Matrix representations and analytical solution methods for stochastic activity networks

Abstract

Stochastic activity networks, a probabilistic extension of Petri nets, can be used to evaluate the performance, dependability, and performability of a wide variety of systems. When analytical solution methods are used, it is necessary to generate a state-level representation of a model prior to solution. The transition-rate matrices obtained from this representation tend to be very large and sparse. Analytical solutions to such problems can only be obtained by exploiting the matrix sparsity both in storage and computation. We do this, by studying alternative matrix representation schemes and steady-state and transient solution methods, and implementing methods appropriate for problems of this type. The results suggest that the implemented techniques can yield analytical solutions for many realistic models of computer systems and networks. This is evidenced by the performance evaluation of a CSMA/CD Local area network.