Computing Closed-Form Stochastic Bounds on Transient Distributions of Markov Chains

Abstract

In {3, 2} we have defined a particular class of time homogeneous discrete time Markov chains, called class C, having closed-form steady-state solution. In this paper, we show that transient distributions of this particular class have also closed-form solutions. Therefore, it is possible to apply the stochastic comparison approach to compute bounds on transient distributions by means of the closed-form solutions. This approach may be attractive for high-speed networks, where QoS requirements are the thresholds and exact values are not necessary.