在随机启动(p,N)-策略控制下不中断多重休假排队系统的性能分析  

Performance Analysis for a Queueing System with Uninterrupted Multiple Vacations Under the Control of Randomized Setup(p,N)-Policy

作　　者：袁雨梅 唐应辉 刘雨欣 陈镰元 YUAN Yumei;TANG Yinghui;LIU Yuxin;CHEN Lianyuan(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610068

出　　处：《应用数学》2023年第4期1069-1085,共17页Mathematica Applicata

基　　金：国家自然科学基金项目(71571127);四川师范大学学科建设专项项目(XKZX2021-04);河西学院校长基金创新团队项目(CXTD2022013)。

摘　　要：本文研究在随机启动(p,N)-策略控制下不中断多重休假的M/G/1排队模型.通过运用全概率分解技术和拉普拉斯变换工具,直接讨论了系统从任意初始状态出发在任意时刻t队长的瞬态分布,得到了队长瞬态分布的拉普拉斯变换表达式.基于瞬态分析,使用洛必达法则得到了系统在任意时刻t队长的稳态分布的递推表达式,同时求出了系统其他一些重要排队性能指标,如稳态队长分布的概率母函数、平均稳态队长和附加队长分布的显示表达式等,并讨论了一些特殊情形.最后,通过数值计算实例讨论了系统空闲率和附加平均队长关于一些参数的敏感性以及系统容量的优化设计.This paper deals with an M/G/1 queue with uninterrupted multiple vacations under the control of randomized setup(p,N)-policy.Using the total probability decomposition technique and the Laplace transform tool,the transient distribution of the queue-length at any time t of the system that starts from any initial state is directly discussed,and the expressions of the Laplace transform of the transient queue-length distribution are obtained.Then,based on the transient analysis,the recursive expressions of the steady-state queue-length distribution are easily derived by employing L′Hospital’s rule.Meanwhile,some other important queueing performance measures,such as the explicit expressions for the probability generating function of the steady-state queue-length distribution,the expected queue size,the explicit expressions of the additional queue-length and so on,are presented.Furthermore,some special cases are also discussed.At last,numerical examples are provided to investigate the sensitivity of system parameters on the system’s idle rate and the additional average queue-length and the system capacity optimization design.

关 键 词：不中断多重休假 (p N)-策略 队长分布 全概率分解技术 系统容量设计 

分 类 号：O213.2[理学—概率论与数理统计]