Project number: MT-16-16

Funding source: US DOT

Contract number: DTRT13-G-UTC57

Funding amount: $99,957

Performance period: 1/1/2017 to 12/31/2017

Project description

We consider traffic flow dynamics for a network of signalized intersections, where the outflow from every link is constrained to be equal to a given capacity function if the queue length is positive, and equal to the minimum of cumulative inflow and capacity function otherwise. Inter-link travel times are modeled by fixed parameters. In spite of the resulting dynamics being discontinuous, recent work has proved existence and uniqueness of the resulting queue length trajectory if the inter-link travel time parameters are strictly bounded away from zero. The proof, which also suggests a constructive procedure, relies on showing desired properties on contiguous time intervals of length equal to the minimum among all link travel time parameters. We provide an alternate framework to obtain queue length trajectories as solution to delay differential equations, where link outflows are obtained from the provably unique solution to a linear program. Existence and uniqueness of the solution to the proposed model for traffic flow dynamics is established for piecewise constant external inflow and capacity functions. Additionally, if the external inflow and capacity functions are periodic and satisfy a stability condition, then there exists a globally attractive periodic orbit. We provide an iterative procedure to compute this periodic orbit. A periodic trajectory is iteratively updated for every link based on updates to a specific time instant when its queue length transitions from being zero to being positive. The update for a given link is based on the periodic trajectories computed in the previous iteration for its upstream links. The resulting iterates are shown to converge uniformly monotonically to the desired periodic orbit.