Topic
Retrial queue
About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.
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TL;DR: This paper treats an M/G/1 retrial queue with non-persistent customers, where the server is subject to failure due to the negative arrivals and uses embedded Markov chain technique and the supplementary variable method to present the necessary and sufficient condition for the system to be stable and the joint queue length distribution in steady state.
48 citations
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TL;DR: For a retrial queue accepting two types of positive customers and negative arrivals, mixed priorities, unreliable server and multiple vacations, stability conditions and the system state probabilities are investigated both in a transient and in a steady state.
47 citations
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TL;DR: The steady state analysis of the queueing model is performed in which customers arrive according to a batch Markovian arrival process in which one customer from the arriving batch enters into service immediately while the rest join the orbit.
47 citations
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TL;DR: A discrete-time Geo/G/1 retrial queue with starting failures in which all the arriving customers require a first essential service while only some of them ask for a second optional service is considered.
Abstract: We consider a discrete-time Geo/G/1 retrial queue with starting failures in which all the arriving customers require a first essential service while only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained. We also obtain two stochastic decomposition laws regarding the probability generating function of the system size. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.
47 citations
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TL;DR: In this article, the authors considered an M / M / s queue with balking, reneging and retrials, where the customers who balked at entering the system or reneged on waiting line can join the virtual pool of customers, called orbit and repeat its request after random amount of time.
46 citations