Demonstration of a nonlinear dynamic model of traffic flow planning in intelligent transport systems

¹ National Aviation University, Air Transportation Management Department, 1 Liubomyra Huzara ave, Kyiv, Ukraine
² State University of Trade and Economics, Department of Software Engineering and Cyber Security, 19 Kyoto St., Kyiv, Ukraine
³ State University of Trade and Economics, Department of Advanced Technology Development, 19 Kyoto St., Kyiv, Ukraine
⁴ Kharkiv National Automobile and Highway University, Department of Transport Systems and Logistics, 25 Yaroslava Mudrogo St., Kharkiv, Ukraine
⁵ Ukrainian State University of Railway Transport, Department of Railway Stations and Hubs, 7 Oboronniy Val, Kharkiv, Ukraine

^* Corresponding author: sllitvinenko1982@gmail.com

Abstract

The significant relevance of the problems of traffic flow planning in intelligent transport systems is pointed out, with a critical analysis of previous scientific studies on this issue. The proposed nonlinear dynamic model of traffic flow planning in intelligent transport systems was characterised. Mathematical modelling methods, methods of correlation and regression analysis, and expert assessments were used. A demonstration of the nonlinear dynamic model of traffic flow planning was carried out, with an example of data developed, and a corresponding optimisation problem formulated and solved. A separate matrix was prepared for each group of constraints. The problem prepared for optimisation was written in the format of the Portfolio Safeguard package. To solve the problem, Solver VANGRB was chosen, which uses the Gurobi optimisation package. The problem contained 1,280 variables C^k_sr and y^k_sr each, as well as approximately 50,000 variables x_jsrkt. The matrices contained about 1,280, 30,000, 18,000, 1,176 rows of constraints. The optimal values of the variables C^k_sr and y^k_sr were found for pairs AB, AC, AD, AE, BA, CA for all types of agreements.