Related papers: Stationary solutions of discrete and continuous Pe…
Dynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamics, specifically using Petri nets with priority rules. A…
We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We…
We analyze a timed Petri net model of an emergency call center which processes calls with different levels of priority. The counter variables of the Petri net represent the cumulated number of events as a function of time. We show that…
Place/transition Petri nets are a standard model for a class of distributed systems whose reachability spaces might be infinite. One of well-studied topics is the verification of safety and liveness properties in this model; despite the…
A fundamental issue in the analysis of emergency call centers is to estimate the time needed to return to a congestion-free regime after an unusual event with a massive arrival of calls. Call centers can generally be represented by timed…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We introduce stochastic decision Petri nets (SDPNs), which are a form of stochastic Petri nets equipped with rewards and a control mechanism via the deactivation of controllable transitions. Such nets can be translated into Markov decision…
We study the existence of critical points of stable stationary solutions to reaction-diffusion problems on topological tori. Stable nonconstant stationary solutions are often called patterns. We construct topological tori and patterns with…
Computing steady-state distributions in infinite-state stochastic systems is in general a very dificult task. Product-form Petri nets are those Petri nets for which the steady-state distribution can be described as a natural product…
Our objective is to design a controlled system with a simple method for discrete event systems based on Petri nets. It is possible to construct the Petri net model of a system and the specification separately. By synchronous composition of…
We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
Petri Nets are an increasingly used modeling framework for the spread of disease across populations or within an individual. For example, the Susceptible-Infectious-Recovered (SIR) compartment model is foundational for population…
We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on…
This work studies two types of computer networking models. The primary focus is to understand the different dynamical phenomena observed in practice due to the presence of severe nonlinearities, delays and widely varying operating…
We consider a dynamic network in continuum time and space in which nodes, with initial locations given by a Poisson point process, move according to i.i.d. isotropic $\alpha$-stable processes. Each node is additionally equipped with an…
We study a non-linear dynamical system on networks inspired by the pitchfork bifurcation normal form. The system has several interesting interpretations: as an interconnection of several pitchfork systems, a gradient dynamical system and…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
This paper is devoted to the use of hybrid Petri nets (PNs) for modeling and control of hybrid dynamic systems (HDS). Modeling, analysis and control of HDS attract ever more of researchers' attention and several works have been devoted to…