Softening the Impact of Collisions in Contention Resolution

TL;DR

A randomized algorithm, Collision Aversion Backoff (CAB), that optimizes both the makespan and the collision cost, and gives 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).

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 $1 \leq \mathcal{C} \leq n^κ$ for a known constant $κ\geq 0$. 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 $\mathcal{C}$.

Figures (3)

• Figure 1: Illustration of the ranges discussed in Section \ref{['sec:algorithm']}.
• Figure 2: Collision-Aversion Backoff
• Figure 3: The elimination of ranges as discussed in Section \ref{['sec:algorithm']}.

Theorems & Definitions (69)

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