New Formulation to Analyze Signalized Approaches

The procedures generally used in calculating capacity, level of service, saturation flow rate, delay, queue lengths, and signal timing for approaches to signalized intersections are based on disaggregating traffic flow into lane groups. These procedures can be complex if the approaches exhibit geometries with lanes that are both exclusive (i.e., dedicated to servicing a single traffic movement) and shared (i.e., servicing at least two traffic movements). The complexity is exacerbated if the signal timing contains multiple phases servicing the approach, particularly if both permitted and protected signal phases are involved. Finally, the averaging of the differing flow characteristics on each lane making up a lane group could yield results that are unrealistic. The Highway Capacity Manual (HCM) devotes many pages in Chapter 16 and its appendices to delineating these procedures. To a large extent, the HCM uses queue accumulation polygons as part of these procedures and is now considering an extension called the incremental queue accumulation method. This paper presents a new formulation that yields estimates of the traffic demand in each lane, by turn movement, for virtually all geometric configurations of signalized approaches and for all signal phasing plans. The formulation also yields the saturation flow rates by lane and the required signal phase durations for any stated phasing plan. The basis for this method is a variation of Wardrop's laws. The formulations are presented for common approach configurations, and illustrative numerical examples are presented to demonstrate their applicability.