tailieunhanh - Queueing Theory

In general we do not like to wait. But reduction of the waiting time usually requires extra investments. To decide whether or not to invest, it is important to know the e ect of the investment on the waiting time. So we need models and techniques to analyse such this course we treat a number of elementary queueing models. Attention is paid to methods for the analysis of these models, and also to applications of queueing models. Important application areas of queueing models are production systems, transportation and stocking systems, communication systems and information processing systems. Queueing models are particularly useful for the design of. | Queueing Theory Ivo Adan and Jacques Resing Department of Mathematics and Computing Science Eindhoven University of Technology . Box 513 5600 MB Eindhoven The Netherlands February 28 2002 Contents 1 Introduction 7 Examples . 7 2 Basic concepts from probability theory 11 Random variable. 11 Generating function. 11 Laplace-Stieltjes transform. 12 Useful probability distributions . 12 Geometric distribution. 12 Poisson distribution. 13 Exponential distribution. 13 Erlang distribution. 14 Hyperexponential distribution. 15 Phase-type distribution. 16 Fitting distributions . 17 Poisson process. 18 Exercises. 20 3 Queueing models and some fundamental relations 23 Queueing models and Kendall s notation. 23 Occupation rate. 25 Performance measures . 25 Little s law . 26 PASTA property . 27 Exercises. 28 4 M M 1 queue 29 Time-dependent behaviour. 29 Limiting behavior . 30 Direct approach. 31 Recursion . 31 Generating function approach . 32 Global balance principle . 32