Feedback Control Theory For Dynamic Traffic Assignment

Conventional traffic assignment methods assume that the origin-destination (OD) demand is uniformly distributed over time to estimate the traffic pattern. This assumption does not hold for modeling peak periods of congestion in which the OD demand is time varying. In this paper, we present a dynamic traffic assignment model with traffic-flow relationships based on a bi-level optimization framework. Our assignment variable is the number of vehicles present on a link during a time step, rather than traffic flow, which is used in static assignment. Using the modified Greenshields speed-density relationship, we derive a link-cost function that is monotonically nondecreasing and convex with respect to density. To capture traffic dynamics, we use short time-steps. The model prevents violations of the first-in-first-out (FIFO) condition using constraints on the distances moved by vehicles during each time step. A solution algorithm which resembles a Stackelberg leader-follower problem is presented, and numerical results from networks of different sizes demonstrate that the proposed model performs satisfactorily.

Traditionally, traffic assignment and traffic control in general have mostly been performed using optimisation techniques which do not lend themselves to real-time control. This volume presents feedback control techniques for performing traffic assignment in real-time, where traffic diversion control variables are instantaneous functions of sensed traffic variables.

The authors outline the whole theory behind Intelligent Transportation Systems (ITS) which allows traffic variables to be sensed in real-time and microprocessors to use the sensed traffic variable input to perform the traffic actuation tasks. They show how to design feedback controllers to perform dynamic traffic routing and assignment, and present the theory of feedback control as applied to this problem, with many new approaches for solving it.

Not only is the theory presented but a wide range of information on applications in terms of simulations and deployment. It is a valuable contribution to the subject, and will be of great use to researchers and all those with an interest in traffic control, including professional from highway administration and all those working in this industry.


Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

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