AN M^X/E_k/c QUEUING SYSTEM WITH BERNOULLI SCHEDULE SERVER VACATIONS AND RANDOM BREAKDOWNS

Abstract

In this work, the batch arrival multiple server queuing system with Bernoulli schedule server vacations and random breakdowns was analyzed. In this queuing system, it has been assumed that the customers arrive to the system in batches of variable size, but are served individually by a multiple server in a first come, first served (FCFS) basis. It has been assumed that the service time’s distribution is an Erlang-k service time. After any service completion, the server may take a single vacation of random length. On the other hand, it has also been assumed that the system is subject to random breakdowns. Whenever the system breaks down, the customer whose service is interrupted comes back to the head of the queue and the system undergoes a repair process of variable length. Introducing the elapsed service time as a supplementary variable enabled us to obtain a set of time-dependent differential equations. It has been shown how to solve these equations to obtain the queue length at an arbitrary point of time.