🤖 AI Summary
This study addresses the problem of dynamically allocating cores in multicore systems to minimize the steady-state average number of jobs—equivalently, average response time—for two classes of variable-parallelism workloads with unknown speedup parameters. The authors propose an iterative learning-and-control framework that alternates, during job execution, between maximum likelihood estimation of the speedup parameters and updating a core allocation policy derived from a Markov decision process (MDP). Within each class, cores are equally shared among jobs, while the inter-class resource split is determined by the MDP’s optimal solution under the current parameter estimates. This work is the first to integrate online parameter learning with dynamic resource allocation in a closed-loop manner. Numerical experiments demonstrate that the proposed strongly consistent estimator and adaptive scheduling policy significantly reduce the average job count, confirming the estimator’s consistency, policy convergence, and performance gains.
📝 Abstract
We study dynamic resource allocation in a multicore computing system with a fixed number of processing cores and a stream of {\it malleable} jobs. Each job may adjust its level of parallelism during execution, allowing adaptive redistribution of resources across concurrently active jobs. Jobs belong to one of two observable classes, each characterized by a distinct speed-up function with unknown parameters. The objective is to learn a core-allocation policy that minimizes the long-run mean number of jobs in the system, equivalently the mean response time in steady state.
\noindent To address this uncertainty, we develop an iterative learning-and-control framework. The system alternates between estimating the unknown speed-up parameters from observed job completions and solving the associated Markov decision process (MDP) to update the allocation policy. Within each job class, cores are shared equally among active jobs; the fraction of capacity assigned to each class is obtained from the MDP formulation of \cite{berg2017}, evaluated at the current parameter estimates. We construct a maximum likelihood estimator based on state-dependent inter-departure times and prove its strong consistency under a fixed allocation policy. We further propose two learning algorithms that combine this estimation step with dynamic programming-based policy updates, and illustrate their through numerical experiments.