Age of Information in an Overtake-Free Network of Quasi-Reversible Queues

TL;DR

This paper derives formulas for the Age of Information in a network of quasi-reversible queues with multiple classes of update packets, showing how shared queues and saturation affect information freshness.

Contribution

It provides a method to calculate Age of Information in overtake-free networks of quasi-reversible queues with multiple classes and different network configurations.

Findings

Individual classes maintain their age levels unless queues saturate.

Shared queues lead to increased age when saturated.

Results apply to tandem M/M/1 queues and two-class networks.

Abstract

We show how to calculate the Age of Information in an overtake-free network of quasi-reversible queues, with exponential exogenous interarrivals of multiple classes of update packets and exponential service times at all nodes. Results are provided for any number of M/M/1 First-Come-First-Served (FCFS) queues in tandem, and for a network with two classes of update packets, entering through different queues in the network and exiting through the same queue. The main takeaway is that in a network with different classes of update packets, individual classes roughly preserve the ages they would achieve if they were alone in the network, except when shared queues become saturated, in which case the ages increase considerably.