Short or Long—Which is Better?: Probabilistic Approach to Cycle Length Optimization

Traffic signal timing would be a trivial undertaking if demand were constant and uniform. Once stochastic factors and demand fluctuation are taken into consideration, however, the optimization of signal timing becomes challenging, if not impossible, even for an isolated, fixed-time signal. To answer the question of whether a longer cycle—more than 150 s, for example—or a shorter one—less than 60 s, for example—is better under fluctuating demand conditions, a probabilistic approach is employed to study minimal average delay by the use of mathematical formulations and Monte Carlo simulations. The idea is to select a cycle length that is small enough to ensure low delay, and hence level of service, but can provide adequate capacity to handle most of the fluctuating demand conditions. A five-step framework is presented for carrying out the analyses, which are demonstrated with a hypothetical example. Subsequent sensitivity analyses, level-of-service assessment, and cycle failure rate estimation were conducted on the basis of random demand and are presented here. Conclusions of the study include the following: (a) introduction of a fluctuating demand level increases the average delay in general, (b) longer cycle lengths do not yield optimal delay results, and (c) with extremely short cycle lengths, delay is usually high because of a lack of capacity and hence frequent cycle failures are guaranteed. A major contribution of this study is a proposed framework for optimizing cycle length under stochastic inter- and intracycle demand levels based on the expectation function of delay. When deployed, this framework can aid traffic engineers in choosing the desirable cycle length for minimal delay or for any reasonable level-of-service requirements.