Retrial queue

About: Retrial queue is a research topic. Over the lifetime, 784 publications have been published within this topic receiving 12354 citations.

Control F-policy for Markovian retrial queue with server breakdowns

Abstract: The present study is concerned with the control policy for the retrial queue with server breakdowns. Customers are not allowed to join if the system becomes full but still service is being provided with slower rate than that of the normal busy period. To deal with the more practical scenario, the startup time taken into account to develop Markov model. Chapman-Kolmogorov equations governing the system states have been framed to analyze the performance indices of the queueing system. To explore the effect of system descriptors on various performance indices, numerical simulation and sensitivity analysis have been conducted by taking numerical example. A cost function is also constructed to determine the optimal service rate and minimum cost. Adaptive neuro fuzzy interface system (ANFIS) has also considered to compare the numerical results obtained with neuro-fuzzy results.

On the virtual waiting time for an M/G/1 retrial queue with two types of calls

Abstract: We consider an M/G/1 retrial queueing system with two types of calls which models a telephone switching system. In the case that arriving calls are blocked due to the channel being busy, the outgoing calls are queued in priority group whereas the incoming calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the Laplace-Stieltjes transform of the distribution of the virtual waiting time for an incoming call. When the arrival rate of outgoing calls is zero, it is shown that our result is consistent with the known result for a retrial queueing system with one type of call.

Analysis of a retrial queue with two-phase service and server vacations

Abstract: A queueing system with a single server providing two stages of service in succession is considered. Every customer receives service in the first stage and in the sequel he decides whether to proceed to the second phase of service or to depart and join a retrial box from where he repeats the demand for a special second stage service after a random amount of time and independently of the other customers in the retrial box. When the server becomes idle, he departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service times are arbitrarily distributed. For such a system the stability conditions and the system state probabilities are investigated both in a transient and in a steady state. A stochastic decomposition result is also presented. Numerical results are finally obtained and used to investigate system performance.

Equilibrium Customer Strategies in the Single-Server Constant Retrial Queue with Breakdowns and Repairs

Abstract: We consider a single-server constant retrial queueing system with a Poisson arrival process and exponential service and retrial times, in which the server may break down when it is working. The lifetime of the server is assumed to be exponentially distributed and once the server breaks down, it will be sent for repair immediately and the repair time is also exponentially distributed. There is no waiting space in front of the server and arriving customers decide whether to enter the retrial orbit or to balk depending on the available information they get upon arrival. In the paper, Nash equilibrium analysis for customers’ joining strategies as well as the related social and profit maximization problems is investigated. We consider separately the partially observable case where an arriving customer knows the state of the server but does not observe the exact number of customers waiting for service and the fully observable case where customer gets informed not only about the state of the server but also about the exact number of customers in the orbit. Some numerical examples are presented to illustrate the effect of the information levels and several parameters on the customers’ equilibrium and optimal strategies.