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We consider traffic flow dynamics for a network of signalized intersections,where the outflow from every link is constrained to be equal to a givencapacity function if the queue length is positive, and equal to the minimum ofcumulative inflow and capacity function otherwise. In spite of the resultingdynamics being discontinuous, recent work has proved existence and uniquenessof the resulting queue length trajectory if the inter-link travel times arestrictly bounded away from zero. The proof, which also suggests a constructiveprocedure, relies on showing desired properties on contiguous time intervals oflength equal to the minimum among all link travel times. We provide analternate framework to obtain queue length trajectories by direct simulation ofdelay differential equations, where link outflows are obtained from theprovably unique solution to a linear program. Existence and uniqueness of thesolution to the proposed model for traffic flow dynamics is established forpiecewise constant external inflow and capacity functions, and the proposedmethod does not require travel times to be bounded away from zero.Additionally, if the external inflow and capacity functions are periodic andsatisfy a stability condition, then there exists a globally attractive periodicorbit. We provide an iterative procedure to compute this periodic orbit. Aperiodic trajectory is iteratively updated for every link based on updates to aspecific time instant when its queue length transitions from being zero tobeing positive. The update for a given link is based on the periodictrajectories computed in the previous iteration for its upstream links. Theresulting iterates are shown to converge uniformly monotonically to the desiredperiodic orbit.

Queue Length Simulation for Signalized Arterial Networks and Steady State Computation under Fixed Time Control