Time-Continuous Instantaneous and Past Memory Routing on Traffic Networks: A Mathematical Analysis on the Basis of the Link-Delay Model - Bayen, Alexandre M.; Keimer, Alexander; Porter, Emily; Spinola, Michele (SIAM Journal on Applied Dynamical Systems, 2019)
This article presents an extensive theoretical framework to mathematically defined and information-based routing operators, applied to the continuous-time dynamic traffic assignment problem. Because of the difficulty of the mathematical framework required to provide existence and uniqueness proofs of the solution to the problem in the presence of a routing operator at nodes, the approach is instantiated with a link model, consisting of a system of ordinary delay differential equations and modeling traffic flow macroscopically. The routing operators distributing the incoming flow can encompass a wide range of information patterns, which can include past knowledge of the network state (statistical, or past deterministic information) up to real time and thus satisfying a nonanticipative character. We show, for a rather broad class of routing operators, the existence and uniqueness of solutions on the full network. This framework can be extended to more advanced traffic flow models such as partial differential equation models.<br
Keywords: link-delay model; traffic flow on networks; routing; delay differential equation; dynamic traffic assignment; instantaneous routing; existence of a solution on the network; uniqueness of a solution on the network