Waiting time distributions in an M/G/1 retrial queue with two classes of customers

Bara Kim () and Jeongsim Kim ()
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Bara Kim: Korea University
Jeongsim Kim: Chungbuk National University

Annals of Operations Research, 2017, vol. 252, issue 1, No 8, 134 pages

Abstract: Abstract We consider an $$\textit{M/G/1}$$ M / G / 1 retrial queueing system with two classes of customers, in which the service time distributions are different for both classes of customers. When the server is unavailable, an arriving class-1 customer is queued in the queue with infinite capacity, whereas class-2 customer enters the retrial group. In this paper, we are concerned with the analysis of the waiting time distribution. We obtain the joint transform of the waiting time of a class-2 customer and the number of class-2 customers as well as the Laplace–Stieltjes transform of the waiting time of a class-1 customer. We also obtain all the moments of the waiting time distributions of class-1 and class-2 customers.

Keywords: Retrial queue with two classes of customers; Queue length; Waiting time; Transform; Primary; 60K25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-015-1979-1

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