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

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. The results are extensible for other quasi-reversible queues for which sojourn time distributions are known, such as M/M/c FCFS queues and processor-sharing queues.