A spatial queuing approach to optimize coordinated signal settings to obviate gridlock in adjacent work zones

Gridlock is defined when traffic comes to a complete halt inducing huge delays. If a work zone on a two-lane two-way highway is set up, in which one of the traffic lanes is closed for maintenance road works, the remaining lane has to be controlled to serve the two-way traffic alternatively. The study objective is to optimize the traffic signal controls across two closely spaced work zones to prevent a gridlock, which can occur easily if upstream and downstream signals are not well coordinated. When vehicle queues build up in the middle sections between two work zones and further expand to occupy the single available lanes in both directions, the two-way traffic is then blocked and no vehicle can leave from the queues generating a gridlock. To address this problem, spatial queues are important parameters that must be explicitly analyzed. The cell transmission model, which is known to be a robust mathematical tool for the modeling of queue dynamics, is adopted in this study. A signal cell is used to represent each traffic signal control, the exit flow capacity of which is defined in accordance with the signal plan. A set of linear constraints is established to relate all of the model parameters and variables. The objective function is taken as the total number of vehicles in the critical section between the two work zones. The minimization of this objective function can effectively obviate the occurrence of a gridlock. The optimization problem is formulated as a Binary-Mixed- Integer-Linear-Program that can be solved by the standard branch-and-bound technique. Numerical examples are given to demonstrate the effectiveness of the proposed methodology.