A Control Approach Based on Colored Hybrid Petri Nets and (Max, plus ) Algebra: Application to Multimodal Transportation Systems
Résumé
This article is devoted to the study and the control of a multimodal transportation system (MTS) modeled by colored hybrid Petri nets (CHPNs) and (max, +) algebra. The studied MTS is composed of multiple connected stations served by large capacity transportation modes (such as trains and subways) and a finite number of bus shuttles with limited capacities that ensure the exchange of passengers between these stations. The MTS is studied in this article as a hybrid dynamical system (HDS). A nonstationary linear (max, +) model based on the CHPN model representing the behavior of the MTS is developed by taking into account the delays of bus shuttles that may be caused by unpredictable incidents (such as breakdowns and accidents). Through the resultant model, we analyze the system evolution over time and evaluate arrival/departure times of transportation means to/from the various connected stations and also passengers waiting times. In addition, an optimal control approach regarding just-in-time criterion is proposed to optimize two crucial parameters, namely: waiting times of passengers at the connected stations and the number of bus shuttles to be deployed on the network. In addition, the ability of the adapted control approach to deal with bus shuttle delays caused by unpredictable incidents and how the impact of these delays on passengers waiting times can be prevented will be studied. Finally, some relevant scenarios will be studied and discussed in order to illustrate and validate the suggested approach. Note to Practitioners-In recent years, the management of connected stops (or passengers exchange hubs) has been the subject of many research works in order to reduce their socio-economic and environmental impacts (e.g., congestion, unbearable passengers waiting times, and CO2 emissions). The explosion of passengers number within public transportation systems as well as the increasing complexity of multimodal networks requires the investment in more adapted services to ensure the efficient and competitive management for passenger displacement especially when using different transportation modes. For this end, the proposed approach in this work is conducted by using a hybrid approach based on graphical and mathematical tools for optimal management of passengers exchange through the exchange hubs. This article suggests a new hybrid approach, thus allowing modeling both the transportation means and related events, and passenger flows. We then show how such an approach can efficiently allow transportation companies to be more attractive and competitive. The proposed approach can be considered as a decision-making system for assisting transportation companies to provide relevant services for their clients in terms of transportation while minimizing engaged costs in terms of used transportation means. The added value of this system is more significant in the peak periods and when unpredictable incidents occur. This will considerably participate to increase the MTS performance indicators.