Learning and Balancing Unknown Loads in Large-Scale Systems with Time-Varying Arrival Rates and Non-Exponential Service Times

Core Concepts

The authors develop and analyze adaptive load balancing policies that can maintain a balanced distribution of tasks across server pools, even when the arrival rate of tasks is time-varying or the service time distribution is non-exponential. The policies integrate a threshold-based dispatching rule with online learning schemes to dynamically adjust the threshold in response to changes in the unknown offered load.

Abstract

The paper considers a service system with n identical server pools, where tasks with exponentially or Coxian distributed service times arrive as a (possibly time-inhomogeneous) Poisson process. To maintain a balanced distribution of the load across the server pools, the authors propose a threshold-based dispatching rule that assigns incoming tasks to server pools based on their current occupancy levels. The key aspects of the paper are: Dispatching rule: Tasks are dispatched to server pools with fewer than a threshold number of tasks, chosen uniformly at random. The threshold is dynamically adjusted over time to track the unknown offered load. Learning schemes: A basic scheme tracks the total number of tasks in the system to estimate the offered load. A refined scheme uses more detailed occupancy information to adjust the threshold. Analysis: For the refined scheme with time-varying exponential service times, the authors prove that the threshold reaches an equilibrium value during intervals where the offered load is suitably bounded. This results in an asymptotically balanced distribution of the load. For the basic scheme with time-homogeneous Coxian service times, the authors establish similar results on the threshold convergence and load balancing. Methodology: The authors develop a novel proof technique that leverages process-level dynamical properties through strong approximations, rather than relying on traditional fluid limit analysis. This approach allows the authors to handle rapid threshold adjustments triggered by small occupancy fluctuations, and to characterize the asymptotic behavior without detailed state descriptors. Extensions: The results can be extended to other combinations of learning schemes and traffic scenarios, as discussed in the paper. Overall, the paper presents adaptive load balancing policies that can effectively maintain a balanced distribution of tasks in large-scale systems with uncertain and time-varying demand, while requiring limited state information and communication overhead.

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Key Insights Distilled From

Learning and balancing unknown loads in large-scale systems

by Diego Goldsz... at arxiv.org 04-08-2024

https://arxiv.org/pdf/2012.10142.pdf

Deeper Inquiries

How can the proposed load balancing policies be extended to settings with multiple dispatchers or heterogeneous server pools

The proposed load balancing policies can be extended to settings with multiple dispatchers or heterogeneous server pools by adapting the token-based implementation of the threshold-based dispatching rule. In the case of multiple dispatchers, each dispatcher can maintain its set of tokens corresponding to the server pools under its control. Communication between dispatchers can be established to ensure that the load balancing decisions are coordinated across the system. This approach reduces the communication overhead and allows for efficient load balancing in systems with multiple dispatchers. For heterogeneous server pools, the threshold-based dispatching rule can be modified to account for different capacities or capabilities of the server pools. Each server pool can be assigned a specific threshold value based on its capacity or performance characteristics. The learning schemes can be adjusted to take into consideration the heterogeneity of the server pools, ensuring that the load is balanced effectively across all types of server pools.

What are the implications of the load balancing performance on the quality of service experienced by the tasks, in terms of metrics like throughput, delay, or utility

The load balancing performance has significant implications on the quality of service experienced by the tasks in the system. The metrics like throughput, delay, and utility are directly influenced by how effectively the load is balanced across the server pools. Throughput: Efficient load balancing ensures that tasks are distributed evenly among the server pools, maximizing the overall throughput of the system. By avoiding bottlenecks and overloading of specific server pools, the system can achieve higher throughput levels. Delay: Proper load balancing helps in reducing the delay experienced by tasks in the system. By ensuring that tasks are evenly distributed and processed efficiently across the server pools, the overall delay in task completion is minimized. Utility: The quality of service provided to tasks is directly related to the utility function used to measure it. By optimizing the load balancing policies to maximize the utility function, the system can enhance the overall user experience and satisfaction. Overall, effective load balancing leads to improved system performance, reduced delays, and enhanced quality of service for the tasks in the system.

Can the novel proof methodology developed in this paper be applied to analyze other types of adaptive control policies in large-scale stochastic systems

The novel proof methodology developed in this paper, which focuses on leveraging process-level dynamical properties through strong approximations, can be applied to analyze other types of adaptive control policies in large-scale stochastic systems. By adapting the methodology to different control policies and system configurations, researchers can gain insights into the asymptotic behavior and performance of various adaptive control strategies. The methodology can be extended to analyze the stability, convergence, and optimality of different control policies in large-scale systems with complex dynamics. By applying similar techniques to other adaptive control schemes, researchers can uncover new insights into the behavior of these systems and develop strategies to optimize their performance. Overall, the novel proof methodology developed in this paper has the potential to be a valuable tool for analyzing and understanding the behavior of adaptive control policies in large-scale stochastic systems.