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

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.