高代价碰撞下的动态唤醒
Dynamic Wakeup under Costly Collisions
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- Mississippi State University（密西西比州立大学）
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中文总结 AI 辅助
本文针对动态时隙多址信道的唤醒问题，在考虑碰撞代价的场景下，提出无需碰撞检测和数据包数量信息的随机算法Lowball，给出不同代价阈值下的延迟与碰撞代价保证，并证明相关下界。
中文摘要 AI 辅助
唤醒问题刻画了共享通信信道的设备之间一项基本的对称性破缺挑战。本文研究动态场景：在时隙化的多址接入信道上，数据包可在任意时间激活。在每个时隙中，当且仅当恰好一个数据包传输时，传输才会成功；两个或更多数据包同时传输会引发碰撞。研究目标是快速实现一次成功传输。\n此前关于唤醒的研究大多聚焦于首次成功传输前的时隙数，即延迟。然而，一次碰撞可能带来显著的额外延迟，以单次碰撞代价$C$表示。因此，本文旨在同时控制执行过程的延迟和碰撞代价，其中碰撞代价定义为$C$乘以碰撞次数。\n本文设计并分析了一种用于动态唤醒的随机算法Lowball，该算法无需碰撞检测，也无需知晓数据包数量$n$。固定常数$0<ε\ne 1/2$，存在常数$K>0$，使得当$C\re K\rg^{1/ε} n$时，Lowball的期望延迟为$O(C^{1/2+ε}\n C)$，期望碰撞代价为$O(\rt{C})$。低于该阈值时，两项期望均为$O(n\bg^{Θ(1/ε)} n)$。这些保证在自适应、非预测型敌手模型下依然成立，且算法以概率1成功。对于每个数据包的传输概率仅取决于$C$和数据包本地存活时间、且同时激活的数据包使用相同概率调度策略的算法，本文证明其期望延迟与期望碰撞代价的最大值为$Ω(\rt{C})$。
英文摘要
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 $0<ε\le 1/2$. There is a constant $K>0$ such that, when $C\ge K\lg^{1/ε} n$, Lowball has expected latency $O(C^{1/2+ε}\ln C)$ and expected collision cost $O(\sqrt{C})$. Below this threshold, both expectations are $O(n\log^{Θ(1/ε)} n)$. 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 $Ω(\sqrt{C})$.
