(1) General Motors R&D Center, 30500 Mound Road, Mail Code 480-106-359, Warren, MI, 48090-9055;(2) Department of Industrial Engineering, Texas A&M University, College Station, Texas, 77843-3131
Abstract:
We develop tight bounds and a fast parallel algorithm to compute the Markov renewal kernel. Knowledge of the kernel allows us to solve Markov renewal equations numerically to study non-steady state behavior in a finite state Markov renewal process. Computational error and numerical stability for computing the bounds in parallel are discussed using well-known results from numerical analysis. We use our algorithm and computed bounds to study the expected number of departures as a function of time for a two node overflow queueing network.