Capacity of a signalized road junction: Critique and extensions

Abstract Earlier methods for maximizing capacity at a signalized at-grade road junction are examined and compared. Allsop's linear programming method is considered in detail and its shortcomings discussed. His basic method is reformulated and extended to increase the scope of application. The proposed method is able to treat intersections where saturation flows may vary from one stage of the traffic signal cycle to another even though vehicles from certain approaches may legally move in both stages. Such variations in saturation flow might arise, for example due to vehicles in a certain approach having absolute right-of-way in one stage but needing to find gaps in a priority stream during another stage. Some attention is given to mixed movements in a single lane. Also, the effective lost time is treated in a manner based on Webster's method. End-of-stage bulk turning movements are treated in terms of saturation rates by allowing the possibility of negative effective lost times. Examples identical to Allsop's are treated by the proposed method except that some limited gap-seeking is allowed. The increase in predicted capacity ranges only from 0 to 2 per cent in the particular examples used, the proposed method yielding the higher estimate due to its ability to represent gap-seeking as well as ultimate right-of-way. The flows on the various approaches are constrained to be in a given ratio.