Fair sharing of resources in a supply network with constraints
Abstract
This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an allimportant issue for the efficiency of transportation networks all around us. We analyze a generic mechanism that distributes network capacity fairly among existing flow demands. The problem can be solved by semianalytical methods on a nearestneighbor 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 semianalytical framework suggests possible explanations for the wellknown 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.
 Publication:

Physical Review E
 Pub Date:
 April 2012
 DOI:
 10.1103/PhysRevE.85.046101
 arXiv:
 arXiv:1108.0025
 Bibcode:
 2012PhRvE..85d6101C
 Keywords:

 89.75.Hc;
 05.10.a;
 89.20.Hh;
 89.40.a;
 Networks and genealogical trees;
 Computational methods in statistical physics and nonlinear dynamics;
 World Wide Web Internet;
 Transportation;
 Physics  Physics and Society;
 Condensed Matter  Statistical Mechanics
 EPrint:
 15 pages, 12 figures, minor changes