Theoretical Background

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Abstract

The performance modeling and investigation of computer, communications, and manufacturing systems, whether it is done with analytical methods or with simulation, requires a basic knowledge on probability theory. In all types of targeted systems, there exist many sources of randomness; for example the arrival time and the processing requirement of a job in computer system, the length of messages and the transmission delay in a communications system, or the batch size and the amount of work required by an item in manufacturing system. Both analytical methods and simulation use stochastic modeling to represent the dynamic behavior of systems. This chapter gives a short overview on the basic concepts of probability theory giving special focus on the different distributions functions and mainly on the practical introduction of Markov chains which are very important in the context of the stochastic modeling of systems.