Drawing on the strong connection between traffic modelling and physics we apply the principle of least action to traffic flow in an urban setting. research questions and hypothesis In this article we draw on the strong connection between traffic modelling and physics to discuss the following two questions: methods and data In Fermat's principle of least time, vehicles move between two points in space ( and ) in the least amount of time possible. 1 We consider a total travel time as a

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... principle of least action: for an instantaneous travel time , and a total travel time . This travel time can be generalized to a cost function if desired, so long as the units remain consistent throughout the problem. The problem can also consider vehicle speed along a path , by understanding that an instantaneous path length , divided by the speed at any point produces the instantaneous travel time, or • How can the principle of least action be used to consider traffic flow in an urban setting? • How can this formulation be expanded to include stochastic effects analogous to quantum mechanical effects to capture phenomenon not typically found in traffic models? Civil Engineering, University of Calgary ORCID iD: 0000-0002-4142-6409