Analysis of an M[X]/(G1, G2)/1 retrial queueing system with balking, optional re-service under modified vacation policy and service interruption

A batch arrival retrial queue with balking and reneging is considered. If an arriving batch finds the server free, then one of the customers receives the service immediately and others join the orbit. Otherwise the batch has the option to join the orbit or to leave the system. The server provides two phases of service essential and optional. The server is subject to breakdown while it is working. The repair of the failed server starts instantaneously. After completion of the repair, the server is not allowed to accept new customers until the interrupted customer leaves the system. Whenever the orbit is empty the server takes atmost J vacations repeatedly until at least one customer appears in the orbit on return from a vacation. Using generating function technique, the steady state distributions of the server state and the number of customers in the orbit are obtained along with performance measures. Reliability indices of the system are obtained. Special cases are discussed. Numerical results are presented.

/pdf/two-phase-batch-arrival-retrial-queue-with-impatient-1lfwqenzrz.pdf

Two Phase Batch Arrival Retrial Queue with Impatient Customers, Server Breakdown and Modified Vacation

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.

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

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of services and negative customers. Any arriving batch of positive customers finds the server is free, one of the customers from the batch enters into the service area and the rest of them get into the orbit. The negative customer, is arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters the orbit or leaves the system. If the orbit is empty at the service completion of each type of service, the server takes at most J vacations until at least one customer is received in the orbit when the server returns from a vacation. While the busy server may breakdown at any instant and the service channel may fail for a short interval of time. The steady state probability generating function for the system size is obtained by using the supplementary variable method. Numerical illustrations are discussed to see the effect of the system parameters.

https://www.pvamu.edu/sites/mathematics/journal/aam/2015/vol-10-issue-1/02_r779-durai-vol.-10-issue-1-posted-06-18-15.pdf

Analysis of repairable M (X) /(G 1 ,G 2 )/1 - feedback retrial G-queue with balking and starting failures under at most J vacations

In this paper we consider a single server batch arrival non-Markovian retrial queueing model with non persistent customers. In accordance with Poisson process, customers arrive in batches with arrival rate  and are served one by one with first come first served basis. The server is being considered as unreliable that it may encounter break down at any time. In order to resume its service the server has to be sent for repair, but the repair does not start immediately so that there is a waiting time before the repair process. The customer, who finds the server busy upon arrival, can either join the orbit with probability p or he/she can leave the system with probability 1-p.  More details can be found in the full paper. Key words : Batch size, break down, delay time, transient solution, steady solution,  reliability indices.

/pdf/transient-behavior-of-m-x-g-1-retrial-queueing-model-with-4jdck1uke8.pdf

Transient behavior of M[x]/G/1 Retrial Queueing Model with Non Persistent Customers, Random break down, Delaying Repair and Bernoulli Vacation

A retrial queue with general retrial times, a modified vacation policy and server breakdowns is investigated in this paper. We study the embedded Markov chain underlying the considered queueing system and its stable condition. By applying the supplementary variable technique, some analytical results for the system size distribution as well as some other performance measures of the system are derived. The effects of various parameters on the system performance are analyzed numerically.

Yijuan Zhu

Papers

A retrial queue with modified vacations and server breakdowns