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Poisson Flows with Alternating Intensity and Their Application

Poisson Flows with Alternating Intensity and Their Application Poisson flow of arrivals is considered in a case when flow intensity is an inconstant value. It is supposed that a random environment exists in which the flow operates. The environment is described as alternating Markov chain. The sojourn times in the alternating two states are independent random variables having the exponential distributions with known parameters. The intensity of the flow equals λi, i = 1, 2, if the i-th state of the random environment takes place. The following indices of the flow are considered: the distribution, the expectation and the variance of the number of arrivals on a given interval; the correlation of the numbers of arrivals for two adjacent intervals, etc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatic Control and Computer Sciences Springer Journals

Poisson Flows with Alternating Intensity and Their Application

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Publisher
Springer Journals
Copyright
Copyright © Allerton Press, Inc. 2020
ISSN
0146-4116
eISSN
1558-108X
DOI
10.3103/S0146411620050028
Publisher site
See Article on Publisher Site

Abstract

Poisson flow of arrivals is considered in a case when flow intensity is an inconstant value. It is supposed that a random environment exists in which the flow operates. The environment is described as alternating Markov chain. The sojourn times in the alternating two states are independent random variables having the exponential distributions with known parameters. The intensity of the flow equals λi, i = 1, 2, if the i-th state of the random environment takes place. The following indices of the flow are considered: the distribution, the expectation and the variance of the number of arrivals on a given interval; the correlation of the numbers of arrivals for two adjacent intervals, etc.

Journal

Automatic Control and Computer Sciences – Springer Journals

Published: Sep 16, 2020

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