A Numerical Method to Obtain the Equilibrium Results for the Multiple Finite Source Priority Queueing Model

In this paper a numerical method is presented to obtain the equilibrium results of the multiple finite source queueing model having a single server using a nonpreemptive fixed priority service discipline and where each class of customers has a different exponential interarrival density function and arbitrary service time distribution function. This solution method uses the method of imbedded Markov Chain and the renewal reward theorem to find the proportion of time the server is busy with the customers of different classes. The equilibrium results are then related to these proportions using an extension of Little's formula.