Representation and analysis of behavior for multiprocess systems by using stochastic Petri nets

This paper proposes a new approach to visually represent the behavior of multiprocess in a computer network system using stochastic Petri net (SPN) and an aggregate approach of SPN and Markov renewal process (MRP) to conduct behavior analysis and performance evaluation for the system. SPN is employed because of its highly visual nature that can give insight into the nature of the modeled system and because of its expressive power for an exponentially distributed event. In order to increase the analytical power of the SPN model, MRP is introduced and an embedded transference probability matrix is applied to obtain the steady-state solution of the model, from which it is possible to obtain automatically the performance measures of the multiprocess computer network system.     

SimHPN: A MATLAB toolbox for simulation, analysis and design with hybrid Petri nets

This paper presents a MATLAB embedded package for hybrid Petri nets called SimHPN. It offers a collection of tools devoted to simulation, analysis and synthesis of dynamical systems modeled by hybrid Petri nets. The package supports several server semantics for the firing of both, discrete and continuous, types of transitions. Besides providing different simulation options, SimHPN offers the possibility of computing steady state throughput bounds for continuous nets. For such a class of nets, optimal control and observability algorithms are also implemented. The package is fully integrated in MATLAB which allows the creation of powerful algebraic, statistical and graphical instruments that exploit the routines available in MATLAB.     

Spectral analysis for performance evaluation in a bus network

This paper deals with the performance evaluation of a public transportation system in terms of waiting times at various connection points. The behaviour of a bus network is studied in the framework of Discrete Event Systems (DES). Two possible operating modes of buses can be observed at each connection stop: periodic and non-periodic mode. Two complementary tools, Petri nets and (max, +) algebra, are used to describe the network by a non-stationary linear state model. This one can be solved after solving the structural conflicts associated to the graphical representation. From the characteristic matrix of the mathematical model, we determine eigenvalues and eigenvectors that we use to evaluate the connection times of passengers. This work is finally illustrated with a numerical example.