Development of a mathematical model of urban freight transportation

Abstract

A methodical approach to the development of a mathematical model of urban freight transportation is proposed. Based on the identified analogies in the patterns of the processes in electrical circuits and urban traffic flows, a mathematical model of urban freight traffic has been developed. The main difference of the developed model from the previously known ones is that the model works in real time and, using Internet resources, for example, Google Maps (Kharkiv) and videoprobki.ua (Kharkiv), determines the workload of the road network sections or the presence of traffic jams. Expressions are obtained that allow to determine the resistance to movement of vehicles on the route. Applying the provisions of cluster analysis, a method was developed for calculating the resistance of a complex route, which contains sections with different density of motion, which is also a difference from the previously developed models. A criterion for choosing rational routes is proposed - the quality of the route. The criterion takes into account the capabilities of the logistics center (its information content), the mass of the cargo being transported, the route (traffic) load, the transportation distance and the actual delivery time of the cargo. This is the difference between the proposed criterion and the known wound, the distinctive feature of which is that it is determined online and takes into account the dynamics of the congestion of routes during the work shift. The analysis of the presented dependences allows us to conclude that the presence of traffic jams on the route changes the value of Qм by 4 times and is a more significant parameter than the length of the route. Changing lм from 10 to 30 km reduces the value of the quality factor of the route by 3 times. This is the difference between the proposed criterion м Q and the previously known criterion, the distinguishing feature of which is that it is determined online. Consequently, the criterion м Q takes into account the dynamics of changes in the load of routes during the working day or during the time of cargo delivery. For this purpose, the information feedback of the vehicle with the logistic center should be included in the information model scheme. This allows you to manage the delivery process, making corrections while the vehicle is moving along the route.