Determination of storage lengths of left-turn lanes at unsignalized intersections using M/G2/1 queuing

Inadequate lengths of left-turning lanes can have negative effects on the performance of unsignalized intersections. Existing methods are inadequate for recommending appropriate storage lengths as a function of the traffic demands. This study uses an M/G2/1 queuing system to develop a model for determining storage lengths of left-turning lanes for unsignalized intersections based on probability of lane overflow. Left-turning vehicle arrivals are assumed to be Poisson arrival processes. Service times of left-turning vehicles are categorized into two groups: (a) service times incurred by the vehicles that arrive when the left-turning lane is empty, and (b) service times incurred by the vehicles that arrive when the left-turning lane is not empty. The effects of heavy vehicles on lengths of left-turning lanes are also taken into account. Recommended storage lengths of left-turning lanes are estimated using the proposed method and are provided for various combinations of opposing volumes, left-turning volumes, and threshold probabilities of lane overflow. To select values of the threshold probability of lane overflow, many factors should be considered, such as safety, site-specific conditions, accident records, operating speeds, and economics. The results of the proposed method were compared to those provided in the 2001 AASHTO Green Book. The 2001 AASHTO Green Book overestimates the storage lengths required for left-turning lanes when opposing and left-turning volumes have fewer than 900 vehicles per hour and 500 vehicles per hour, respectively, but it underestimates storage lengths when left-turning volumes are near capacity.