A multi-echelon queueing model with dynamic priority scheduling

In this paper, we consider a multiple finite source queueing model with multiple servers and a nonpreemptive dynamic priority service discipline. The model consists of several classes of customers each of which calls for service at the service facility after spending a random amount of time at the source. The service facility has several servers for serving all customer classes. The service time of customers is exponentially distributed. A nonpreemptive dynamic priority service discipline is used by the servers. In this type of scheduling, a customer's priority function value increases linearly with actual waiting time in the queue. We propose a recursive algorithm that approximates the mean waiting time in the queue of each type of customer classes. Although our solution is only approximate, results from a variety of test problems indicate that the approximation is quite accurate.