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Broadcasting on Adversarial Multiple Access Channels

Bader A. Aldawsari, Bogdan S. Chlebus, Dariusz R. Kowalski

TL;DR

The paper addresses deterministic broadcasting on adversarial multi-access channels under leaky-bucket traffic, examining latency and queue stability across perpetual and ad-hoc channel settings. It introduces a four-step bucket process to formalize packet generation and extends the model with randomized adversaries and individual station rates, enabling both worst-case and probabilistic analyses. The study derives worst-case latency and queue bounds for several algorithm families, including old-go-first token schemes, ad-hoc 1-activating methods, and randomized backoff protocols, and validates insights via simulations that mimic randomized injections. Overall, the work clarifies how channel structure and injection constraints shape the effectiveness of broadcasting strategies and offers a framework for evaluating algorithms under realistic adversarial traffic, with practical implications for protocol design and performance benchmarking.

Abstract

We study deterministic distributed algorithms for broadcasting on multiple-access channels. Packet injection is modeled by leaky-bucket adversaries. There is a fixed set of stations attached to a channel. Additional features of the model of communication include an upper bound on the number of stations activated in a round, an individual injection rate, and randomness in generating and injecting packets. We demonstrate that some broadcast algorithms designed for ad-hoc channels have bounded latency for increased ranges of injection rates than in ad-hoc channels when executed on channels with a fixed number of stations against adversaries that can activate at most one station per round. Individual injection rates are shown to impact latency, as compared to the model of general leaky bucket adversaries. Outcomes of experiments are given that compare the performance of broadcast algorithms against randomized adversaries. The experiments include deterministic algorithms and randomized backoff algorithms.

Broadcasting on Adversarial Multiple Access Channels

TL;DR

The paper addresses deterministic broadcasting on adversarial multi-access channels under leaky-bucket traffic, examining latency and queue stability across perpetual and ad-hoc channel settings. It introduces a four-step bucket process to formalize packet generation and extends the model with randomized adversaries and individual station rates, enabling both worst-case and probabilistic analyses. The study derives worst-case latency and queue bounds for several algorithm families, including old-go-first token schemes, ad-hoc 1-activating methods, and randomized backoff protocols, and validates insights via simulations that mimic randomized injections. Overall, the work clarifies how channel structure and injection constraints shape the effectiveness of broadcasting strategies and offers a framework for evaluating algorithms under realistic adversarial traffic, with practical implications for protocol design and performance benchmarking.

Abstract

We study deterministic distributed algorithms for broadcasting on multiple-access channels. Packet injection is modeled by leaky-bucket adversaries. There is a fixed set of stations attached to a channel. Additional features of the model of communication include an upper bound on the number of stations activated in a round, an individual injection rate, and randomness in generating and injecting packets. We demonstrate that some broadcast algorithms designed for ad-hoc channels have bounded latency for increased ranges of injection rates than in ad-hoc channels when executed on channels with a fixed number of stations against adversaries that can activate at most one station per round. Individual injection rates are shown to impact latency, as compared to the model of general leaky bucket adversaries. Outcomes of experiments are given that compare the performance of broadcast algorithms against randomized adversaries. The experiments include deterministic algorithms and randomized backoff algorithms.
Paper Structure (22 sections, 6 theorems, 3 equations, 6 figures)

This paper contains 22 sections, 6 theorems, 3 equations, 6 figures.

Table of Contents

  1. Introduction
  2. An overview of the document.
  3. Technical Preliminaries
  4. Sharing a channel.
  5. Dynamic broadcasting.
  6. Categories of broadcast algorithms.
  7. Performance metrics.
  8. Adversarial Packet Injection
  9. Leaky-bucket adversaries.
  10. The four step bucket process.
  11. Randomized adversaries.
  12. Individual injection rates.
  13. Review of Broadcast Algorithms
  14. Algorithms for perpetual channels.
  15. Algorithms for $1$-activating ad-hoc channels.
  16. ...and 7 more sections

Key Result

Proposition 1

Consider a sequence of packets generated at each round by an adversary in an unbounded execution. The sequence is consistent with a leaky-bucket adversarial type $(\rho,\beta)$ if and only if it is consistent with the four-step bucket process of type $(\rho,\beta)$.

Figures (6)

  • Figure 1: A comparison of ad-hoc and backoff algorithms with respect to the average packet latency on $n=10$ stations for the full range of injection rates.
  • Figure 2: A comparison of ad-hoc and backoff algorithms with respect to the average packet latency on $n=250$ stations for the full range of injection rates.
  • Figure 3: A comparison of the average packet latency of token algorithms on $n=50$ stations for injection rates in the range $[0.05,0.80]$.
  • Figure 4: A comparison of the average packet latency of token algorithms on $n=250$ stations for injection rates in the range $[0.05,0.80]$.
  • Figure 5: A comparison of the average packet latency of token algorithms on $n=10$ stations for injection rates in the range $[0.80 , 0.98]$.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Proposition 1
  • Proposition 2
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Conjecture 1
  • Theorem 4