Dynamic Aspect of Two Dimensional Single Server Markovian Queueing Model With Multiple Vacations and Reneging

Abstract

Abstract This work deals with “the dynamic analysis of Two-dimensional M/M/1 queuing model with reneging and multiple vacations”. Customers renege according to negative exponential distribution. Dynamic aspect is more appropriate in understanding the behaviour of the system. Two dimensions represent respectively the number of arrivals at, and departure from, the system at a given time. The system starts with “i units at the time “t=0”.Allowing server to take vacationmakes queuing model more feasible in studying the waiting time system appropriately. For example in ticket booking counter, messages to be delivered, patients form queue to have appointments before the clinic open or arrival of doctor. The solution for this model is obtained recursively with the help of Laplace transformation and results are achieved_without involving complex functions.