Heavy Traffic Limits for GI/H/n Queues: Theory and Application

TL;DR

This paper develops practical heavy traffic limit models for GI/H/n queues with hyper-exponential service times, enabling efficient cloud system design under QoS constraints.

Contribution

It introduces two new heavy traffic limits for GI/H/n queues that are simpler to apply than existing stochastic differential equation approaches.

Findings

Heavy traffic limits are derived for GI/H/n queues.

These limits facilitate practical system design for cloud computing.

Application examples demonstrate improved power efficiency.

Abstract

We consider a GI/H/n queueing system. In this system, there are multiple servers in the queue. The inter-arrival time is general and independent, and the service time follows hyper-exponential distribution. Instead of stochastic differential equations, we propose two heavy traffic limits for this system, which can be easily applied in practical systems. In applications, we show how to use these heavy traffic limits to design a power efficient cloud computing environment based on different QoS requirements.