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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Vydáno v:	Applied mathematics and computation Ročník 422; s. 126993
Hlavní autoři:	Giorno, Virginia, Nobile, Amelia G.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 01.06.2022
Témata:	[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
On-line přístup:	Získat plný text
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Popis
Shrnutí:	•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