Optimal signal controls and effects of flow uncertainty

This study examines effectiveness of a manual procedure for signal timing optimization, consisting of a modified Webster cycle length formulation applicable in saturated conditions and the equalized degree-of-saturation principle for green time allocation. Effects of statistical uncertainty of flows on control actions and delay performance are also investigated. The results indicate that the proposed procedure produces near-optimal delay performance, and performs as well as the state-of-the-art solution algorithms such as SOAP and TRANSYT with much less computation time. To evaluate effects of flow uncertainty, both stochastic mean and variance of control actions are derived based on approximation. The results show that approximations are reasonably accurate. Magnitude of changes in control actions relative to their means is linearly related to magnitude of statistical uncertainty in arrival flows. The control actions, especially cycle lengths, are less sensitive to flow uncertainty in saturated conditions. Delay performance is subjected to both direct and indirect effects from flow uncertainty. The stochastic mean of delay is always greater than the deterministic mean, indicating that ignoring flow uncertainty will substantially underestimate delay if degree of uncertainty is significant. When control actions are composed based on the actual flows, the mean of stochastic delay will reduce significantly, confirming that the adaptive control is much effective than the deterministic control. The Monte-Carlo simulation study also shows that if control actions deviate more than 3% to 7% from the perfect state, delay performance will substantially deteriorate. Error in flow predictions will affect the effectiveness of control actions and, consequently, delay performance. This study shows that the adverse effect of error in flow prediction on delay is slightly less than the imperfect controls. The margin of error in flow predictions, ranging from 4% to 10%, increases as the flow uncertainty grows.