One-side Energy costs of the RBO receiver

TL;DR

This paper provides tighter bounds on the energy costs of the RBO receiver's variables, improving previous bounds and contributing to more efficient broadcast scheduling protocols.

Contribution

It establishes new upper bounds on the number of changes in the RBO receiver's variables, refining the understanding of energy costs in broadcast scheduling.

Findings

Left-side energy changes are at most k+1.

Right-side energy changes are at most k+2.

Extra energy is bounded by 2k+3, improving previous bounds.

Abstract

Let $n = 2^k$ be the length of the broadcast cycle of the RBO broadcast scheduling protocol (see [arXiv:1108.5095] and [arXiv:1201.3318]). Let $lb$ and $ub$ be the variables of the RBO receiver as defined in [ arXiv:1201.3318 ]. We show that the number of changes of $lb$ (the "left-side energy") is not greater than $k + 1$. We also show that the number of changes of $rb$ (the "right-side energy") is not greater than $k + 2$. Thus the "extra energy" (defined in [arXiv:1201.3318]) is bounded by $2 k + 3$. This updates the previous bound from [arXiv:1201.3318], which was $4 k + 2$.