具有插队行为的M/M/c/m+c排队系统等待时间分析

Analysis of waiting time of customers in an M/M/c/m+c queueing system with customer interjections

本文研究具有插队行为和容量有限的多服务台排队系统中顾客的等待时间分布函数。将进入系统的顾客按照插队与否分为常规顾客和插队顾客,常规顾客进入系统后在等待队尾排队等待服务,插队顾客进入系统后总是尽可能地靠近队首插队接受服务。利用负指数分布和位相型分布的性质推导了处于等待队列位置n的顾客、常规顾客、插队顾客的等待时间分布函数的矩阵表达式,并在此基础上给出了等待时间分布函数随时间的变化情况。

This paper studies waiting time distributions of customers in a multiserver queueing system with customer interjections and finite buffer.The customers who enter the system are divided into regular customers and interjection customers according to whether they interject the queue or not.After entering the system,the regular customers queue up at the end of the waiting line and wait for service,while the interjection customers queue up as close as possible to the head of the waiting line to receive service.By using the properties of negative exponential distribution and phase type distribution,the matrix expressions of waiting time distribution of customers in waiting queue position n,regular customers and interjection customers are derived.Further,the plots of waiting time distributions with time t are given.