Transient Analysis of an queue with Multiple Exponential Vacation and-Policy

A single server Markovian queueing model is considered. The arrivals are allowed to join the queue according to a Poisson distribution and the service takes place according to an exponential distribution. Whenever the system is empty, the server goes for a vacation and return back to the system after N or more customers are found in the system. If the number of customers in the system is less than „ ‟ then the server takes another vacation. In this paper, we obtain explicit expressions for the time dependent system size probabilities of such a model using Laplace transform and generating function techniques. Numerical illustrations are added to support the theoretical results obtained