On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes

•First passage densities for time-inhomogeneous birth-death (BD) chains and restricted BD processes.•Volterra integral equations.•Computational algorithms.•Extinction density and busy period density.•Polya BD process.•Gompertz BD process.•Linear BD processes with immigration.•M(t)/M(t)/∞ queueing sy...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 422; p. 126993
Main Authors: Giorno, Virginia, Nobile, Amelia G.
Format: Journal Article
Language:English
Published: Elsevier Inc 01.06.2022
Subjects:
[formula omitted] Queue
Computational algorithms
First-passage time
Gompertz process
Polya process
First-passage time
Gompertz process
Computational algorithms
60J80
60J28
60J27
M(t)/M(t)/1 Queue
M(t)/M(t)/∞ Queue
Polya process
60J22
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:•First passage densities for time-inhomogeneous birth-death (BD) chains and restricted BD processes.•Volterra integral equations.•Computational algorithms.•Extinction density and busy period density.•Polya BD process.•Gompertz BD process.•Linear BD processes with immigration.•M(t)/M(t)/∞ queueing system.•M(t)/M(t)/1 queueing system. New integral equations are proposed to determine first-passage-time densities for time-inhomogeneous birth-death processes. Such equations, particularly suitable for computational purposes, are also used to obtain closed-form expressions for the first-passage-time densities of special birth-death processes of interest in various application fields.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2022.126993