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: An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service, and the necessary and sufficient condition for the system stability is derived.
Abstract: An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served (FCFS) discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.
10 citations
TL;DR: The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times with steady-state analysis for the considered queueing system and obtains the generating functions of the number of customers in the orbit and in the system.
Abstract: The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number J of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.
10 citations
TL;DR: A model queueing system in which customers cannot be in continuous contact with the server, but must call in to request service, is analyzed and several characterstic quantities are calculated for both the constant rate of reapplying for service and for the case when customers are discouraged and reduce their rate of demand.
Abstract: We analyze a model queueing system in which customers cannot be in continuous contact with the server, but must call in to request service. If the server is free, the customer enters service immediately, but if the server is occupied, the unsatisfied customer must break contact and reapply for service later. There are two types of customer present who may reapply. First transit customers who arrive from outside according to a Poisson process and if they find the server busy they join a source of unsatisfied customers, called the orbit, who according to an exponential distribution reapply for service till they find the server free and leave the system on completion of service. Secondly there are a number of recurrent customers present who reapply for service according to a different exponential distribution and immediately go back in to the orbit after each completion of service. We assume a general service time distribution and calculate several characterstic quantities of the system for both the constant rate of reapplying for service and for the case when customers are discouraged and reduce their rate of demand as more customers join the orbit.
10 citations
01 Jan 2008
TL;DR: In this paper, a retrial queue system in which the number of retrials of each customer is limited by a finite number, say m is considered, and if a customer fails to enter the service facility at mth retrial, then the customer leaves the system without service.
Abstract: Retrial queues are frequently observed in a real world system likewise call center or internet service industries. In this paper, a retrial queue system in which the number of retrials of each customer is limited by a finite number, say m is considered. That is, if a customer fails to enter the service facility at mth retrial, then the customer leaves the system without service. The effects of restricting the number of retrials are investigated numerically by using the algorithmic method and simulation experiments.
10 citations
10 citations