Fuzzy model of transport demand

Abstract

The development of transport networks is costly and cannot solve all transport problems. In this regard, scientifically based planning of the development of the transport complex acquires an important role to improve the quality of the functioning of the transport system, such as improving the organization of traffic in various parts of the network, optimizing the system of public transport routes, creating convenient transfer hubs, etc. To solve such problems, the paper considers the development of intelligent transport systems and mathematical modeling of transport demand. The central task of developing a transport model is to determine the equilibrium state of the transport system, i.e., the problem of the distribution of flows in the network, which involves two main stages. In the first stage, one or several correspondence matrices are evaluated based on the traffic flow's initial data and behavior. The second stage consists of the distribution of traffic matrices on the graph of the transport network, i.e., in solving the problem of finding traffic flows or the problem of transport equilibrium. The problem of transport equilibrium is reduced to an optimization problem in which restrictions are imposed depending on the values of the elements of the traffic matrix. The search for new methods for solving optimization problems of weakly formalized processes is caused by the presence of processes and phenomena, which is difficult to describe by methods of classical mathematics due to their indeterminacy and unreliability, incompleteness, and fuzziness of the initial information. The mathematical model of the optimization problem is described by the objective function and constraints. Classical mathematical programming and its variations are largely a normative methodology for effective choice. Fuzzy programming highlights the natural multiplicity of inaccurately defined goals, restrictions, and their meanings.