On the Estimation of Performance Measures in a Single M/Ek/1 Queue

Chowdhury Shovan ()
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Chowdhury Shovan: Indian Institute of Management Kozhikode

No 301, Working papers from Indian Institute of Management Kozhikode

Abstract: An Erlang - k (Ek) distributed random variable can be represented as the sum of k independent exponentially distributed random variables with the same means. In an M/Ek/1 queueing model service process is assumed to follow Erlang distribution. Other than its conventional uses in traffic flow, scheduling, facility design, and telecommunication, such queueing model is widely used in manufacturing systems and inventory management to investigate their operational performance. In this paper, the focus is on estimating measures of performance such as traffic intensity, and the average queue size in a single M/Ek/1/8/8 queueing model based on number of customers present in the queue at successive departure epochs. Both classical and Bayesian methods of estimation are used to obtain the estimates. A comprehensive simulation study starting with the transition probability matrix has been carried out along with the comparison of errors associated with the estimates.

Keywords: M/Ek/1/8 queue; Queue length; Performance measures; Bayes estimator; Root mean square error; Transition Matrix (search for similar items in EconPapers)
Pages: 17 pages
Date: 2019-01
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