Age-of-Information in Tandem Queues with Delayed Feedback: Zero-Wait vs. Pipelining

An established policy for updating systems is zerowait: a source immediately sends a new sample as soon as the sink acknowledges the receipt of the previous one. The rationale of zero-wait is that with instantaneous feedback, the transmission of samples can fully utilize the forward link without ever causing a queue. However, this ideal behavior does not extend to multihop networks and two-way delay. One approach to generalize zero-wait for use in larger networks is message pipelining, where there is a fixed number of samples and acknowledgments $k \geq 1$ in the network at any time. We analyze the peak age-of-information of updating systems with pipelining in multi-hop networks with arbitrarily many queues in the forward and feedback paths. While pipelining improves network utilization, it also increases queuing delays, and the optimal degree k must strike a balance between the two. We show how this depends on the diameter and topology of the network, the presence of bottlenecks, and the statistical distribution of service times. In an a priori unknown and changing network, it is beneficial to adjust the pipelining adaptively. We demonstrate how basic delay-based congestion control can be effectively used to achieve this goal.