Pull-based load distribution in large-scale heterogeneous service systems

TL;DR

This paper analyzes a pull-based load distribution algorithm in large-scale heterogeneous cloud systems, proving its asymptotic optimality in minimizing customer blocking and waiting as system size grows.

Contribution

It introduces and proves the asymptotic optimality of the PULL load distribution algorithm in large, heterogeneous server pools under sub-critical load.

Findings

Asymptotic probability of blocking or waiting vanishes as system size increases.

PULL algorithm remains optimal under various generalizations.

Effective load balancing in large-scale heterogeneous systems.

Abstract

The model is motivated by the problem of load distribution in large-scale cloud-based data processing systems. We consider a heterogeneous service system, consisting of multiple large server pools. The pools are different in that their servers may have different processing speed and/or different buffer sizes (which may be finite or infinite). We study an asymptotic regime in which the customer arrival rate and pool sizes scale to infinity simultaneously, in proportion to some scaling parameter $n$. Arriving customers are assigned to the servers by a "router", according to a {\em pull-based} algorithm, called PULL. Under the algorithm, each server sends a "pull-message" to the router, when it becomes idle; the router assigns an arriving customer to a server according to a randomly chosen available pull-message, if there are any, or to a random server, otherwise. Assuming sub-critical system load, we prove asymptotic optimality of PULL. Namely, as system scale $n\to\infty$, the steady-state probability of an arriving customer experiencing blocking or waiting, vanishes. We also describe some generalizations of the model and PULL algorithm, for which the asymptotic optimality still holds.