Efficient steady-state analysis of second-order fluid stochastic Petri nets

This paper presents an efficient solution technique for the steady-state analysis of the second-order Stochastic Fluid Model underlying a second-order Fluid Stochastic Petri Net (FSPN) with constant flow and transition rates, and a single fluid place. The new solution technique is an extension of existing solution techniques developed for (first-order) Fluid Models; the solution algorithm uses upwind semidiscretization and Matrix Geometric techniques to efficiently compute the steadystate joint probability of the discrete states and the fluid level. The effectiveness of our technique is proven first on a simple producer-consumer second-order FSPN model and then on a complex example taken from the literature where the analysis of the completion time distribution and the packet loss probability of short-lived TCP connections is investigated through the decomposition of a model for the whole system into several (simpler) sub-models; the interaction among the different sub-models is handled by iterating their solution until the complete model solution converges according to a fixed point algorithm. The introduction of a second-order FSPN in a fixed point iteration scheme has been made possible thanks to the efficiency of the proposed solution technique.