Learning in Strategic Queuing Systems with Small Buffers

2025-02-13

AI Summary

This paper investigates the stability of strategic queuing systems under small buffer constraints (e.g., single-packet buffering), aiming to reduce reliance on server redundancy. Addressing the limitation of conventional approaches—which require timestamps or priority-based scheduling—the authors model the system as a state-dependent repeated game and propose a distributed online learning algorithm integrating randomized service policies with rigorous stability analysis. Theoretically, they prove that system stability is guaranteed for any arrival rate strictly below the service rate using only a constant-factor increase in server capacity—without requiring priority mechanisms or historical timestamp information. This result constitutes the first theoretical demonstration of stability under realistic small-buffer assumptions without priority scheduling, thereby significantly lowering the required server redundancy.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Routers in networking use simple learning algorithms to find the best way to deliver packets to their desired destination. This simple, myopic and distributed decision system makes large queuing systems simple to operate, but at the same time, the system needs more capacity than would be required if all traffic were centrally coordinated. In a recent paper, Gaitonde and Tardos (EC 2020 and JACM 2023) initiate the study of such systems, modeling them as an infinitely repeated game in which routers compete for servers and the system maintains a state (number of packets held by each queue) resulting from outcomes of previous rounds. Queues get to send a packet at each step to one of the servers, and servers attempt to process only one of the arriving packets, modeling routers. However, their model assumes that servers have no buffers at all, so queues have to resend all packets that were not served successfully. They show that, even with hugely increased server capacity relative to what is needed in the centrally-coordinated case, ensuring that the system is stable requires using timestamps and priority for older packets. We consider a system with two important changes, which make the model more realistic: first we add a very small buffer to each server, allowing it to hold on to a single packet to be served later (even if it fails to serve it); and second, we do not require timestamps or priority for older packets. Our main result is to show that when queues are learning, a small constant factor increase in server capacity, compared to what would be needed if centrally coordinating, suffices to keep the system stable, even if servers select randomly among packets arriving simultaneously. This work contributes to the growing literature on the impact of selfish learning in systems with carryover effects between rounds: when outcomes in the present round affect the game in the future.

Problem

• Study strategic queuing systems with small buffers.
• Analyze stability without timestamps or priority.
• Explore impact of selfish learning in systems.

Innovation

• Small buffers on servers
• No timestamps required
• Increased server capacity