An optimal network for passenger traffic

TL;DR

This paper models an optimal inter-city passenger transport network using Zipf's law and the Gravity law, revealing a scale-free structure at finite link density and comparing it with India's real air-route network.

Contribution

It introduces a model combining Zipf's law and the Gravity law to determine optimal network structure and compares it with real-world data.

Findings

Total traffic cost decreases with increased link density.

Total wiring cost increases with link density.

The network becomes scale-free at finite link density.

Abstract

The optimal solution of an inter-city passenger transport network has been studied using Zipf's law for the city populations and the Gravity law describing the fluxes of inter-city passenger traffic. Assuming a fixed value for the cost of transport per person per kilometer we observe that while the total traffic cost decreases, the total wiring cost increases with the density of links. As a result the total cost to maintain the traffic distribution is optimal at a certain link density which vanishes on increasing the network size. At a finite link density the network is scale-free. Using this model the air-route network of India has been generated and an one-to-one comparison of the nodal degree values with the real network has been made.