Estimation of delays at traffic signals for variable demand conditions

This paper proposes a delay model for signalized intersections that is suitable for variable demand conditions. The model is applicable to the entire range of expected operations, including highly oversaturated conditions with initial queues at the start of the analysis period. The proposed model clarifies several issues related to the determination of the peak flow period, as well as the periods immediately preceding and following the peak. Separate formulas are provided for estimating delay in each of the designated flow periods as well as in the total flow period. Formulas are also provided to estimate the duration of the oversaturation period where applicable. The strength of the model lies in the use of simple rules for determining flow rates within and outside the peak, using the peak flow factor, a generalization of the well-known peak hour factor parameter. Simple rules are also provided for the identification of the location and duration of the peak flow period from observations of the demand profile. Such information is considered vital from an intersection design and evaluation viewpoint. Application of the model to a variety of operating conditions indicates that the estimated delay for vehicles arriving in the peak flow period is an acceptable predictor of the average delay incurred during the total flow period, even when oversaturation persists beyond the total flow period. On the other hand, the use of the average degree of saturation with no consideration of peaking can lead to significant underestimation of delay, particularly when operating at or near capacity conditions. These findings were confirmed by comparing the model results with other models found in the literature. The significant contribution of this work is not simply in the development of improved delay estimates, but, more important, in providing an integrated framework for an estimation process that incorporates (a) the peaking characteristics in the demand flow pattern, (b) the designation of flow-specific periods within the total flow period in accordance with the observed peaking and (c) the estimation of performance parameters associated within each flow period and in combination with other periods. A revised delay formula for the U.S. Highway Capacity Manual (HCM) is proposed. The revised formula has no constraints on the peak flow period degree of saturation, unlike the current HCM formula. It is also recommended that a simple formula for estimating the duration of oversaturation be used in conjunction with the revised delay formula.