An unreliable M [X] /G/1 retrial Queue with multi optional stages of service and delay in repair
01 Nov 2017-Vol. 263, Iss: 4, pp 042149
TL;DR: Unreliable vacation retrial queue and multi stages of service delay in repair and unit waiting in the system to complete the remaining service (delay time) is discussed and the system is analyzed using the method of supplementary variable.
Abstract: Unreliable vacation retrial queue and multi stages of service delay in repair is studied. After completion of the i th (i=1,2,...k) stage of service, the unit may have the option to choose (i+1)th stage of service with probability θi , or with pi may join into orbit to give feedback or may leave the station with probability qi = 1 – pi – θi , (i = 1,2,...k –1) and qi = 1 – pi , (i = k). After service completion if the orbit has no units, server takes avacation. During repair, the unit waiting in the system to complete the remaining service (delay time) is discussed. We analyzed the system using the method of supplementary variable. Simulation results are given using MATLAB.
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01 Jan 2022
TL;DR: In this article , a general service batch arrival feedback retrial G-queue with vacation is considered, where the server provides service in S phases and there are several different optional services available at each level.
Abstract: General service batch arrival feedback retrial G-queue with vacation is considered. Along with the essential service, the server provides service in S phases. There are several different optional services available at each level. The server’s status determines whether or not each individual customer is admitted to the system. According to the Poisson process, positive customers arrive in batches. When a negative consumer enters the system, the server goes down and the customer in service is removed from the system. The failing server is immediately dispatched for repair. If the server is idle, one of the admitted customer instantly enters the service and the others join the orbit; otherwise, all admitted customers enter the orbit. After the completion of essential or optional services, the server may join the queue if they are dissatisfied with the service. The server will leave on vacation with certain probability, after providing service to a customer. The system’s probability generating functions are carried out using the supplemental variable approach, and various performance measurements are developed. Stochastic decomposition property is verified and the special cases are deduced. The joint distributions of the server state and the number of customers in the retrial group are obtained. The influence of parameters on system performance metrics is investigated.
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TL;DR: In this article, the authors considered a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time and showed that the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables.
Abstract: This paper considers a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time. As has been noted by other researchers, for several specific models of this type, the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables, one of which is the stationary number of customers present in the standard M/G/1 queue i.e., the server is always available at a random point in time. In this paper we demonstrate that this type of decomposition holds, in fact, for a very general class of M/G/1 queueing models. The arguments employed are both direct and intuitive. In the course of this work, moreover, we obtain two new results that can lead to remarkable simplifications when solving complex M/G/1 queueing models.
664 citations
314 citations
TL;DR: This paper deals with the steady state behaviour of an M/G/1 retrial queue with an additional second phase of optional service subject to breakdowns occurring randomly at any instant while serving the customers.
85 citations
TL;DR: This paper discusses a retrial queue with Bernoulli feedback, where the server is subjected to starting failure, and the necessary and sufficient condition for the stability of the system is derived.
80 citations