Age of Information in Relay-Assisted Status Updating Systems

Abstract

In this paper we consider the age of information (AoI) of a status updating system with a relay, where the updates are delivered to destination either from the direct line or the two-hop link via the relay. An updating packet generated at source is sent to receiver and the relay simultaneously. When the direct packet transmission fails, the relay replaces the source and retransmits the packet until it is eventually obtained at the receiver side. Assume that the propagation delay on each link is one time slot, we determine the stationary distribution of the AoI for three cases: (a) relay has no buffer and the packet delivery from relay cannot be preempted by fresher updates from source; (b) relay has no buffer but the packet substitution is allowable; (c) relay has size 1 buffer and the packet in buffer is refreshed when a newer packet is obtained. The idea is invoking a multiple-dimensional state vector which contains the AoI as a part and constituting the multiple-dimensional AoI stochastic process. We find the steady state of each multiple-dimensional AoI process by solving the system of stationary equations. Once the steady-state distribution of larger-dimensional AoI process is known, the stationary AoI distribution is also obtained as it is one of the marginal distributions of that process's steady-state distribution. For all the situations, we derive the explicit expression of AoI distribution, and calculate the mean and the variance of the stationary AoI. All the results are compared numerically, including the AoI performance of the non-relay state updating system. Numerical results show that adding the relay

Minimizing the AoI in Resource-Constrained Multi-Source Relaying Systems: Dynamic and Learning-Based Scheduling

“…The age-energy tradeoffs in a relay-aided status update system were studied in [45], where the expressions for the AAoI and average energy cost were derived. In [42], the expression of the AoI distributions in a singlesource relaying system under different circumstances were derived. Minimization of the AAoI through optimizing the blocklengths in short-packet communications in decode-andforward relaying IoT networks was conducted in [46].…”

Strategic Age of Information Aware Interaction Over a Relay Channel

“…In this work, we consider a scenario, in which a sensor is aided by a relay node [14]- [16]: transmissions from the sensor may fail, leading to a higher AoI, but the relay can recover from these failures by retransmitting the message, ensuring that it is delivered to the receiver. We analyze the average AoI in this scenario, providing a closed-form solution, and define a game theoretic optimization, in which transmissions from the node and relay have a cost: the Nash equilibrium (NE) of the game between the sensor and relay represents an easily computable, Pareto efficient solution to the problem of optimizing their activity rate [17].…”

“…To the best of our knowledge, this is the first work to consider the distributed optimization of such a relay scenario, including both expected AoI and PAoI violation probability and providing exact theoretical guarantees for performance. Previous works on AoI in relay-aided systems [15], [16], [18] either compute the age without considering the optimization of the network or optimize the scenario in a centralized fashion, using heuristics and approximate formulations of the age.…”

“…Also, [15] considers a similar relay channel model, but their focus is on an opportunistic relay (not controlled by a rational player) and the only optimization takes place in the choice of the update generation probability p by the source, which is chosen to minimize the AoI. This very same model is also analyzed in [16] from the perspective of a stateful stochastic optimization of the system, with nodes acting in a coordinated fashion.…”

Minimizing the AoI in Multi-Source Two-Hop Systems under an Average Resource Constraint

“…Related Work: Recently, the AoI in relaying systems has been studied in, e.g., [6], [9], [11], [18]- [25]. The work [6] studied the AoI minimization in a multi-source relaying system with the generate-at-will model (i.e., possibility of generating a new update at any time) and error-prone channels.…”