Improvement of the methods for determining optimal characteristics of transportation networks

Abstract

An improved method of approaching the calculation of maximum flow is developed, which implies applying the method of trees and capacities of tabular processors. The solution can be extended for a problem with several sources and runoffs. This will solve the problem on the optimization of transportation networks with and without limitations in throughput capacity. We designed an improved method for calculating the shortest path, which is resolved by using the Minty Dijkstra's algorithm. By solving the shortest path problem, we receive the shortest route and a list of vertices that it passes. By having indicators of freight traffic from each vertex to all others, we build a tree of the shortest paths. Going from one vertex to another vertex, we obtain density of traffic in the network without limitation in the throughput capacity. When the network has a throughput capacity limitation, imposing flows on the network is a bit complicated. In this case, it is necessary to subtract each elementary flow from the existing throughput capacity of the arc, on which it is imposed. For finding the shortest path, it is possible to correct the flows manually. The process of transforming network models for the process of cargo transportation to the matrix models is presented, through the use of the modified Dijkstra's algorithm. Elements of transportation networks in this case are set in the form of directed graphs. Graphic representation of the results of solving a network traffic problem is given.