Some initial formulations of general overflow delay formulas that can be applied to isolated intersection approaches as well as those contained in a signalized arterial network are discussed. The main issues addressed are the deficiencies in models of arrival that have been developed to account for the filtering effect of upstream signals, which use the Poisson arrival process as their foundation. A cycle-by-cycle simulation model is the investigation tool. This level of modelling allows for the estimation of the uniform and overflow delay components separately. The results of the model are first tested for the isolated intersection scenario. The simulation model results are then extended to a two-intersection system, and a generalized delay model is calibrated to encompass both the isolated and the system cases. The initial work is limited, however, to fixed-time signal control with no platoon dispersion and no secondary or midblock flows between the two approaches. Only single-lane flow cases are considered. It was found from the simulation results that the inclusion of a parameter X sub o (a value of the degree of saturation below which the overflow delay is negligible) in the delay model is justified. The study also confirmed that progression quality has no effect on the overflow delay estimate. Two competing overflow delay model forms were investigated; one used the variance-to-mean ratio of upstream departures and the other used the capacity differential between intersections to reflect the filtering effect. Whereas the first form has been widely quoted and advocated in the literature, the second approach provided better predictions in this study.
TARKO, A., ROUPHAIL, N.M. and AKÇELIK, R. (1993). Overflow Delay at a Signalized Intersection Approach Influenced by an Upstream Signal: An Analytical Investigation. Transportation Research Record, No. 1398, pp 82-89.