Contents LIST OF TABLES... LIST OF FIGURES... xvii. LIST OF LISTINGS... xxi PREFACE. ...xxiii

Transcription

1 LIST OF TABLES... xv LIST OF FIGURES... xvii LIST OF LISTINGS... xxi PREFACE...xxiii CHAPTER 1. PERFORMANCE EVALUATION Performance evaluation Performance versus resources provisioning Performance indicators Resources provisioning Methods of performance evaluation Direct study Modeling Modeling Shortcomings Advantages Cost of modeling Types of modeling Analytical modeling versus simulation... 8

2 vi Simulation and Analysis of Computer Networks PART 1. SIMULATION CHAPTER 2. INTRODUCTION TO SIMULATION Presentation Principle of discrete event simulation Evolution of a event-driven system Model programming Relationship with mathematical modeling CHAPTER 3. MODELING OF STOCHASTIC BEHAVIORS Introduction Identification of stochastic behavior Generation of random variables Generation of U(0, 1) r.v Importance of U(0, 1) r.v Von Neumann s generator The LCG generators Advanced generators Precaution and practice Generation of a given distribution Inverse transformation method Acceptance rejection method Generation of discrete r.v Particular case Some commonly used distributions and their generation Uniform distribution Triangular distribution Exponential distribution Pareto distribution Normal distribution Log-normal distribution Bernoulli distribution Binomial distribution Geometric distribution Poisson distribution Applications to computer networks... 48

3 vii CHAPTER 4. SIMULATION LANGUAGES Simulation languages Presentation Main programming features Choice of a simulation language Scheduler Generators of random variables Data collection and statistics Object-oriented programming Description language and control language Validation Generality Verification of predictions Some specific and typical errors Various tests CHAPTER 5. SIMULATION RUNNING AND DATA ANALYSIS Introduction Outputs of a simulation Nature of the data produced by a simulation Stationarity Example Transient period Duration of a simulation Mean value estimation Mean value of discrete variables Mean value of continuous variables Estimation of a proportion Confidence interval Running simulations Replication method Batch-means method Regenerative method Variance reduction Common random numbers Antithetic variates Conclusion... 80

4 viii Simulation and Analysis of Computer Networks CHAPTER 6. OMNET A summary presentation Installation Preparation Installation Architecture of OMNeT Simple module Channel Compound module Simulation model (network) The NED langage The IDE of OMNeT The project Workspace and projects Creation of a project Opening and closing of a project Import of a project A first example Creation of the modules Compilation Initialization Launching of the simulation Data collection and statistics The Signal mechanism The collectors Extension of the model with statistics Data analysis A FIFO queue Construction of the queue Extension of MySource Configuration An elementary distributed system Presentation Coding Modular construction of a larger system The system Configuration of the simulation and its scenarios Building large systems: an example with INET

5 ix The system Ethernet card with LLC The new entity MyApp Simulation Conclusion PART 2. QUEUEING THEORY CHAPTER 7. INTRODUCTION TO THE QUEUEING THEORY Presentation Modeling of the computer networks Description of a queue Main parameters Performance indicators Usual parameters Performance in steady state The Little s law Presentation Applications CHAPTER 8. POISSON PROCESS Definition Definition Distribution of a Poisson process Interarrival interval Definition Distribution of the interarrival interval Relation between N(t) and Erlang distribution Superposition of independent Poisson processes Decomposition of a Poisson process Distribution of arrival instants over a given interval The PASTA property

6 x Simulation and Analysis of Computer Networks CHAPTER 9. MARKOV QUEUEING SYSTEMS Birth-and-death process Definition Differential equations Steady-state solution The M/M/1 queues The M/M/ queues The M/M/m queues The M/M/1/K queues The M/M/m/m queues Examples Two identical servers with different activation thresholds A cybercafe CHAPTER 10. THE M/G/1 QUEUES Introduction Embedded Markov chain Length of the queue Number of arrivals during a service period Pollaczek Khinchin formula Examples Sojourn time Busy period Pollaczek Khinchin mean value formula M/G/1 queue with server vacation Priority queueing systems CHAPTER 11. QUEUEING NETWORKS Generality Jackson network Closed network PART 3. PROBABILITY AND STATISTICS CHAPTER 12. AN INTRODUCTION TO THE THEORY OF PROBABILITY Axiomatic base

7 xi Introduction Probability space Set language versus probability language Conditional probability Definition Law of total probability Independence Random variables Definition Cumulative distribution function Discrete random variables Continuous random variables Characteristic function Some common distributions Bernoulli distribution Binomial distribution Poisson distribution Geometric distribution Uniform distribution Triangular distribution Exponential distribution Normal distribution Log-normal distribution Pareto distribution Joint probability distribution of multiple random variables Definition Independence and covariance Mathematical expectation Some interesting inequalities Markov s inequality Chebyshev s inequality Cantelli s inequality Convergences Types of convergence Law of large numbers Central limit theorem

8 xii Simulation and Analysis of Computer Networks CHAPTER 13. AN INTRODUCTION TO STATISTICS Introduction Description of a sample Graphic representation Mean and variance of a given sample Median Extremities and quartiles Mode and symmetry Empirical cumulative distribution function and histogram Parameters estimation Position of the problem Estimators Sample mean and sample variance Maximum-likelihood estimation Method of moments Confidence interval Hypothesis testing Introduction Chi-square (χ 2 ) test Kolmogorov Smirnov test Comparison between the χ 2 test and the K-S test CHAPTER 14. MARKOV PROCESS Stochastic process Discrete-time Markov chains Definitions Properties Transition diagram Classification of states Stationarity Applications Continuous-time Markov chain Definitions Properties Structure of a Markov process

9 xiii Generators Stationarity Transition diagram Applications BIBLIOGRAPHY INDEX