Analysis of repairable M[X]/(G1,G2)/1 - feedback retrial G-queue with balking and starting failures under at most J vacations

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

Analysis of repairable M[X]/(G1,G2)/1 - feedback retrial G-queue with balking and starting failures under at most J vacations

In this paper, we discuss the steady state analysis of a batch arrival feedback retrial queue with two types of service 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 join into the orbit. The negative customer, arriving during the service time of a positive customer, will remove the positive customer in-service and the interrupted positive customer either enters into 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. The busy server may breakdown at any instant and the service channel will 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 system parameters

Analysis of an M[X]/G/1 Feedback Retrial Queue with Two Phase Service, Bernoulli Vacation, Delaying Repair and Orbit Search

In this paper, we considered a batch arrival feedback retrial queue with two phase of service under Bernoulli vacation schedule and orbit search. At the arrival epoch of a batch, if the server is busy, under repair or on vacation then the whole batch joins the orbit. Where as if the server is free, then one of the arriving customers starts his service immediately and the rest join the orbit. At the completion epoch of each service, the server either goes for a vacation or may wait for serving the next customer. While the server is working with any phase of service, it may breakdown at any instant and the service channel will fail for a short interval of time. The repair process does not start immediately after a breakdown and there is a delay time for repair to start. After vacation completion, the server searches for the customers in the orbit (i.e. customer in the orbit, if any taken for service immediately) or remains idle. The probability generating function of the number of customers in the system and orbit are found using the supplementary variable technique. The mean numbers of customers in the system/orbit and special cases are analyzed. The effects of various parameters on the performance measure are illustrated numerically. Keywords: Feedback, retrial queue, Bernoulli vacation, delaying repair, orbit searc

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

Abstract: 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