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A First Course in Stochastic Models
John Wiley & Sons Ltd. | ISBN 0-471-49881-5 | English | PDF | Pages: 491 | Size: 2.11 MB | RAR Compressed | No Password
INTRODUCTION
The Poisson process is a counting process that counts the number of occurrences of some specific event through time. Examples include the arrivals of customers at a counter, the occurrences of earthquakes in a certain region, the occurrences of breakdowns in an electricity generator, etc. The Poisson process is a natural modelling tool in numerous applied probability problems. It not only models many real-world phenomena, but the process allows for tractable mathematical analysis as well. The Poisson process is discussed in detail in Section 1.1. Basic properties are derived including the characteristic memoryless property. Illustrative examples are given to show the usefulness of the model. The compound Poisson process is dealt with in Section 1.2. In a Poisson arrival process customers arrive singly, while in a compound Poisson arrival process customers arrive in batches. Another generalization of the Poisson process is the non-stationary Poisson process that is discussed in Section 1.3. The Poisson process assumes that the intensity at which events occur is time-independent. This assumption is dropped in the non-stationary Poisson process. The final Section 1.4 discusses the Markov modulated arrival process in which the intensity at which Poisson arrivals occur is subject to a random environment.
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