Online TCP Acknowledgment under General Delays

2026-04-14

AI Summary

This study addresses the online TCP acknowledgment problem under a generalized delay cost model, focusing on balancing the number of acknowledgments against the total packet delay. For both batch-oblivious and batch-aware settings, the work presents the first systematic analysis of greedy algorithms: it establishes that the greedy algorithm remains 2-competitive in the batch-oblivious model, while in the batch-aware sum model, its competitive ratio is shown to be Ω(n). To overcome this limitation, the paper introduces the first deterministic online algorithm achieving a Θ(log n) competitive ratio for the batch-aware setting. Relying solely on the monotonicity of the delay function, the analysis integrates competitive analysis, submodular function theory, and ℓₚ-norm techniques to reveal how fundamental differences between the models critically affect algorithmic performance.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Algorithm Configuration
• Planning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

In a seminal work, Dooly, Goldman, and Scott (STOC 1998; JACM 2001) introduced the classic Online TCP Acknowledgment problem. In this problem, a sequence of $n$ packets arrives over time, and the objective is to minimize both the number of acknowledgments sent and the total delay experienced by the packets. They showed that a greedy algorithm -- acknowledge when the delay of pending packets equals the acknowledgment cost -- is $2$-competitive. Online TCP Acknowledgment is the canonical online problem with delay, capturing the fundamental tradeoff between reducing service cost through batching and the delay incurred by pending requests. Prior work has largely focused on different types of service costs, e.g., Joint Replenishment. However, to the best of our knowledge, beyond the work of Albers and Bals (SODA 2003), which studies maximum delay and closely related objectives, not much is known for more general delay cost models. In this work, we study the Online TCP Acknowledgment under two new generalized delay costs that we call batch-oblivious and batch-aware. In the former, the delay cost is a function of the vector of packet delays. We show that the classic greedy approach is also $2$-competitive for continuous submodular functions and $\ell_p$ norms. In the batch-aware model, each batch incurs a delay cost that is a function $f$ of the vector of delays incurred by its packets. When the overall delay cost is the maximum of the batch delay costs, we show that the greedy approach is also $2$-competitive. Our main technical contribution is for the batch-aware setting, where the overall delay cost is the sum of the batch delay costs. We show that the greedy approach is $Ω(n)$-competitive and that the deterministic competitive ratio is $Θ(\log n)$. Remarkably, our algorithm only requires the bare minimum assumption that $f$ is monotone.

Problem

• Online TCP Acknowledgment
• delay cost
• batch-aware
• batch-oblivious
• competitive ratio

Innovation

• Online TCP Acknowledgment
• Batch-aware delay
• Competitive analysis
• Submodular functions
• Monotone delay cost