Stability and Capacity Regions for Discrete-Time Queueing Networks: A Comprehensive Review

In this paper, we explore the challenge of reducing network delay in overloaded data centers. We focus on a single-hop network with unlimited link capacity and identify a condition that minimizes both average and maximum delay metrics. Our result can be extended to general N and also considers zero initial queue length for brevity.
Imagine a network like a busy highway, where multiple cars (packets) are trying to reach their destinations simultaneously. Overloading occurs when the number of cars exceeds the capacity of the road, causing delays and congestion. Network overload is common in data centers due to increased traffic demands from machine learning applications and larger training models.
To address this challenge, we first identify a sufficient and necessary condition for the transmission rate vector (g) that minimizes both average and maximum delay metrics. We then extend our result to general N and discuss how initial queue length affects the outcome.
Our findings demonstrate that by carefully managing the transmission rates of each link, network providers can significantly reduce delay under overload conditions. This is crucial for maintaining network performance and ensuring efficient communication in data centers. By using this strategy, providers can improve network efficiency and reduce delays, resulting in better overall performance.
In summary, our work provides a valuable tool for network providers to manage overloaded networks and ensure efficient communication under heavy traffic demands. By minimizing delay metrics, we help maintain network performance and improve communication quality, ensuring that data centers can handle the growing demands of machine learning applications.