Steady state solution for models with geometric and finite support activity duration

This paper addresses steady state solution of discrete time stochastic models in which every activity duration is given either by a geometric or a finite support distribution. Finite support distributions can be described by discrete time phase type (DPH) distributions. The behaviour of the whole stochastic model is given by a discrete time Markov chain (DTMC). The DTMC is subject to the so-called state space explosion. We present a technique for obtaining the steady state solution that alleviates this problem. The technique is based on Gaussian elimination combined with an iterative technique.