Abstract
This chapter started with the definition of point process as a basic stochastic process, continued with the definitions of the arrival time and the interarrival time; and based on the definition of point process, counting process has been defined. The definition of renewal process as a special counting process, and the definition of Poisson process as a special renewal process have been provided. Poisson process has been classified as homogeneous and nonhomogeneous Poisson process, and the basic properties of a homogeneous Poisson process including the stationary and independent increments, exponential random variable as the interarrival time distribution, and gamma random variable as the arrival time distribution have been explained. In addition to the typical example of the arrival of the customers; other illustrative examples including the breakdown of the machines, time of the earthquakes, and the two-server systems have also been presented, and solved by using the basic formulae and the schematic representations.
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- 1.
A review of regenerative processes by Sigman and Wolff.
- 2.
This question is borrowed from Introduction to Probability Models, 10th Edition by Sheldon Ross.
- 3.
This question is adapted from Introduction to Probability Models, 10th Edition by Sheldon Ross
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© 2019 Springer Nature Switzerland AG
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Bas, E. (2019). A Brief Introduction to Point Process, Counting Process, Renewal Process, Regenerative Process, Poisson Process. In: Basics of Probability and Stochastic Processes. Springer, Cham. https://doi.org/10.1007/978-3-030-32323-3_9
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DOI: https://doi.org/10.1007/978-3-030-32323-3_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32322-6
Online ISBN: 978-3-030-32323-3
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