Transient Analysis of Single Server queueing system with Vacation Interruptions

The main objective of this research paper is to analyse the Transient behaviour of single server queueing system with vacation interruptions. In the literature of queueing theory several methods have been proposed for the study of transient behaviour of queueing system. In this paper Laplace transform ,Generating Function and partial differential equation methodology are used to find the closed form solutions of transient probability of number of customers in the system at time t. These expressions are obtained in terms of Modified Bessel’s functions of first kind.Steady state distribution of queueing system is also deduced from this expression and various system performance measures have been derived.