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 va...

Full description

Saved in:
Bibliographic Details
Published inAutomatic control and computer sciences Vol. 54; no. 5; pp. 403 - 411
Main Authors Andronov, A. M., Dalinger, I. M.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.09.2020
Springer Nature B.V
Subjects
Arrivals
Computer Science
Control Structures and Microprogramming
Independent variables
Markov chains
Random variables
Poisson flow
random environment
Online AccessGet full text

Cover

More Information
Summary: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 λ i , 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.
ISSN:0146-4116
1558-108X
DOI:10.3103/S0146411620050028