Random walk with priorities in communication-like networks

TL;DR

This paper analyzes a prioritized random walk model for two particle species on networks, revealing how high-degree nodes trap the lower-priority particles and proposing strategies to prevent this trapping.

Contribution

It provides analytical solutions for diffusion coefficients and explores strategies to prevent particle trapping in scale-free networks.

Findings

B particles tend to localize at hubs in scale-free networks.

Certain strategies can mitigate trapping of B particles.

Analytical results are obtained for both lattices and networks.

Abstract

We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et al., Phys. Rev. E 77, 020103 (2008); here we provide additional results. We solve analytically the diffusion coefficients of the two species in lattices for a number of protocols. In networks, we find that the probability of a B particle to be free decreases exponentially with the node degree. In scale-free networks, this leads to localization of the B's at the hubs and arrest of their motion. To remedy this, we investigate several strategies to avoid trapping of the B's: moving an A instead of the hindered B; allowing a trapped B to hop with a small probability; biased walk towards non-hub nodes; and limiting the capacity of nodes. We obtain analytic results for lattices and networks, and discuss the advantages and shortcomings of the possible strategies.