The average speed of a dense traffic flow with one slow-moving vehicle on a road section with limited manoeuvring opportunities

Abstract

Vehicle speed is the main parameter that defines the quality of service for private transport users since a driver’s ability to choose it freely determines the comfort level when travelling in urban road networks. In present transport science, only the regularities in speed values in free flow conditions, where the speed variable fits with the normal distribution, are well-researched and generally recognised. The distribution of speed in other traffic conditions remains poorly studied. From this point of view, it is relevant to study the reasons for speed fluctuations in traffic conditions opposite to free flow, i.e., the movement of a dense vehicle platoon on a single-lane section of a road where overtaking and passing are impossible. This study should begin with determining the formula for calculating the average speed of a dense traffic flow at the exit of a section with the mentioned traffic restrictions, provided that the order of vehicles in the platoon at the entrance to the section is random. This article is devoted to obtaining the desired formula in the simplest situation – when there is only one slow-moving vehicle in the flowing platoon that limits the speed of the other vehicles. Obtaining such a formula establishes the basis for further research on the regularities in the traffic speed values in dense traffic conditions. It means that it is possible to approach the estimation of the first moment – mean – which is one of the main characteristics of the studied random variable.

Keywords: traffic speed, average speed, traffic flow, flow density, traffic lane, traffic conditions, analytical modelling, transport system.