Numerical Computations and Tail Asymptotics for Stationary Indices of a Discrete-time Queue

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  • 1 School of Statistics and Mathematics, Henan Finance University, Zhengzhou 450046, Henan, China;
    2 Digital Technology School, Sias University, Zhengzhou 450003, Henan, China

Received date: 2024-01-09

  Revised date: 2024-06-27

  Online published: 2026-07-06

Supported by

This research was supported by the foundation for university key research project of Henan province (No.22B110002).

Abstract

This paper considers numerical computations and tail asymptotics for stationary queue length and sojourn time distribution of the Geo/T-IPH/1 queue, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death chain with countably many states. By analysis of probability generating functions, recursive formulas for queue length and sojourn time, and factorial moments of queue length and sojourn time are given. Moreover, a complete characterization of the regions of system parameters for exact tail asymptotic characterizations for such indices is also given, and the results show that there are three types of exact tail asymptotics for the indices in different regions.

Cite this article

Hong-Bo Zhang . Numerical Computations and Tail Asymptotics for Stationary Indices of a Discrete-time Queue[J]. Journal of the Operations Research Society of China, 2026 , 14(2) : 730 -747 . DOI: 10.1007/s40305-024-00557-w

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