Abstract
This paper focus on a server delayed vacation of M/M (a, b) / 1queueing system switch over state. In this model it is assumed that the arrival pattern is Poisson fashion with parameter λ and service is done in batches which is exponentially distributed with parameter µ according to the general bulk service rule introduced by Neuts (11).The batches are served according to FCFS discipline. The length of the vacations can be controlled by means of the number of customers ‘kb’ arriving to the system during vacation, and the level ‘k’ may be chosen according to the arrival rate, the service rate, the cost per unit of waiting time and the cost of the server being transferred from vacation to work. Secondly a server allowed for a delay time before a vacation begins. During the delay time, the server is situated in warm standby state and the service starts immediately if the batches of ‘a’ customers are present. If server finds (a-1) customers, then server will stay idle in the system called delay time before he goes for vacation. If the server finds (a-2) customers in the system the server switch over the system. So in this system, sever can take only one vacation between two successive service times.
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