TRANSIENT ANALYSIS OF MARKOVIAN QUEUE WITH MULTIPLE WORKING VACATIONS AND IMPATIENT CUSTOMERS UNDER BERNOULLI SCHEDULE VACATION INTERRUPTION

Abstract

In this thesis transient analysis of an infinite capacity of M/M/1 queue with multiple working vacations, balking and reneging under Bernoulli schedule vacation interruption was analyzed. Whenever the system becomes empty, the server takes a working vaca tion during which service is provided with a lower rate and if there are customers at a service completion moment, vacation is interrupted and the server resumes a normal working period with probability q or continues the vacation with probability 1 − q. The arrivals are allowed to join the queue according to a Poisson distribution and the ser vice times during regular busy period, working vacation period and vacation times are exponentially distributed. It was assumed that customers become impatient only during working vacation period and the impatient timer follows an exponential distribution. Explicit expressions for the time dependent system size probabilities are obtained in terms of the modified Bessel function of first kind by making use of Laplace transforms and probability generating function techniques along with continued fractions and the confluent hypergeometric function. Finally, numerical illustrations in a form of graphs were presented to show the behavior of the system size probabilities.