Probabilistic Model in Describing Traffic Flows at a Signal-Controlled Junction. Selection of the Optimal Control Criteria and Algorithm

Abstract

The paper considers a problem of mathematical description of the traffic flows and their control at the signal-controlled junctions. It is assumes that the situation is controlled using the automatic traffic light signals. Solution to the problem is based on the probabilistic approach based on selection and construction of the distribution density functions using the probability theory methods. The paper provides a developed mathematical model describing the vehicles motion random process through a signal-controlled junction. The model determines a criterion for optimizing the traffic flow control at junctions. An algorithm for the traffic lights optimal control at the signal-controlled junctions is presented. The maximum probability of no-queue at the input sections is adopted as the universal and measurable quality criterion. The proposed quality criterion has the unimodality and continuity properties guarantying existence and uniqueness of an optimal control solution. The developed mathematical optimal control algorithm allows finding optimal values of the traffic light phase durations and minimizes the queue length at the inbound sections. The paper provides examples of computing the probability distribution functions of the waiting queue length for a test X-shaped junction. These functions reflect the declared features of the adopted optimal control criterion

Please cite this article in English as:

Sofronova E.A., Voronin E.A. Probabilistic model in describing traffic flows at a signal-controlled junction. Selection of the optimal control criteria and algorithm. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2024, no. 4 (149), pp. 128--139 (in Russ.). EDN: ZSBRMZ

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