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On the performance of the M1,M2/G1,G2/1 retrial queue with pre emptive resume policy

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Priority mechanism is an invaluable scheduling method that allows customers to receive different quality of a service. Service priority is clearly today a main feature of the operation of any manufacturing system. We are interested in an M1,M2/G1,G2/1 priority retrial queue with pre-emptive resume policy. | Yugoslav Journal of Operations Research 25 (2015), Number 1, 153-164 DOI: 10.2298/YJOR130217001B ON THE PERFORMANCE OF THE M1,M2/G1,G2/1 RETRIAL QUEUE WITH PRE-EMPTIVE RESUME POLICY Leila BOUTARFA University of 08 May 1945, Guelma, Algeria Leila.bout@gmail.com Natalia DJELLAB Laboratory LaPS,University Badji Mokhtar, Annaba,Algeria djellab@yahoo.fr Received: February 2013 / Accepted: December 2013 Abstract: Priority mechanism is an invaluable scheduling method that allows customers to receive different quality of a service. Service priority is clearly today a main feature of the operation of any manufacturing system. We are interested in an M1,M2/G1,G2/1 priority retrial queue with pre-emptive resume policy. For the model in question, we discuss the problem of ergodicity, and by using the method of supplementary variables, we find the partial generating functions of the steady state system state distribution. Moreover, some pertinent performance measures are obtained and numerical study is also performed. Keywords: Retrial Queue, Pre-emptive Resume Policy, Steady-state Distribution, Performance Measure, Priority Customer. MSC: 60K25. 1. INTRODUCTION Retrial queuing systems or systems with repeated attempts are characterized by the requirement that customers finding the service space busy must join the retrial group and reply for service at random intervals. A review of the main results on this topic can be found in [7], [12]. A comparison between retrial queues and their standard counter parts with classical waiting line is released in [3]. Retrial queues have been widely used as mathematical models of different communication systems: shared bus local area 154 L. Boutarfa, N. Djellab / On the Performance of The M1,M2/G1,G2/1 Retrial networks operating under transmission protocols like CSMA/CD (Carrier Sense Multiple Access with Collision Detection), cellular mobile networks, IP networks [9], [1], [6]. In this paper, we are interested in single server retrial