Retrial queue

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

• performance analysis of repairable m/g/1 retrial queue with bernoulli vacation and orbital search

Abstract: In this paper we consider a repairable M/G/1 retrial queue with Bernoulli vacation and orbital search. By supplementary variable technique, the probability generating functions of the system size distribution and the orbit size distribution under steady state are obtained. Queueing as well as reliability indices to predict the behavior of the system are derived. Various models studied earlier are deduced as special cases by appropriate choice of parameter values.

Cost optimisation of a discrete-time retrial queue with Bernoulli feedback and starting failure

Abstract: In this paper, we explore the performance characteristics of a discrete-time Geo/G/1 retrial queue with Bernoulli feedback where the server is subjected to starting failure. On the arrival of a customer, the server may either resume its service successfully with probability υ or may not resume its service successfully with probability ῡ = 1 − υ due to some faults which in turn force the server to repair and the customer may join the orbit. The service time, retrial time and repair time are general distributed. The purpose of this paper is two-fold. Firstly, we use generating function method and supplementary variable technique to derive expressions for system size, orbit size and other performance measures. Secondly, for a cost-effective system, we have found the optimal values of some critical system parameters such that the total system cost is minimised using particle swarm optimisation (PSO) technique. Finally, sensitivity analysis is also provided.

A Discrete-Time Geo/G/1 Retrial Queue with Balking Customer, Second Optional Service, Bernoulli Vacation and General Retrial Time

Abstract: In this paper, we study a discrete-time Geo/G/1 retrial queue with a balking customer and a second optional service where retrial time follows a general distribution. If an arriving customer finds the server free, he begins the service immediately. If an arriving customer finds the server busy or to be on vacation, then he will consider whether he enters into the system. After a customer accepts his first essential service, he may leave the system or ask for a second service. In this model, we assume that the server, after each service completion, may begin a vacation or wait to serve the following customer. This paper studies the Markov chain underlying this model, we establish the probability generating functions of the orbit size and system size. Finally, some performance measures and some numerical examples are presented.

A note on fluid approximation of retrial queueing system with two orbits, abandonment and feedback

Abstract: This paper deals with the asymptotic analysis of a queueing system model consisting of two orbits, ctservers, t ≥ 0, abandoned and feedbackcustomers. Two independent Poisson streams of customers arrive to the system, an arriving one of type i, i = 1, 2 is handled by an available server, ifthere is any; otherwise, he waits in an infinite buffer queue. A waiting customer of type i who did not get connected to a server will lose his patience andabandon after an exponentially distributed amount of time, the abandoned onemay leave the system (loss customer) or move to the orbit depending of itstype, from which he makes a new attempts to reach the primary queue, thislatter may lose his patience and leave the system definitively (from the orbit)after an exponentially distributed amount of time. When a customer finisheshis conversation with a server, he may comeback to the system for anotherservice