Packet Latency of Deterministic Broadcasting in Adversarial Multiple Access Channels

We study broadcasting in multiple access channels with dynamic packet arrivals and jamming. Communication environments are represented by adversarial models that specify constraints on packet arrivals and jamming. We consider deterministic distributed broadcast algorithms and give upper bounds on the worst-case packet latency and the number of queued packets in relation to the parameters defining adversaries. Packet arrivals are determined by a rate of injections and a number of packets that can be generated in one round. Jamming is constrained by a rate with which an adversary can jam rounds and by a number of consecutive rounds that can be jammed.

💡 Research Summary

The paper investigates deterministic distributed broadcasting on multiple‑access channels under adversarial traffic and jamming. Unlike the traditional stochastic models that assume random packet arrivals and random back‑off, the authors adopt an adversarial queuing framework that imposes only two types of constraints: (i) a packet‑injection rate ρ together with a burstiness parameter β limiting the maximum number of packets that may be injected in a single round, and (ii) a jamming rate λ together with a burstiness J limiting the maximum number of consecutive jammed rounds. The fundamental performance metrics are (a) queue size – the maximum total number of packets stored across all stations at any time, and (b) packet latency – the worst‑case number of rounds a packet spends in the system from injection until successful transmission.

The study is divided into two main settings. In the first setting (λ = 0, i.e., no jamming), the authors analyze five algorithms: four non‑adaptive algorithms (OF‑RRW, RRW, OF‑SRR, SRR) and one adaptive algorithm (MBTF). For each algorithm they derive explicit upper bounds on queue size and latency as functions of ρ, β, and the number of stations n. For example, OF‑RRW and RRW achieve queue size O((1‑ρ)⁻¹·n + β) and latency O((1‑ρ)⁻¹·(1 + ρ)·n + β). The adaptive MBTF algorithm can keep queues bounded even when ρ = 1 (O(n² + β)), but its latency grows as O((1‑ρ)⁻¹·n²) when ρ approaches 1. The authors observe that non‑adaptive algorithms inevitably suffer unbounded growth of both queue size and latency as ρ→1, leading to Conjecture 1 and Conjecture 2.

In the second setting (ρ + λ < 1), the paper introduces jamming. Two non‑adaptive algorithms (OF‑JRRW(J) and JRRW(J)) and three adaptive algorithms (OF‑C‑RRW, C‑RRW, C‑MBTF) are examined. The derived bounds now contain additional factors (1‑λ) and (1‑ρ‑λ)⁻¹, reflecting the impact of jammed rounds. For instance, OF‑JRRW(J) has queue size O((β + 1)/(1‑ρ‑λ)·n + β) and latency O((β + 1)/(1‑ρ‑λ)·(1 + ρ‑λ)·n + β). Adaptive algorithms can tolerate the full load condition ρ + λ = 1 while keeping queues bounded, but latency again blows up as ρ + λ→1, supporting Conjecture 4.

The proofs rely on a round‑by‑round worst‑case analysis. The authors model the adversary’s actions as a sequence of packet injections and jammed rounds that respect the (ρ,β) and (λ,J) constraints. By constructing a potential function that captures the total number of pending packets and the “distance” of each packet from the head of its station’s queue, they bound how much the potential can increase in a single round. The burstiness parameters β and J appear explicitly in the code of the non‑adaptive algorithms, allowing the algorithms to recognize when a worst‑case burst may be occurring and to adjust their transmission schedule accordingly.

The paper’s contributions are threefold: (1) it provides the first systematic set of upper bounds for deterministic broadcast algorithms under combined injection and jamming adversaries; (2) it distinguishes clearly between adaptive and non‑adaptive strategies, showing that adaptivity (i.e., the ability to embed control bits and sense collisions) is essential for achieving bounded queues when the channel is heavily loaded; and (3) it formulates several conjectures that capture inherent limitations of deterministic broadcasting—namely, that any algorithm guaranteeing bounded queues (or bounded latency) will see those bounds grow arbitrarily large as the load approaches the theoretical maximum.

Overall, the work deepens our understanding of how deterministic protocols behave in hostile environments where traffic bursts and intentional interference coexist. It offers concrete guidelines for protocol designers: if the system must operate under high load or in the presence of jamming, adaptive mechanisms are indispensable, and the parameters β and J must be accounted for in the algorithm’s logic. The results also suggest that, without randomness, achieving both small queues and low latency simultaneously may be impossible when the adversarial load approaches the channel capacity.