An analytical model of pedestrian delay for pedestrian-actuated cycle length preserving signal traffic control

This paper considers the problem of developing a rigorous analytical model for estimating pedestrian delays at a signalized intersection when the pedestrian traffic at this intersection is controlled by a “smart” algorithm that operates according to the following principle: if “the pedestrian call button has not been pressed”, skip the pedestrian service interval reserved by the control scheme and pass the unused time to conflicting road users (thereby preserving the length of the control cycle), otherwise activate the reserved interval and serve the pedestrians. Under the assumption of a Poisson process of arrivals, a rigorous development of the corresponding model and its comparison with the existing best-known and used analogue is performed based on the apparatus of probability theory. By means of a computational experiment it is shown that the proposed model is much more accurate and correct than this analogue. Finally, a primary analysis of the model is performed, with results allowing to assess the appropriateness of implementing such a control algorithm in terms of the significant increase in individual pedestrian delays.