Age of Information for Queues in Tandem

As a stepping stone towards understanding the freshness of information in multi-hop networks, we study the age of information metric for queues in tandem. Applying the recent stochastic hybrid systems approach for age of information, we derive the average age for two non-preemptive first-come, first-served queues in tandem with memoryless arrival and departure processes and queue capacities equal to 1. We verify our results via simulation, and we also simulate the case of infinite capacity queues in tandem for up to four hops. Our simulations include cases with deterministic arrival or departure processes, and we assess the impact of the number of hops in the line network on the average age for the various models. We observe that for queues in tandem with a memoryless arrival process and memoryless departures, as the number of hops increase, the average age increases linearly at high arrival rates. For memoryless arrivals and deterministic departures, the ages increase sublinearly, while for deterministic arrivals and memoryless departures, the ages increase superlinearly at high arrival rates. We also study the behavior of the optimal arrival rates as a function of the number of hops, and we observe that the optimal arrival rate decreases with the number of hops when the departure process is memoryless, but for deterministic departure processes, the optimal arrival rate is independent of the number of hops.