Basic Server Semantics and Performance Monotonicity of Continuous Petri Nets

Continuous Petri nets were introduced as an approximation to deal with the state explosion problem which can appear in discrete event models. When time is introduced, the flow through a fluidified transition can be defined in many ways. The most used in literature are constant and variable speed (David and Alla, Discrete, continuous and hybrid Petri nets, Springer-Verlag, 2005), which can be seen as some kind of finite and infinite server interpretations of the transitions behavior, and derived from stochastic (discrete) Petri nets (Silva and Recalde, Annu Rev Control 28(2):253-266, 2004). In this paper we will compare the results obtained with both relaxations for the broad class of mono-T-semiflow reducible nets, and prove that, under some frequently true conditions, infinite server semantics offers a throughput which is closer to the throughput of the discrete system in steady state. In the second part, it will be proved that the throughput of mono-T-semiflow reducible net systems is monotone with respect to the speed of the transitions and the initial marking of the net.