Multiple finite source queueing model with dynamic priority scheduling

This article involves the study of a multiple finite source queueing model with a single server and dynamic, nonpreemptive priority service discipline. The input to the queue is comprised of customers from multiple finite sources. The time which the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang, or hyperexponential probability density function, with the same mean regardless of the class. Using an extension of mean value analysis, a recursive algorithm is developed to obtain approximate values of the mean waiting time in queues for each priority class. The mean number of waiting customers and the server utilization of each priority class can be obtained using the result of this recursive algorithm and Little's formula. Numerical examples are presented to illustrate the methodology. The algorithm developed in this article is validated using simulation.