On the Analysis of Spatially Constrained Power of Two Choice Policies

TL;DR

This paper analyzes spatially constrained power of two choice policies for user-server assignment on a plane, balancing load and communication costs, and proposes improved policies with experimental validation.

Contribution

It introduces the spatial Power of two (sPOT) policy, analyzes its load balancing limits, and proposes non-uniform sampling policies for better tradeoffs.

Findings

sPOT maps to classical POT on Delaunay graphs

sPOT does not fully achieve POT load balancing benefits

Proposed policies improve communication cost and load balancing

Abstract

We consider a class of power of two choice based assignment policies for allocating users to servers, where both users and servers are located on a two-dimensional Euclidean plane. In this framework, we investigate the inherent tradeoff between the communication cost, and load balancing performance of different allocation policies. To this end, we first design and evaluate a Spatial Power of two (sPOT) policy in which each user is allocated to the least loaded server among its two geographically nearest servers sequentially. When servers are placed on a two-dimensional square grid, sPOT maps to the classical Power of two (POT) policy on the Delaunay graph associated with the Voronoi tessellation of the set of servers. We show that the associated Delaunay graph is 4-regular and provide expressions for asymptotic maximum load using results from the literature. For uniform placement of servers, we map sPOT to a classical balls and bins allocation policy with bins corresponding to the Voronoi regions associated with the second order Voronoi diagram of the set of servers. We provide expressions for the lower bound on the asymptotic expected maximum load on the servers and prove that sPOT does not achieve POT load balancing benefits. However, experimental results suggest the efficacy of sPOT with respect to expected communication cost. Finally, we propose two non-uniform server sampling based POT policies that achieve the best of both the performance metrics. Experimental results validate the effctiveness of our proposed policies.