Fair sharing of resources in a supply network with constraints

TL;DR

This paper explores how network topology influences fair resource allocation in transportation networks, revealing patterns of flow distribution and potential throughput reductions due to fairness constraints.

Contribution

It introduces a semi-analytical framework for analyzing fair resource sharing in networks with specific topologies and routing rules, highlighting the impact on throughput and flow distribution.

Findings

Maximum intersections reduce throughput by at least 50%.

Flow allocations follow a power-law decay with exponent -1.

Network topology and routing can cause uneven but fair resource distributions.

Abstract

This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an all-important issue for the efficiency of transportation networks all around us. We analyse a generic mechanism that distributes network capacity fairly among existing flow demands. The problem can be solved by semi-analytical methods on a nearest neighbour graph with one source and sink pair, when transport occurs over shortest paths. For this setup, we uncover a broad range of patterns of intersecting shortest paths as a function of the distance between the source and the sink. When the number of intersections is the maximum and the distance between the source and the sink is large, we find that a fair allocation implies a decrease of at least 50% from the maximum throughput. We also find that the histogram of the flow allocations assigned to the agents decays as a power-law with exponent -1. Our semi-analytical framework suggests possible explanations for the well-known reduction of the throughput in fair allocations. It also suggests that the combination of network topology and routing rules can lead to highly uneven (but fair) distributions of resources, a remark of caution to network designers.