多服务员串联排队的强逼近

近年来，多服务员排队常用来为大型电话中心网络建模，以便分析其动态行为．笔者研究了一个多服务员串联排队系统，并假设到达过程为更新过程，服务时间独立同分布．利用随机过程极限，在服务强度大于等于1的条件下，得到了队长过程和加权闲期过程的强逼近，从而也将原离散的排队系统近似到一个连续的布朗运动过程，为该系统的进一步分析提供了理论基础．

STRONG APPROXIMATION FOR A MULTI-SERVER SERIES STRUCTURE QUEUE

Recently, multi - server queue is usually used to model large call center network and to analyse its dynamic performance. We study a multi - server series structure queue, in which the arrival process is assumed to be renewal process and service times are assumed to be independent and identically distributed. Using stochastic process limit, we obtain the strong approximation of queue length and weighed idle processes under traffic intensity larger than or equal 1. As a result, we approximate the original discrete queueing system to a continuous Brownian motion system, which offer a basis for further theoretical research.