Optimal combined traffic routing and signal control in simple road networks: an analytical solution

ABSTRACT

Advanced traffic management systems aim at enhancing the traffic performance of urban networks. In addition to traffic signal control, the current paper includes traffic routing as another control measure in the traffic management system. Combined model of traffic routing and traffic signal control has a long history. In this paper, similar to previous works, both traffic routing and signal control are coupled in a continuous-time model for simple traffic networks. Unlike previous works, (i) the developed model considers dynamic transient periods, rather than steady-state periods or equilibrium conditions, and (ii) system optimum via optimal control is found analytically. The optimal analytical solutions, which are derived based on Pontryagin Maximum Principle, are verified via numerical solutions. A feedback routing and signal control policy based on link queue lengths is presented.

Keywords:

• Traffic signal and routing
• queue feedback control
• optimal control
• traffic control synthesis
• Pontryagin Maximum Principle

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The proof of sufficiency of the optimal solutions for this class of problems is given in Section 3 in Ioslovich and Gutman (2016).

Additional information

Funding

This work was supported by Ministry of Transport and Road Safety [9/2016].