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Probabilistic Fair Ordering of Events

Muhammad Haseeb, Jinkun Geng, Aurojit Panda, Radhika Mittal, Nirav Atre, Srinivas Narayana, Anirudh Sivaraman

TL;DR

The paper tackles fair ordering in distributed systems under unavoidable clock-uncertainty by introducing Tommy, a probabilistic sequencer that leverages clock-correction distributions to compare noisy timestamps. By formulating pairwise precedence as a probability $\xrightarrow{p}$ and mapping multi-event ordering to social-choice ranking, Tommy produces a partial order that is robust to intransitive comparisons and online arrival of events. It combines a statistical model with Smith-set–based partial ordering to avoid forcing a total order when not warranted by evidence, and it demonstrates improved fairness over a TrueTime baseline in ns-3 simulations and a realistic data-center workload. The approach offers a practical fair ordering primitive that does not rely on near-perfect clocks, with implications for financial exchanges, online gaming, and ad auctions where fairness matters.

Abstract

A growing class of applications depends on fair ordering, where events that occur earlier should be processed before later ones. Providing such guarantees is difficult in practice because clock synchronization is inherently imperfect: events generated at different clients within a short time window may carry timestamps that cannot be reliably ordered. Rather than attempting to eliminate synchronization error, we embrace it and establish a probabilistically fair sequencing process. Tommy is a sequencer that uses a statistical model of per-clock synchronization error to compare noisy timestamps probabilistically. Although this enables ordering of two events, the probabilistic comparator is intransitive, making global ordering non-trivial. We address this challenge by mapping the sequencing problem to a classical ranking problem from social choice theory, which offers principled mechanisms for reasoning with intransitive comparisons. Using this formulation, Tommy produces a partial order of events, achieving significantly better fairness than a Spanner TrueTime-based baseline approach.

Probabilistic Fair Ordering of Events

TL;DR

The paper tackles fair ordering in distributed systems under unavoidable clock-uncertainty by introducing Tommy, a probabilistic sequencer that leverages clock-correction distributions to compare noisy timestamps. By formulating pairwise precedence as a probability and mapping multi-event ordering to social-choice ranking, Tommy produces a partial order that is robust to intransitive comparisons and online arrival of events. It combines a statistical model with Smith-set–based partial ordering to avoid forcing a total order when not warranted by evidence, and it demonstrates improved fairness over a TrueTime baseline in ns-3 simulations and a realistic data-center workload. The approach offers a practical fair ordering primitive that does not rely on near-perfect clocks, with implications for financial exchanges, online gaming, and ad auctions where fairness matters.

Abstract

A growing class of applications depends on fair ordering, where events that occur earlier should be processed before later ones. Providing such guarantees is difficult in practice because clock synchronization is inherently imperfect: events generated at different clients within a short time window may carry timestamps that cannot be reliably ordered. Rather than attempting to eliminate synchronization error, we embrace it and establish a probabilistically fair sequencing process. Tommy is a sequencer that uses a statistical model of per-clock synchronization error to compare noisy timestamps probabilistically. Although this enables ordering of two events, the probabilistic comparator is intransitive, making global ordering non-trivial. We address this challenge by mapping the sequencing problem to a classical ranking problem from social choice theory, which offers principled mechanisms for reasoning with intransitive comparisons. Using this formulation, Tommy produces a partial order of events, achieving significantly better fairness than a Spanner TrueTime-based baseline approach.
Paper Structure (23 sections, 1 theorem, 15 equations, 17 figures, 5 algorithms)

This paper contains 23 sections, 1 theorem, 15 equations, 17 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Financial Exchanges
  4. Departing from Arbitrary Order
  5. Background
  6. Fair Ordering
  7. Applications requiring fair ordering
  8. Clock Drift vs. Offset Considerations
  9. Ranking Under Uncertainty and Social Choice Theory
  10. Tommy Sequencer Design
  11. Constructing Likely-Happened Before, $\xrightarrow{p}$, Relation
  12. Achieving Partial Order
  13. Online Sequencing
  14. Evaluation
  15. Tommy vs. TrueTime Baseline
  16. ...and 8 more sections

Key Result

proposition 1

Let $X,Y,Z$ be independent normal random variables Define the preference relation Then $\succ$ is transitive: if $X\succ Y$ and $Y\succ Z$, we necessarily have $X\succ Z$.

Figures (17)

  • Figure 1: The sequencer, Tommy, uses clock correction distributions & timestamps to achieve a fair ordering of events.
  • Figure 2: Three distributions that have intransitive behavior: $P(A>B) > 0.5, P(B>C) > 0.5, P(C > A) > 0.5$.
  • Figure 3: Tommy mostly achieves better fairness than the baseline.
  • Figure 4: Optimal point for fairness arrives at edge threshold of 0.5.
  • Figure 5: Number of clients (with no change in total events) have no effect on fairness.
  • ...and 12 more figures

Theorems & Definitions (2)

  • proposition 1
  • proof