# Light traffic behavior under the power-of-two load balancing strategy: The case of heterogeneous servers

## TL;DR

This paper analyzes the performance of a multi-server queueing system with heterogeneous servers under the power-of-two load balancing policy in light traffic, revealing how server diversity impacts response time.

## Contribution

It provides the first analytical evaluation of light traffic response time derivatives for heterogeneous servers under the power-of-two policy.

## Key findings

- Response time decreases with small arrival rates for unequal server capacities.
- Greater server speed diversity leads to larger performance gains.
- Theoretical results are supported by simulation evidence.

## Abstract

We consider a multi-server queueing system under the power-of-two policy with Poisson job arrivals, heterogeneous servers and a general job requirement distribution; each server operates under the first-come first-serve policy and there are no buffer constraints. We analyze the performance of this system in light traffic by evaluating the first two light traffic derivatives of the average job response time. These expressions point to several interesting structural features associated with server heterogeneity in light traffic: For unequal capacities, the average job response time is seen to decrease for small values of the arrival rate, and the more diverse the server speeds, the greater the gain in performance. These theoretical findings are assessed through limited simulations.