Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations

Sherif I. Ammar

Applied Mathematics and Computation, 2015, vol. 260, issue C, 97-105

Abstract: In this paper, we carry out an analysis for a single server queue with impatient customers and multiple vacations where customers impatience is due to an absentee of servers upon arrival. Customers arrive at the system according to a Poisson process and exponential service times. Explicit expressions are obtained for the time dependent probabilities, mean and variance of the system size in terms of the modified Bessel functions, by employing the generating functions along with continued fractions and the properties of the confluent hypergeometric function. Finally, some numerical illustrations are provided.

Keywords: M/M/1 queue; Exponential vacation; Impatience; Continued fraction; Confluent hypergeometric functions; Modified Bessel functions (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:260:y:2015:i:c:p:97-105

DOI: 10.1016/j.amc.2015.03.066

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