Softening the Impact of Collisions in Contention Resolution

TL;DR

This paper introduces a randomized contention resolution algorithm, CAB, that optimizes both the total time and collision costs in shared communication channels, addressing a gap in existing methods.

Contribution

The paper presents the Collision Aversion Backoff (CAB) algorithm, which minimizes both makespan and collision costs, and provides tight bounds for fair algorithms in this context.

Findings

CAB achieves expected collision cost of  O(nsqrt{\u210C}) with high probability.

A matching lower bound for fair algorithms is established, tight up to polylogarithmic factors.

The algorithm effectively balances collision minimization and overall completion time.

Abstract

Contention resolution addresses the problem of coordinating access to a shared communication channel. Time is discretized into synchronized slots, and a packet can be sent in any slot. If no packet is sent, then the slot is empty; if a single packet is sent, then it is successful; and when multiple packets are sent at the same time, a collision occurs, resulting in the failure of the corresponding transmissions. In each slot, every packet receives ternary channel feedback indicating whether the current slot is empty, successful, or a collision. Much of the prior work on contention resolution has focused on optimizing the makespan, which is the number of slots required for all packets to succeed. However, in many modern systems, collisions are also costly in terms of the time they incur, which existing contention-resolution algorithms do not address. In this paper, we design and analyze a randomized algorithm, Collision Aversion Backoff (CAB), that optimizes both the makespan and the collision cost. We consider the static case where an unknown $n\geq 2$ packets are initially present in the system, and each collision has a known cost $\mathcal{C}$, where $1 \leq \mathcal{C} \leq n^{\kappa}$ for a known constant $\kappa\geq 0$. With error probability polynomially small in $n$, CAB guarantees that all packets succeed with makespan and a total expected collision cost of $\tilde{O}(n\sqrt{\mathcal{C}})$. We give a lower bound for the class of fair algorithms: where, in each slot, every packet executing the fair algorithm sends with the same probability (and the probability may change from slot to slot). Our lower bound is asymptotically tight up to a $\texttt{poly}(\log n)$-factor for sufficiently large $\mathcal{C}$.