Optimal Timer Based Selection Schemes

TL;DR

This paper derives the optimal timer-based node selection scheme that maximizes success probability or minimizes selection time, providing a closed-form solution and demonstrating superior performance over common methods.

Contribution

It introduces a novel discrete metric-to-timer mapping for optimal node selection, with a closed-form solution and asymptotic analysis, outperforming existing inverse metric schemes.

Findings

Optimal scheme maps metrics to discrete timers

Closed-form expression for the optimal scheme

Outperforms inverse metric and splitting-based methods

Abstract

Timer-based mechanisms are often used to help a given (sink) node select the best helper node among many available nodes. Specifically, a node transmits a packet when its timer expires, and the timer value is a monotone non-increasing function of its local suitability metric. The best node is selected successfully if no other node's timer expires within a 'vulnerability' window after its timer expiry, and so long as the sink can hear the available nodes. In this paper, we show that the optimal metric-to-timer mapping that (i) maximizes the probability of success or (ii) minimizes the average selection time subject to a minimum constraint on the probability of success, maps the metric into a set of discrete timer values. We specify, in closed-form, the optimal scheme as a function of the maximum selection duration, the vulnerability window, and the number of nodes. An asymptotic characterization of the optimal scheme turns out to be elegant and insightful. For any probability distribution function of the metric, the optimal scheme is scalable, distributed, and performs much better than the popular inverse metric timer mapping. It even compares favorably with splitting-based selection, when the latter's feedback overhead is accounted for.