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

doi:10.1007/s40305-024-00557-w

Journal of the Operations Research Society of China ›› 2026, Vol. 14 ›› Issue (2): 730-747.doi: 10.1007/s40305-024-00557-w

• • 上一篇

收稿日期:2024-01-09 修回日期:2024-06-27 出版日期:2026-06-30 发布日期:2026-07-06
通讯作者: Hong-Bo Zhang E-mail:zhanghb-168@163.com

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

Hong-Bo Zhang^1,2

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

Received:2024-01-09 Revised:2024-06-27 Online:2026-06-30 Published:2026-07-06
Contact: Hong-Bo Zhang E-mail:zhanghb-168@163.com
Supported by:
This research was supported by the foundation for university key research project of Henan province (No.22B110002).

摘要/Abstract

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.

Key words: Tail asymptotics, Geometric decay, Geo/T-IPH/1 queue, Stationary indices, Generating functions

中图分类号:

. [J]. Journal of the Operations Research Society of China, 2026, 14(2): 730-747.

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.

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

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