A note on integrals for birth-death processes (Q1595408)
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scientific article; zbMATH DE number 1563821
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on integrals for birth-death processes |
scientific article; zbMATH DE number 1563821 |
Statements
A note on integrals for birth-death processes (English)
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17 July 2001
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A general integral for birth-death Markov processes until the time of extinction is considered. A closed form expression is provided for the expected value in terms of birth and death rates. Several examples are provided: the M/M/1 queue, the M/M/\(\infty\) queue, the linear birth-death process, and the stochastic logistics SIS epidemic. A simple route for numerical evaluation of the integral variance is also suggested. This is a generalization and correction of an article of \textit{C.M. Hernandez-Suarez} and \textit{C. Castillo-Chavez} [ibid. 161, No.1-2, 95-104 (1999; Zbl 0938.60056)].
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birth-death processes
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hitting time
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integrals of Markov processes
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0.9358292
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0.9192681
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0.8978647
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0.8955473
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0.8944976
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0.8936018
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