Utility optimization framework for a distributed traffic control of urban road networks

Route choice behavior has been recognized as an important factor in the traffic management and control strategy design. State-of-the-art research in this field (e.g. anticipatory traffic control approaches) often formulates this as a bi-level optimization problem where users’ reactions to changes in signal control are taken into account in the design of the control policies. Solving such a combined optimization problem is possible but difficult and complex which often involves the determination of the dynamic user equilibrium (UE). Nevertheless, anticipatory control inherently aims to optimize the signal control that anticipates or reacts to the users’ route choice and thus is a reactive control. Furthermore, the approaches used in anticipatory control are based on the coupling between control and traffic assignment where the route choice behavior of road users is unrealistically assumed to be in equilibrium. This paper proposes a novel utility based optimization framework to design a distributed control scheme based on a so-called BackPressure principle that is scalable and proactively influences the drivers’ route choice behavior. In particular, as opposed to the well-studied anticipatory control and bi-level optimization, the proposed utility optimization formulation solves for a system optimal problem where the optimal turning fraction (as an output decision variable) is enforced as a desirable outcome. The optimal turning fractions would then be achieved in a practical deployment either by directly asking the users to follow the systems routing advice or by influencing, i.e. manipulating, the route choice decisions made by them so that the resulting turning fraction is (or is close to) the optimal value. Although drivers may not follow the computed optimal fractions as desire, there exist several ways, e.g. see Groot et al. (2015), to design appropriate incentives for drivers to follow the route guidance, and thus improve the compliance rate and overall journey experience for everyone inside the network. To this end, we demonstrate by numerical results that better network performance is achieved using the proposed framework even with a limited compliance from the users. Furthermore, we have formally proved that our proposed utility optimization based BackPressure scheme stabilizes the network for any feasible traffic demands thus maximizing network throughput. In addition, we show through simulation and numerical results that the new policy outperforms the original BackPressure-based distributed control scheme both in terms of network throughput and other congestion measures such as travel time.

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