Perturbation Theory for Unbounded Markov Processes with Applications to Queueing

摘要

A perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with a possibly unbounded one-step reward function is considered. A perturbation estimate for the finite horizon and average reward function is derived. Existing results are extended to the unbounded case. The analysis is illustrated for one and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.