State Equations in Stochastic Process Algebra Models

Abstract

State equations are usually used for structural or qualitative analysis, such as deadlock checking, in P/T systems. In this paper, we instead consider timed state equations in stochastic process algebra models, to derive quantified dynamic information on the system modeled in the face of the state space explosion problem. The average of these state equations is demonstrated as the linear combination of the system transitions, with the combination coefficients specified by the bias term of the empirical transition rates to their steady state. The approaches of stochastic simulation and fluid approximation, straightforwardly generated from the quantified state equations, are studied, with the consistency being investigated both theoretically and experimentally.