离散时间SM[K]/PH[K]/1/FCFS排队系统的年龄过程改进分析

Analysis and Improvement of the Age Process in a Queuing System of Discrete Time SM[K]/PH[K]/1/FCFS

基于一个离散时间的排队系统:顾客有着多种类型,成批到达,到达过程是一个半马尔可夫过程,按照先来先服务的准则,并且每一个顾客的服务时间服从各自的PH分布。对这个离散时间SM[K]/PH[K]/1/FCFS排队系统年龄过程进行了详细分析,引进一些附加变量构造一个关于年龄过程的马尔可夫链,从而计算出年龄过程的转移矩阵。

We studied a discrete time queuing system with multiple types of customers and a first-come-first-served（FCFS）service discipline. Customers arrive according to a semi-Markov arrival process and the service times of individual customers have PH-distributions. We studied SM[K]/PH[K]/1/FCFS queue and analyzed its generalized age process particularly. We introduced some auxiliary variables to construct a Markov chain associated with ag（t） and obtained the transition probability matrix of this Markov chain.