Random queues in signalized road networks

Average delay is an important criterion of evaluating traffic signals. Traffic signals, stream merges, and stream splits influence vehicular delay in signalized networks through influencing random fluctuation of traffic. This paper proposes a method of estimating the random component of queues and delays at signalized intersections inside a network of urban streets. Equations describing the effect of signals and traffic merging and splitting are derived, as well as a comprehensive equation combining the considered effects. Fixed speeds and capacities are assumed. The derived comprehensive equation is used to discuss certain cases of signalized streets. The equation is evaluated using the Monte Carlo technique. The proposed method can be incorporated into existing procedures for evaluating and optimizing traffic signals.