A New Measure for M/M/1 Queueing System with Non Preemptive Service Priorities

This paper studies M/M/1 queue under non preemptive service priority discipline. The unit with higher priority gets the service first without interrupting the service of non- priority unit if it is already in service. The study obtains the Laplace Transform of explicit time-dependent probabilities of exactly i arrivals, j departures of priority units and k arrivals, l departures of non-priority units by time t by solving the Laplace Transform of difference equations iteratively. By inverting the Laplace Transforms actual probabilities can be known. Few explicit results have been derived which helped in the verification of the model. With the help of these explicit transient state probabilities, other measures of interest can be obtained.