A Parallel Implicit Method for the Steady-State Solution of CTMCs

Abstract

This paper considers the steady-state solution of Continuous Time Markov Chains (CTMCs). CTMCs are a widely used formalism for the performance analysis of computer and communication systems. A large variety of useful performance measures can be derived from a CTMC via the computation of its steady-state probabilities. However, CTMC models for realistic systems are very large. We address this largeness problem in this paper by considering parallelisation of implicit methods. In particular, we consider a modified form of Multi- Terminal Binary Decision Diagrams (MTBDDs) to compactly store CTMCs, and, using Jacobi iterative method, we present a parallel method for the CTMC steady-state solution. Employing a 24-node processor bank, we analyse our parallel implicit method using the experimental results for three widely used CTMC benchmark models, with well over a billion states and sixteen billion transitions.