TAILIEUCHUNG - On the single-server retrial queue

In this work, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Using the decomposition property of M/G/1 retrial queues with breakdowns that holds under exponential assumption for retrial times as an approximation in the non-exponential case, we consider an approximate solution for the steady-state queue size distribution. | Yugoslav Journal of Operations Research 16 (2006), Number 1, 45-53 ON THE SINGLE-SERVER RETRIAL QUEUE Natalia V. DJELLAB Department of Mathematics, University of Annaba, Algeria djellab@ Received: February 2004 / Accepted: December 2005 Abstract: In this work, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Using the decomposition property of M/G/1 retrial queues with breakdowns that holds under exponential assumption for retrial times as an approximation in the non-exponential case, we consider an approximate solution for the steady-state queue size distribution. Keywords: Retrial queue, stochastic decomposition, breakdown, embedded Markov chain. 1. INTRODUCTION Retrial queues are characterized by the feature that any arriving customer who finds all servers (and eventually all waiting positions) occupied may repeat his demand after a random amount of time. They are used to solve many practical problems in computer and other communication networks. A review of the main results can be found in [3], [5], [6], [8]. There are different approaches to study retrial queues. We place emphasis on the stochastic decomposition because it leads to simplifications when solving complex models. Stochastic decomposition property takes place in various retrial models, in particular in retrial queuing systems with server vacations [2]; in retrial models with batch arrivals [12] as well as with priority customers [7], [10]. Some applications of the decomposition property for M/G/1 retrial queues have been performed in [4]. In this paper, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Assuming the decomposition result for retrial queues with breakdowns and

• Kinh tế học
• Retrial queue
• Stochastic decomposition
• Embedded Markov chain
• Decomposition property
• Non exponential case
• Pre emptive resume policy
• Steady state distribution
• Performance measure
• Priority customer
• Principle of maximum entropy
• Impatient customer
• Information theoretic techniques