A Mathematical Model of a Nonsignalized Pedestrian Crossing

A mathematical model is proposed to describe activities at a nonsignalized pedestrian crossing. Starting from a set of simple assumptions, the distributions of times during which a crossing is alternately available to pedestrians and vehicles are given. A batch service queueing analysis is then undertaken, employing the imbedded Markov chain technique, to derive the statistics of the vehicular queueing situation. Such analysis usually leads to rather intractable expressions which require a great deal of further effort before numerical results are obtained, but in the present paper these difficulties are overcome, and an explicit formula is derived for the vehicle mean queue length.