应用数学2024，Vol.37Issue(4)：1133-1153,21.
具有多级适应性休假和Min(N,V)-策略的Geo/G/1排队系统分析
Analysis of Geo/G/1 Queueing System with Multiple Adaptive Vacations and Min(N,V)-Policy
摘要
Abstract
This paper treats the Geo/G/1 queueing system with multiple adaptive vacations and Min(N,V)-policy.Employing the renewal process theory,total probability decomposition technique and z-transform,we analyze the transient distribution of the queue size at any epoch r+.The z-transform expressions for the transient queue size distribution at any epoch n+are obtained.Moreover,in the analysis of transient analysis,the recursive expressions of the steady-state queue length distribution at any epoch n+are explicitly derived by using L'Hospital rule.Then,the explicit expressions of its probability generating function of the steady-state queue size distribution and the expected queue size are presented.Next,the steady-state distribution of queue length at epochs n-,n and outside observer's observation epoch are explored.Finally,applying the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is also presented under a given cost structure.And numerical examples are provided to determine the optimal control policy N*for economizing the system cost as well as the combined control policy(N*,J*)when the number of consecutive vacations is a fixed positive integer J.关键词
离散时间排队/多级适应性休假/Min(N,V)-策略/全概率分解/最优控制策略Key words
Discrete-time queue/Multiple adaptive vacation/Min(N,V)-policy/Total probability decomposition technique/Optimal control policy分类
数理科学引用本文复制引用
旷欣宇,唐应辉..具有多级适应性休假和Min(N,V)-策略的Geo/G/1排队系统分析[J].应用数学,2024,37(4):1133-1153,21.基金项目
国家自然科学基金(71571127) （71571127）
企业信息化与物联网测控技术四川省高校重点实验室开放基金(2023WZJ02) （2023WZJ02）
