Modeling and Analysis of Distributed State Space Generation for Timed Petri Nets

Implementation of complex, real-world systems is usually preceded by extensive studies of their formal models. For systems which exhibit concurrent activities, Petri nets are a popular choice of modeling formalism, because of their ability to express concurrency, synchronization, precedence constraints and nondeterminism. Moreover, Petri nets “with time” (stochastic or timed) include the durations of modeled activities and this allows to study the performance aspects of the modeled system [1, 7, 12]. Three basic approaches to the analysis of Petri net models are known as structural analysis, reachability analysis and discrete-event simulation [8, 13]. Structural methods predict the properties of net models on the basis of their structure (i.e., connections between elements); structural analysis is usually rather simple, but it can be applied only to nets with special properties. Reachability analysis is based on an exhaustive generation of all reachable states; reachability analysis is the most suitable method when a detailed analysis of the model’s behavior is needed [7, 8]. Net simulation is based on the fact that a (timed or stochastic) Petri net is a discrete event system, where the events correspond to the firings (or occurrences) of net transitions; simulation can be applied to a large class of temporal nets, but may be unsuccessful or very inefficient in capturing events which occur rarely. In reachability analysis, the states of the model and the transitions between states are organized in the reachability graph which is used for verifying the required qualitative properties (such as absence of deadlocks or liveness). For timed and stochastic Petri nets, this graph is a Markov chain, whose stationary probabilities can be determined using known numerical methods [10]; these stationary probabilities are used to derive many performance measures of the model [1, 2, 12].