Abstract

In this paper we consider multi-server single queue system in which inter-arrival and service times are exponentially distributed. When assessing the performance of such queuing model, information regarding the parameter traffic intensity (ρ), also called the utilization factor of the service station, is very essential. The unknown factor ρ is therefore our parameter of interest in the present work. Maximum likelihood (ML) and uniformly minimum variance unbiased (UMVU) estimators of ρ are proposed in the context of classical paradigm. A Bayes estimator of ρ is derived assuming that the prior density of ρ belongs to the family of Beta distributions. The performance of estimators is evaluated in terms of their relative efficiency. The proposed procedures are illustrated through a simulation study.

摘要

在本文中，我们考虑多服务器单队列系统，其中到达间隔和服务时间呈指数分布。在评估这种排队模型的性能时，有关参数流量强度 ( ρ ) 的信息非常重要，也称为服务站的利用率。因此，未知因素ρ是我们在当前工作中感兴趣的参数。在经典范式的背景下提出了ρ的最大似然 (ML) 和一致最小方差无偏 (UMVU) 估计量。假设ρ的先验密度推导了ρ的贝叶斯估计量属于 Beta 分布家族。估计器的性能是根据它们的相对效率来评估的。拟议的程序通过模拟研究进行说明。