Mean-field approximation for large-scale transport networks with a small parameter

The solution of mathematical simulation problems of complex transport networks at this stage is more difficult because of the large amount of data that must be analyzed. For example, a huge number of possible options of traffic makes it difficult to obtain sufficient economical plan through empirical or using expert approach. Application of mathematical methods and use of modern computational algorithms for transport planning gives considerable economic benefit. It is shown this approach is effective for solving a wide range of technical and technological problems of design, construction and operation of transport systems. In this approach manages to create an efficient algorithm for minimizing the cost of design, construction and operation of such systems. The transportation problem can be solved by simplex method but the matrix of the constraints of the transportation problem is often so complex that its solution developed special methods. In this paper it is studied large-scale transport network using Dobrushin's mean-field approximation. It is shown that the analysis of the evolution of large-scale transport systems can be described using systems of differential equations of infinite order. For this system, it is formulated the Cauchy problem Tikhon type with a small parameter ϵ, which introduces a singular perturbation. The theorem of existence of the solution of this Cauchy problem is proved. © 2017 CEUR-WS. All rights reserved.