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

作者：

Highlights：

• 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.

摘要

•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.

论文关键词：First-passage time,Polya process,Gompertz process,M(t)/M(t)/1 Queue,M(t)/M(t)/∞ Queue,Computational algorithms

论文评审过程：Received 16 November 2021, Revised 19 January 2022, Accepted 27 January 2022, Available online 6 February 2022, Version of Record 6 February 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.126993