Solving simultaneous route guidance and traffic signal optimization problem using space-phase-time hypernetwork

• Combine network route guidance and explicit traffic signal control in an optimization model.
• Decompose model into two less computationally complex subproblems through Lagrangian relaxation.
• Define space-phase-time hypernetwork to jointly consider traffic dynamics and signals in network.
• The structure of the relaxed problem is naturally suitable for parallel computing techniques.

This paper addresses the problem of simultaneous route guidance and traffic signal optimization problem (RGTSO) where each vehicle in a traffic network is guided on a path and the traffic signals servicing these vehicles are set to minimize their travel times. The network is modeled as a space-phase-time (SPT) hyper-network to explicitly represent the traffic signal control phases and time-dependent vehicle paths. A Lagrangian-relaxation-based optimization framework is proposed to decouple the RGTSO problem into two subproblems: the Route Guidance (RG) problem for multiple vehicles with given origins and destinations and the Traffic Signal Optimization (TSO) problem. In the RG subproblem, the route of each vehicle is provided subject to time-dependent link capacities imposed by the solution of the TSO problem, while the traffic signal timings are optimized according to the respective link travel demands aggregated from the vehicle trajectories. The dual prices of the RG subproblem indicate search directions for optimization of the traffic signal phase sequences and durations in the TSO subproblem. Both RG and TSO subproblems can be solved using a computationally efficient finite-horizon dynamic programming framework, enhanced by parallel computing techniques. Two numerical experiments demonstrated that the system optimum of the RGTSO problem can be quickly reached with relatively small duality gap for medium-size urban networks.

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