Continuum modelling of spatial and dynamic equilibrium in a travel corridor with heterogeneous commuters—A partial differential complementarity system approach

• We model the continuous spatial and dynamic equilibrium travel pattern in a linear travel corridor.
• Partial differential complementarity system approach is applied.
• Heterogeneous commuters and late arrival are considered.
• Proof of solution existence of the model is provided.

This paper studies on modelling and solving spatial and dynamic equilibrium travel pattern in a travel corridor. Consider a travel corridor connecting continuously distributed commuters to the city centre. The traffic is subject to flow congestion and the commuter heterogeneity is captured. The traffic flow dynamics is described by flow continuity equation and the equilibrium travel pattern is assumed to follow trip-timing condition. The continuous spatial and dynamic equilibrium travel pattern is formulated into a partial differential complementarity system, which is then solved through Godunov scheme. The proof of solution existence is provided, and a set of numerical experiments are demonstrated.