ML and UMVU estimation in the M/D/1 queuing system

V. Srinivas and B. K. Kale

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 19, 5826-5834

Abstract: In the imbedded Markov chain (IMC) analysis of M/G/1 queuing system, X1, X2, …, Xn, … form a sequence of i.i.d random variables. where Xn denotes the number of customer arrivals during the service time of nth$n{\text{th}}$ customer. In the M/D/1 queue, the distribution of common random variable X is the Poisson distribution with mean ρ, the traffic intensity. This fact is utilized for maximum likelihood (ML) and uniformly minimum variance unbiased (UMVU) estimation of traffic intensity, performance measures, transition probabilities of IMC, and correlation functions of departure process, based on a sample of fixed size n from P(ρ) distribution. Also, consistent asymptotic normality (CAN) property of ML estimators (MLEs) is established. The MLEs and UMVUEs are compared.

Date: 2016
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DOI: 10.1080/03610926.2014.950750

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