Analysis of a single server batch arrival unreliable queue with balking and general retrial time. Issue 6 (2nd November 2019) - Zirem, Djamila; Boualem, Mohamed; Adel-Aissanou, Karima; Aïssani, Djamil
ABSTRACT: This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and reserved time. Here we assume that customers arrive according to compound Poisson processes. Any arriving batch of primary customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. The primary customers who find the server busy or failed are allowed to balk or are queued in the orbit in accordance with FCFS retrial policy. The customer whose service is interrupted can stay at the server waiting for repair or enter into service orbit. After the repair is completed, the server resumes service immediately if the customer in service has remained in the service position. This model has a potential applications in various fields, such as in the cognitive radio network and the manufacturing systems. By using supplementary variables technique, we carry out an extensive analysis of the considered model. Then, we obtain some important performance measures, stochastic decomposition property of the system size distribution and the reliability indices. Next, by setting the appropriate parameters, some special cases are discussed. Finally, some numerical examples and cost analysis are presented.