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

TL;DR

This paper develops a stochastic recurrence equation framework for analyzing multiserver-job queuing models in cloud computing, introducing algorithms for workload sampling and stability estimation that leverage GPU parallelization.

Contribution

It introduces a novel SRE-based approach for analyzing MJQM systems, including algorithms for workload sampling and stability estimation, with extensions to complex resource-typed systems.

Findings

Algorithms enable efficient workload sampling on GPUs

The approach accurately estimates system stability conditions

Framework extends to systems with typed resources

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.