Urban transportation network analysis from a thermodynamic perspective

The paper explores the application of thermodynamic formalism to model and control transportation networks. Specifically, by considering the vehicles as the abstract energy supplied to the system, we show in certain circumstances that certain thermodynamic concepts such as temperature, thermal capacity and thermal equilibrium can have the corresponding notions in transportation context. In addition, despite the lack of a natural principle in transportation context that corresponds to the second law of thermodynamic as we will show, the most important thermodynamic notion, which is the entropy, can be also defined in order to measure the disorder of transportation systems. It is then shown that the state when all lanes have the same occupancy corresponds to the thermal equilibrium arising in isolated thermodynamic system. This equilibrium occupancy leads to a minimum entropy corresponding to a minimal disorder. Besides, by taking the transportation entropy as the storage function, a robust dissipativity based control strategy is presented to reduce the disorder and render the system better organized. Finally, an example is worked out to illustrate the results. (C) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.