An approach for analysis of mean delay at a signalized intersection with indisciplined traffic

Heterogeneous traffic consisting of medium sized cars and two-wheeled vehicles, such as motorcycles, arrive at a single-lane leg of a signalized road intersection. The lane is controlled by periodic “green” and “red” periods. The traffic is lane indisciplined in that, instead of standing one behind the other, the two-wheelers fill up the lane width-wise, by standing side-to-side with each other or with the cars. This gives rise to a queueing model in which the vehicles form batches (e.g., up to four motorcycles side-to-side in a batch, or a car and up to two motorcycles side-to-side) and each batch exits the intersection together. Assuming a Poisson point process model for vehicle arrivals, we approximately analyze this interrupted queue system by viewing it as an assembly queue followed by an interrupted M/SM/1 queue (where SM stands for semi-Markov). Analysis of the assembly queue provides a Markov model for the types of the successive batches in the intersection, and thereby characterizes the semi-Markov process of service times. The mean delay in the interrupted M/SM/1 queue is approximately analyzed by employing an extension of the Webster mean delay formula. Numerical results are provided to illustrate how well the approximation works in several examples.