Optimum cost analysis of batch service retrial queuing system with server failure, threshold and multiple vacations

The aim of this paper is to analyze the queuing model entitled to cost optimization in bulk arrival and a batch service retrial queuing system with threshold, server failure, non-disruptive service, and multiple vacations. When bulk arrival of customers find the server is busy, then all customers will join in the orbit. On the other hand, if the server is free, then batch service will be provided according to the general bulk service rule. Batch size varies from a minimum of one and a maximum of ‘b’ number of customers. Customers in the orbit seek service one by one through constant retrial policy whenever the server is in idle state. The server may encounter failure during service. If the server fails, then ‘renewal of service station’ will be considered with probability . If there is no server failure with probability in the service completion or after the renewal process and if the orbit is empty, the server then leaves for multiple vacations. The server stays on vacation until the orbit size reaches the value N. For this proposed queuing model, a probability generating function of the orbit size will be obtained by using the supplementary variable technique and various performance measures will be presented with suitable numerical illustrations. A real time application is also discussed for this system. Additionally, a cost effective model is developed for this queuing model

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