延迟Min(N,D)-策略下M/G/1排队系统的离去过程  

Departure Process of M/G/1 Queueing System Under Delayed Min(N,D)-Policy

作　　者：魏瑛源 唐应辉[2] WEI Yingyuan;TANG Yinghui(School of Mathematics and Statistics,Hexi University,Zhangye 734000,China;School of Mathematics and Software Science,Siehuan Normal University,Chengdu 610066,China)

机构地区：[1]河西学院数学与统计学院,甘肃张掖734000 [2]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《应用数学》2018年第4期820-829,共10页Mathematica Applicata

基　　金：国家自然科学基金(71571127)

摘　　要：考虑延迟Min(N, D)-策略下M/G/1排队系统的离去过程.运用全概率分解技术、更新过程理论和Laplace-Stieltjes变换,从任意初始状态出发,讨论在有限区间(0, t]内离去顾客的平均数,给出了离去过程、服务员状态过程和服务员忙期中的服务更新过程之间的关系,该关系揭示了离去过程的随机分解特性,并得到了离去顾客平均数的渐近展开式.在排队网络中,由于一个排队系统的输出即为下游排队系统的输入,希望本文所得结果为排队网络的研究提供有用的信息.This paper considers the departure process of the M/G/1 queue with delayed Min（N, D）-policy. Using the total probability decomposition technique, renewal process theory and Laplace-Stieltjes transform, we discuss the expected number of departures during time interval（0, t] from an arbitrary initial state. The relation among the departure process, server state process and service renewal process during server busy period is obtained. The relation displays the stochastic decomposition characteristic of the departure process. Furthermore, the approximate expansion of the expected number of departures is obtained. Since the departure process also often corresponds to an arrival process in downstream queues in queueing network, it is hoped that the results obtained in this paper may provide useful information for queueing network.

关 键 词：M/G/1排队系统 延迟Min(N D)-策略 离去顾客的平均数 渐近展开 随机分解 

分 类 号：O226[理学—运筹学与控制论]