Dynamic Wakeup under Costly Collisions

2026-09-28

AI Summary

This study addresses the fundamental trade-off between transmission delay and collision overhead in dynamic wake-up protocols over shared channels, particularly under high-cost collision scenarios. It proposes Lowball, a randomized distributed algorithm that jointly optimizes delay and collision costs without prior knowledge of packet counts or access to collision detection mechanisms. Furthermore, this work establishes an Ω(√C) theoretical lower bound on performance under specific strategies. The proposed algorithm adaptively withstands adversarial environments, achieving an expected delay of O(C^{1/2+ε} ln C) and a collision cost of O(√C), while guaranteeing successful transmission with probability one. Consequently, this research provides a theoretically optimal scheduling framework for communication systems where collisions incur substantial penalties.

Abstract

The wakeup problem captures a fundamental symmetry-breaking challenge among devices sharing a communication channel. We study the dynamic setting, where packets become active at arbitrary times on a time-slotted multiple access channel. In each slot, a transmission succeeds if and only if exactly one packet transmits; two or more simultaneous transmissions cause a collision. The goal is to obtain a successful transmission quickly. Prior work on wakeup has largely focused on the number of slots until the first success, referred to as the latency. However, a collision may incur substantial additional delay, represented by a per-collision cost $C$. We therefore seek to control both latency and the collision cost of an execution, defined as $C$ times its number of collisions. We design and analyze a randomized algorithm for dynamic wakeup, Lowball, without collision detection or knowledge of the number of packets, $n$. Fix a constant $0<\epsilon\le 1/2$. There is a constant $K>0$ such that, when $C\ge K\lg^{1/\epsilon} n$, Lowball has expected latency $O(C^{1/2+\epsilon}\ln C)$ and expected collision cost $O(\sqrt{C})$. Below this threshold, both expectations are $O(n\log^{\Theta(1/\epsilon)} n)$. These guarantees hold against an adaptive, non-anticipating adversary, and the algorithm succeeds with probability 1. For algorithms in which each packet's transmission probability depends only on $C$ and the packet's local age, with packets activated together using the same probability schedule, we prove that the maximum of expected latency and expected collision cost is $\Omega(\sqrt{C})$.

Problem

• dynamic wakeup
• multiple access channel
• collision cost
• latency
• symmetry breaking

Innovation

• dynamic wakeup
• collision cost
• randomized algorithm
• multiple access channel
• lower bound