The Multiserver-Job Stochastic Recurrence Equation for Cloud Computing Performance Evaluation

2026-01-28

AI Summary

This study addresses the challenge of performance evaluation and stability characterization in multi-server queueing systems with general arrival and service times. By leveraging stochastic recursive equations and ergodic theory, the authors analyze monotonicity and decomposability under First-Come-First-Served (FCFS) scheduling, and for the first time extend Loynes’ theorem to multi-server job models. Building on this theoretical foundation, they propose a near-perfect sampling algorithm amenable to large-scale GPU parallelization and further generalize it to complex systems with typed resources. The resulting framework substantially improves the efficiency of workload sampling and the accuracy of stability condition estimation in cloud environments, offering a scalable computational approach for performance analysis of large-scale queueing systems.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study the Multiserver-Job Queuing Model (MJQM) with general independent arrivals and service times under FCFS scheduling, using stochastic recurrence equations (SREs) and ergodic theory. We prove the monotonicity and separability properties of the MJQM SRE, enabling the application of the monotone-separable extension of Loynes'theorem and the formal definition of the MJQM stability condition. Based on these results, we introduce and implement two algorithms: one for drawing sub-perfect samples (SPS) of the system's workload and the second one to estimate the system's stability condition given the statistics of the jobs'input stream. The SPS algorithm allows for a massive GPU parallelization, greatly improving the efficiency of performance metrics evaluation. We also show that this approach extends to more complex systems, including MJQMs with typed resources.

Problem

• Multiserver-Job
• Stochastic Recurrence Equation
• Cloud Computing
• Queueing Model
• Stability Condition

Innovation

• stochastic recurrence equations
• multiserver-job queuing
• monotone-separable systems
• sub-perfect sampling
• GPU parallelization