Performance of Random Walks in One-Hop Replication Networks

TL;DR

This paper analyzes the efficiency of random walks for searching in one-hop replication networks, combining analytical modeling with simulations to estimate search times and coverage, considering revisiting effects.

Contribution

It introduces a detailed model for expected search time in one-hop networks using queueing theory and revisiting effects, validated by simulations.

Findings

Analytical and simulation results closely match

Revisiting effects significantly impact coverage estimates

Model effectively predicts search performance in one-hop networks

Abstract

Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc. This interest on random walks is justified by their inherent properties. They are very simple to implement as nodes only require local information to take routing decisions. Also, random walks demand little processing power and bandwidth. Besides, they are very resilient to changes on the network topology. Here, we quantify the effectiveness of random walks as a search mechanism in one-hop replication networks: networks where each node knows its neighbors' identity/resources, and so it can reply to queries on their behalf. Our model focuses on estimating the expected average search time of the random walk by applying network queuing theory. To do this, we must provide first the expected average search length. This is computed by means of estimations of the expected average coverage at each step of the random walk. This model takes into account the revisiting effect: the fact that, as the random walk progresses, the probability of arriving to nodes already visited increases, which impacts on how the network coverage evolves. That is, we do not model the coverage as a memoryless process. Furthermore, we conduct a series of simulations to evaluate, in practice, the above mentioned metrics. Our results show a very close correlation between the analytical and the experimental results.