Conjectures on Symmetric Queues in Heavy Traffic

TL;DR

This paper discusses open questions about the behavior of symmetric queues in heavy traffic, focusing on how different service-time distributions affect their scaling limits.

Contribution

It highlights unresolved issues related to the scaling limits of symmetric queues, especially distinguishing between finite and infinite variance service times.

Findings

Identifies key open questions in queue scaling limits.

Differentiates effects of finite vs. infinite variance service times.

Provides a foundation for future research in queue theory.

Abstract

This note describes several open questions concerning scaling limits of queue-length processes of symmetric queues in heavy traffic, distinguishing between service-time distributions with finite and infinite variance.