The Age of Updates in a Simple Relay Network

In this paper, we examine a system where status updates are generated by a source and are forwarded in a First-Come-First-Served (FCFS) manner to the monitor. We consider the case where the server has other tasks to fulfill referred to as vacations, a simple example being relaying the packets of another non age-sensitive stream. Due to the server's necessity to go on vacations, the age process of the stream of interest becomes complicated to evaluate. By leveraging specific queuing theory tools, we provide a closed form of the average age of the stream which enables us to optimize its packet generation rate and achieve the minimum possible average age. Numerical results are provided to corroborate the theoretical findings and highlight the interaction between the stream and the vacations in question.