Efficient calculation of available space for multi-NUMA virtual machines

TL;DR

This paper presents a method to efficiently calculate the maximum number of multi-NUMA virtual machines that can be allocated on a physical server, considering complex NUMA topology mappings.

Contribution

It derives closed-form expressions for maximizing VM allocation on multi-NUMA servers, addressing complex topology mapping scenarios.

Findings

Derived formulas for 2- and 4-NUMA VM mappings

Applicable to real-time capacity dashboards

Enhances cloud resource optimization tools

Abstract

Increasing demand for computational power has led cloud providers to employ multi-NUMA servers and offer multi-NUMA virtual machines to their customers. However, multi-NUMA VMs introduce additional complexity to scheduling algorithms. Beyond merely selecting a host for a VM, the scheduler has to map virtual NUMA topology onto the physical NUMA topology of the server to ensure optimal VM performance and minimize interference with co-located VMs. Under these constraints, maximizing the number of allocated multi-NUMA VMs on a host becomes a combinatorial optimization problem. In this paper, we derive closed-form expressions to compute the maximum number of VMs for a given flavor that can be additionally allocated onto a physical server. We consider nontrivial scenarios of mapping 2- and 4-NUMA symmetric VMs to 4- and 8-NUMA physical topologies. Our results have broad applicability, ranging from real-time dashboards (displaying available cluster capacity per VM flavor) to optimization tools for large-scale cloud resource reorganization.