A single SERVER finite population queueing model with compulsory SERVER vacation and with fixed batch service has been considered. For this model the system steady state probabilities are obtained. Some performance measures are calculated and numerical examples are also given.

In this paper, the designing of a parallel channel queuing system is considered in which it is desirable to serve the customers immediately upon their arrival. To design such a service facility, the first and the second moments of the number of customers are obtained in an infinite channel SERVER under the assumption that the arrival process has a general probability structure and the service times of customers are independent and identically distributed random variables. With the knowledge about the above two moments, one can obtain the approximate number of channels such that the queue length becomes zero.