Abstract

In this paper, we analyze an M/PH/1 queuing system with optional re-service. In this queueing system the interarrival time distribution is exponential with mean 1/λ,$1/\lambda ,$$1/\lambda ,$ service time and re-service time distribution follows continuous time phase-type distribution and each customer will be re-serviced with probability ‘p’. We have obtained the expressions of various system performance measures and maximum likelihood method using E-M algorithm and Bayesian procedure based on MCMC method were proposed to estimate system parameters. Numerical illustration of various special cases of the queueing system was carried out using simulated data sets.

摘要

在本文中，我们分析了具有可选重新服务的 M/PH/1 排队系统。在该排队系统中，到达间隔时间分布与均值呈指数关系1 / λ ,$1/\lambda ,$$1/\lambda ,$服务时间和重新服务时间分布遵循连续时间阶段型分布，每个客户将被重新服务的概率为“p”。我们获得了各种系统性能度量的表达式，并提出了使用EM算法的最大似然法和基于MCMC方法的贝叶斯过程来估计系统参数。使用模拟数据集对排队系统的各种特殊情况进行了数值说明。