Performance issues for the iterative solution of Markov decision processes on parallel computers

This paper analyses the implementation of an iterative solution method for Markov decision processes on distributed memory multiple instruction multiple data (MIMD) parallel processors. To preserve the good convergence properties of this method a parallel algorithm must be synchronous and the aim of this paper is to understand the factors which influence the efficiency of synchronous parallel algorithms for iterative methods. Models are developed for processor communication time, processor calculation time and overall run time which are also appropriate for other iterative methods. Such iterative methods are used in many other problem areas, including dynamic programming and the solution of linear and differential equations. The timing models guide the development of a phased pipeline algorithm. For 60,000 state sparse Markov decision processes using 121 processors, this algorithm gives 60-fold speed-ups relative to the best sparse serial algorithm.