Periodic Deterministic Sampling and Scheduling Algorithms for Minimum Age of Information in Time-Slotted Multihop Networks

We consider a time-slotted multihop wireless sensor network used for a remote estimation application. Sensor nodes sample processes of interest and convergecast the sampled data to a sink over the multihop wireless network. The processes are remotely estimated at the sink. For such applications, the Age of Information (AoI) is a relevant performance metric. Motivated by real-world protocols, such as 802.15.4e TSCH, we design novel periodic deterministic sampling and scheduling algorithms for minimizing the average AoI (AAoI) for convergecast in tree network topologies with K-hop interference constraints. We obtain an analytical characterization of the AAoI in terms of the period of the policy as well as hop distances of the source nodes to the sink. For periodic deterministic policies, the AAoI minimization problem is formulated as an integer programming problem which is relaxed to a linear programming problem to obtain numerical lower bounds. Novel analytical lower bounds on the AAoI for periodic deterministic policies in tree networks with K-hop interference constraints are obtained. We simulate and compare the AAoI performance of our periodic deterministic policies and show that they have an AAoI close to the lower bounds for that period. Through simulations, we also show that the AAoI of the proposed policies is smaller compared to other multihop AoI-minimizing policies in prior work, such as Age-Difference and Age-Debt. We also discuss extensions to the case of general functions of the AoI.