2 FINITE-DIFFERENCE METHODS FOR SOLVING MAP(T) PH(T)/1/K QUEUING MODELS/

In this paper two solution methods to the MAP(t)/PH(t)/1/K queueing mo del are introduced, one based on the Backwards Euler Method and the ot her on the Uniformization Method. Both methods use finite-differencing with a discretized, adaptive time-mesh to obtain time-dependent value s for the entire state probability vector. From this vector, most perf ormance parameters such as expected waiting time and expected number i n the system can be computed. Also presented is a technique to compute the entire waiting (sojourn) time distribution as a function of trans ient time. With these two solution methods one can examine any transie nt associated with the MAP(t)/PH(t)/1/K model including time-varying a rrival and/or service patterns. Four test cases are used to demonstrat e the effectiveness of these methods. Results from these cases indicat e that both methods provide fast and accurate solutions to a wide rang e of transient scenarios.