Non-Markovian Petri Nets

Non-Markovian models allow us to capture a very wide range of circumstances in which it is necessary to model phenomena whose times to occurrence is not exponentially distributed. Events such as timeouts in a protocol, service times at a machine performing the same task on each part, and memory access or instruction execution in a low-level h/w or s/w model, have durations which are constant or with a very low variance. Phase-type distributions can be used to approximate a non-exponential, but they increase the size of the state space. The analysis of stochastic systems with nonexponential timing is of increasing interest in the literature and requires the development of suitable modeling tools. Recently, some effort has been devoted to generalize the concept of Stochastic Petri Nets (SPN), by allowing the firing times to be generally distributed. A particular case of non-Markovian SPN, is the class of Deterministic and SPN (DSPN) [1]. A DSPN is a non-Markovian SPN where, in each marking, at most one transition is allowed to have a deterministic firing time with enabling memory policy. A new class of stochastic Petri nets has recently been defined [2, 3] by generalizing the deterministic firing times of the DSPN to generally distributed firing times. The underlying stochastic process for these classes of Petri nets is a Markov Regenerative Process (MRGP). This observation has opened a very fertile line of research aimed at the definition of solvable classes of models whose underlying marking process is an MRGP, and therefore referred to as Markov Regenerative Stochastic Petri Nets (MRSPN). Some of the results in this filed will be described in the session. In particular, Ciardo investigates stochastic confusion by defining the selection probability for transitions attempting to fire at the same time. German introduces the "method of supplementary variables" for the derivation of state equations describing the transient behavior of the marking process. Puliafito describes how, under some constraints, concurrent enabling of several generally distributed timed transitions is allowed. Bobbio and Telek discuss how age memory policy can be included to capture preemptive mechanisms of the resume (prs) type.