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Ann Oper Res (2017) 252:121134
DOI 10.1007/s10479-015-1979-1
Bara Kim1 Jeongsim Kim2
Published online: 25 August 2015 Springer Science+Business Media New York 2015
Abstract We consider an 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 innite 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 LaplaceStieltjes 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
Mathematics Subject Classication Primary 60K25
1 Introduction
Retrial queues are queueing systems in which arriving customers who nd all servers occupied may retry for service again after a random amount of time. Retrial queues have been widely used to model many problems/situations in telephone systems, call centers, telecommunication networks, computer networks and computer systems, and in daily life. For an overview regarding retrial queues, refer to the surveys of Yang and Templeton (1987), Falin (1990) and Kulkarni and Liang (1997). For further details, refer to the books of Falin and
B Jeongsim Kim
Bara [email protected] Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul 02841, Korea2 Department of Mathematics Education, Chungbuk National University, 1, Chungdae-ro, Seowon-gu,
Cheongju, Chungbuk 28644, Korea
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Templeton (1997) and Artalejo and Gmez-Corral (2008) and the bibliographies of Artalejo (1999a,b, 2010).
In this paper, we consider a single server retrial queueing system with two classes of customers (class 1 and class 2). If an arriving class-1 customer or class-2 customer nds the server idle, the customer starts service immediately. If an arriving class-1 customer or class-2 customer nds the server busy, the class-1 customer joins the waiting space (or priority queue) with innite capacity and...