We give a definition of Q-net, a generalization of Petri nets based on a Lawvere theory Q, for which many existing variants of Petri nets are a special case. This definition is functorial with respect to change in Lawvere theory, and we exploit this to explore the relationships between different kinds of Q-nets. To justify our definition of Q-net, we construct a family of adjunctions for each Lawvere theory explicating the way in which Q-nets present free models of Q in Cat. This gives a functorial description of the operational semantics for an arbitrary category of Q-nets. We show how this can be used to construct the semantics for Petri nets, pre-nets, integer nets, and elementary net systems.

One of the important tasks that air traffic management services are faced with today is the task of maximising airport capacity. This can be achieved at the tactical level through proper organisation of air traffic around an airport. In recent years, many methods and algorithms for scheduling aircraft landings have been developed; they take into account various optimisation goals. The aim of this paper was to create a method that would allow one to evaluate landing aircraft sequences resulting from these control algorithms, especially in the presence of random disturbances. This method involves modelling the landing aircraft sequence by using Petri nets. The model and the computer tool that have been developed make it possible to take into account different kinds of disturbances and examine the effectiveness of various control strategies under these conditions. This paper presents two experiments that test disturbances with different characteristics and of different intensities. It has been shown that small but more frequent disturbances lead to the worsening of evaluation scores for a given sequence to a lesser extent than rare but larger disturbances. This is particularly important for control algorithms in which the focus is on high aircraft density. If the type of particular disturbances is properly assessed, then it will be possible to assist the decision-maker (air traffic controller) by providing him/her with quantitative evaluations of possible solutions.

To model the dynamics of discrete deterministic systems, we extend the Petri netsframework by a priority relation between conflicting transitions, which is encoded byorienting the edges of a transition conflict graph. The aim of this paper is to gain someinsight into the structure of this conflict graph and to characterize a class of suitableorientations by an analysis in the context of hypergraph theory.

Collaborative engineering design involves various stakeholders with different perspectives. The design process is relatively complex and difficult to handle. Various conflicts always happen among the design tasks and affect the design team performance. Therefore, to represent the collaborative design process and capture the evolution of design perspectives in a structured way, it is critical to manage the design conflicts and improve the collaborative design productivity. This article provides a generic collaborative design process model based on a sociotechnical design framework. This model has a topological format and adopts process analysis techniques from Petri Nets. By addressing both the technical and social aspects of collaborative design activities, it provides a mechanism to identify the interdependencies among design tasks and perspectives of different stakeholders. Based on this design process model, a methodology of detecting and handling the design conflicts is developed to support collaborative design coordination.

We show in this paper that timed Petri nets, with one resource shared by all the transitions, are directly connected tothe modelling of integer linear programs (ILP). To an ILP can be automatically associated an equivalent Petri net. Theoptimal reachability delay is an optimal solution of the ILP. We show next that a net can model any ILP. I order to dothis, we give a new sufficient reachability condition for the marking equation, which also holds for general Petri netswithout timed transitions.