On the Age of Information of a Queuing System with Heterogeneous Servers

TL;DR

This paper analyzes the age of information in a queuing system with heterogeneous servers, deriving exact and approximate formulas for average AoI, and shows how adding servers reduces AoI.

Contribution

It provides the first exact expression for AoI in a two-server heterogeneous system and introduces an approximate AoI for multi-server systems, linking server utilization to AoI optimization.

Findings

Exact AoI expression for two heterogeneous servers derived.

Approximate AoI useful for multi-server systems.

Adding more servers significantly reduces AoI.

Abstract

An optimal control problem with heterogeneous servers to minimize the average age of information (AoI) is considered. Each server maintains a separate queue, and each packet arriving to the system is randomly routed to one of the servers. Assuming Poisson arrivals and exponentially distributed service times, we first derive an exact expression of the average AoI for two heterogeneous servers. Next, to solve for the optimal average AoI, a close approximation is derived, called the approximate AoI, this is shown to be useful for multi-server systems as well. We show that for the optimal approximate AoI, server utilization (ratio of arrival rate and service rate) for each server should be same as the optimal server utilization with a single server queue. For two identical servers, it is shown that the average AoI is approximately 5/8 times the average AoI of a single server. Furthermore, the average AoI is shown to decrease considerably with the addition of more servers to the system.