Competitive Selection of Ephemeral Relays in Wireless Networks

TL;DR

This paper models the competitive relay selection process in wireless networks as a stochastic game, characterizes equilibrium policies, and evaluates their performance in realistic scenarios with sleep-wake cycling relays.

Contribution

It introduces a game-theoretic framework for relay selection with observable and partially observable rewards, providing structural results and numerical analysis for practical wireless networks.

Findings

Nash Equilibrium policies are characterized for both observable and partially observable cases.

Threshold policies exist as equilibrium strategies in the partial observability setting.

Simple strategies perform nearly optimally in realistic wireless relay scenarios.

Abstract

We consider a setting in which two nodes (referred to as forwarders) compete to choose a relay node from a set of relays, as they ephemerally become available (e.g., wake up from a sleep state). Each relay, when it arrives, offers a (possibly different) "reward" to each forwarder. Each forwarder's objective is to minimize a combination of the delay incurred in choosing a relay and the reward offered by the chosen relay. As an example, we develop the reward structure for the specific problem of geographical forwarding over a network of sleep-wake cycling relays. We study two variants of the generic relay selection problem, namely, the completely observable (CO) case where, when a relay arrives, both forwarders get to observe both rewards, and the partially observable (PO) case where each forwarder can only observe its own reward. Formulating the problem as a two person stochastic game, we characterize solution in terms of Nash Equilibrium Policy Pairs (NEPPs). For the CO case we provide a general structure of the NEPPs. For the PO case we prove that there exists an NEPP within the class of threshold policy pairs. We then consider the particular application of geographical forwarding of packets in a shared network of sleep-wake cycling wireless relays. For this problem, for a particular reward structure, using realistic parameter values corresponding to TelosB wireless mote, we numerically compare the performance (in terms of cost to both forwarders) of the various NEPPs and draw the following key insight: even for moderate separation between the two forwarders, the performance of the various NEPPs is close to the performance of a simple strategy where each forwarder behaves as if the other forwarder is not present. We also conduct simulation experiments to study the end-to-end performance of the simple forwarding policy.