GSPN

Generalized Stochastic Petri Net (GSPN) is a modeling formalism used for representing and analyzing systems that exhibit concurrency, synchronization, and stochastic timing. It extends the traditional Petri net by attaching timing to transitions and by supporting both instantaneous and timed events, enabling performance evaluation of complex systems such as manufacturing, telecommunication networks, and computer systems.

A GSPN comprises places, transitions, arcs, and tokens. A marking assigns a number of tokens to each place. A transition is enabled when its input places contain sufficient tokens, and firing produces and consumes tokens according to the arc structure. Transitions come in two main types: stochastic (timed) transitions, which have a firing delay drawn from a probability distribution (often exponential but not restricted to it), and immediate transitions, which fire without delay as soon as they are enabled. The combination allows the model to capture both discrete events and timing behavior.

Generalized aspects of GSPN include the use of non-exponential timing distributions, priorities between transitions, and sometimes inhibitor arcs or other extensions to express more complex service times and scheduling policies. This enables the representation of semi-Markov processes and other non-Markovian dynamics, providing a more expressive framework than standard stochastic Petri nets.

GSPN is used for performance modeling and analysis of systems where timing and concurrency matter. Typical applications include queueing networks, manufacturing systems, and distributed computing. Analysis methods range from exact or numerical transient and steady-state analysis to Monte Carlo simulation; in exponential-time cases, the model can be related to continuous-time Markov chains for solvable analyses. Several software tools support GSPN modeling and analysis, such as GreatSPN and related environments.