带中途退出的MMAP[K]/PH[K]/1排队系统的性能分析

Performance Analysis of MMAP[K]/PH[K]/1 Queueing System with Reneging

研究了带中途退出的离散时间MMAP[K]/PH[K]/1排队系统,其中到达过程中有K种类型的顾客,不同类型顾客的耐心时间服从不同的一般离散型分布。通过构造GI/M/1型马尔可夫链,分析转移概率矩阵,并利用不可约马尔可夫链转移概率矩阵的UL型RG分解方法,得到了稳态下系统状态的平稳分布。在此基础上,分析了稳态下系统的顾客丢失率、等待队长和k(1≤k≤K)类顾客等待队长的概率分布等性能指标。

A discrete time MMAP[K]/PH[K]/1 queueing system with reneging is studied,where customers are distinguished into K different types and each type has different patience distributions.By means of constructing GI/M/1-type markov chain,analyzing transition probability matrix and using UL-type RG-factorization of transition probability matrix of irreducible markov chain,stationary probability distribution is derived.Based on these,the loss rate,probability distributions of waiting queue length and waiting queue length of a type k customer（1≤k≤K） are obtained.