Travel routes estimation in transportation systems modeled by Petri Nets

This paper develops an algorithm for estimating the route(s) with the least total travel time in transportation systems that are modeled as Petri nets. Each transition in the net is associated with a cost that is related to the travel time from a starting point to a destination. This cost can be computed from the traffic flow and vehicle speed information obtained from the traffic data via an approach called Adaptive Gray Threshold Traffic Parameters Measurement (AGTTPM). Given a transportation system modeled as a Petri net that has cost on each transition, we aim at finding the transition firing sequences (traffic routes) from an initial marking (a starting point) to a final marking (a destination) within a certain time period T and have the least total cost (the least total travel time). In this paper we develop an algorithm that is able to systematically obtain these routes with the least total travel time.