas
16.6. 16.6. M/M/c/K Formulas
16.7. 16.7. M/M/ Formulas
16.8. 16.8. M/M/1/K/K Formulas
16.9. 16.9. M/G/1/K/K Formulas
16.10. 16.10. M/M/c/K/K Formulas
16.11. 16.11. D/D/c/K/K Formulas
16.12. 16.12. M/G/1 Formulas
16.13. 16.13. GI/M/1 Formulas
16.14. 16.14. GI/M/c Formulas
16.15. 16.15. M/G/1 Priority queueing system
16.16. 16.16. M/G/c Processor Sharing system
16.17. 16.17. M/M/c Priority system
A. Appendix
Bibliography

List of Figures

4.1. Transition rates in Example
4.2. components, 2 repairmen
4.3. 2 components, 1 repairman
4.4. Heterogeneous case with 2 repairmen
4.5. FIFO discipline
4.6. Processor Sharing discipline
4.7. Preemptive Priority discipline
9.1. Cold reserve
9.2. Warm reserve
9.3. Detection time
9.4. Parallel-redundant system
9.5. Exercise
11.1. Exact and approximated values of Exact and approximated values of n^{*}
12.1. Values of Values of P_{n}
12.2. Values of Values of P_{k}
12.3. Numerical results
12.4. Probabilities
12.5. Data of Example
12.6. Distribution
12.7. Mean cost per hour
17.1. Some properties of the generating function
17.2. Some properties of the Laplace-transform