No Arabic abstract
We study timely status updates of a real-time system in an adversarial setting. The system samples a physical process, and sends the samples from the source (e.g., a sensor) to the destination (e.g, a control center) through a channel. For real-time monitoring/control tasks, it is crucial for the system to update the status of the physical process timely. We measure the timeliness of status updates by the time elapsed since the latest update at the destination was generated at the source, and define the time elapsed as age of information, or age in short. To sabotage the system, an attacker aims to maximize the age by jamming the channel and hence causing delay in status updates. The system aims to minimize the age by judiciously choosing when to sample and send the updates. We model the ongoing repeated interaction between the attacker and the system as a dynamic game. In each stage game, the attacker chooses the jamming time according to the jamming time distribution, and the system responds by delaying the sampling according to the sampling policy. We prove that there exists a unique stationary equilibrium in the game, and provide a complete analytical characterization of the equilibrium. Our results shed lights on how the attacker sabotages the system and how the system should defend against the attacker.
In this paper, we consider a transmission scheduling problem, in which several streams of status update packets with diverse priority levels are sent through a shared channel to their destinations. We introduce a notion of Lexicographic age optimality, or simply lex-age-optimality, to evaluate the performance of multi-class status update policies. In particular, a lex-age-optimal scheduling policy first minimizes the Age of Information (AoI) metrics for high-priority streams, and then, within the set of optimal policies for high-priority streams, achieves the minimum AoI metrics for low-priority streams. We propose a new scheduling policy named Preemptive Priority, Maximum Age First, Last-Generated, First-Served (PP-MAF-LGFS), and prove that the PP-MAF-LGFS scheduling policy is lex-age-optimal. This result holds (i) for minimizing any time-dependent, symmetric, and non-decreasing age penalty function; (ii) for minimizing any non-decreasing functional of the stochastic process formed by the age penalty function; and (iii) for the cases where different priority classes have distinct arrival traffic patterns, age penalty functions, and age penalty functionals. For example, the PP-MAF-LGFS scheduling policy is lex-age-optimal for minimizing the mean peak age of a high-priority stream and the time-average age of a low-priority stream. Numerical results are provided to illustrate our theoretical findings.
We consider the problem of optimizing the freshness of status updates that are sent from a large number of low-power sources to a common access point. The source nodes utilize carrier sensing to reduce collisions and adopt an asynchronized sleep-wake scheduling strategy to achieve a target network lifetime (e.g., 10 years). We use age of information (AoI) to measure the freshness of status updates, and design sleep-wake parameters for minimizing the weighted-sum peak AoI of the sources, subject to per-source battery lifetime constraints. When the sensing time (i.e., the time duration of carrier sensing) is zero, this sleep-wake design problem can be solved by resorting to a two-layer nested convex optimization procedure; however, for positive sensing times, the problem is non-convex. We devise a low-complexity solution to solve this problem and prove that, for practical sensing times that are short, the solution is within a small gap from the optimum AoI performance. When the mean transmission time of status-update packets is unknown, we devise a reinforcement learning algorithm that adaptively performs the following two tasks in an ``efficient way: a) it learns the unknown parameter, b) it also generates efficient controls that make channel access decisions. We analyze its performance by quantifying its ``regret, i.e., the sub-optimality gap between its average performance and the average performance of a controller that knows the mean transmission time. Our numerical and NS-3 simulation results show that our solution can indeed elongate the batteries lifetime of information sources, while providing a competitive AoI performance.
We consider a joint sampling and scheduling problem for optimizing data freshness in multi-source systems. Data freshness is measured by a non-decreasing penalty function of emph{age of information}, where all sources have the same age-penalty function. Sources take turns to generate update packets, and forward them to their destinations one-by-one through a shared channel with random delay. There is a scheduler, that chooses the update order of the sources, and a sampler, that determines when a source should generate a new packet in its turn. We aim to find the optimal scheduler-sampler pairs that minimize the total-average age-penalty at delivery times (Ta-APD) and the total-average age-penalty (Ta-AP). We prove that the Maximum Age First (MAF) scheduler and the zero-wait sampler are jointly optimal for minimizing the Ta-APD. Meanwhile, the MAF scheduler and a relative value iteration with reduced complexity (RVI-RC) sampler are jointly optimal for minimizing the Ta-AP. The RVI-RC sampler is based on a relative value iteration algorithm whose complexity is reduced by exploiting a threshold property in the optimal sampler. Finally, a low-complexity threshold-type sampler is devised via an approximate analysis of Bellmans equation. This threshold-type sampler reduces to a simple water-filling sampler for a linear age-penalty function.
This work addresses a strategy to mitigate jamming attack on low-latency communication by a Full-Duplex (FD) adversary in fast-fading channel conditions. The threat model is such that the FD adversary can jam a frequency band and measure the jammed bands power level. We first point out that due to the presence of this FD adversary, Frequency Hopping (FH) fails. We then propose a fast-forward cooperative relaying scheme, wherein the victim node hops to the frequency band of a nearby FD helper node that fast-forwards the victims symbol along with its symbol. At the same time, the victim and the helper cooperatively pour some fraction of their power on the jammed band to engage the adversary. Due to fast-fading channel conditions, the victim and the helper use amplitude based non-coherent signalling referred to as Non-Coherent Fast-Forward Full-Duplex (NC-F2FD) relaying. To minimize the error-rate of this strategy, we jointly design the constellations at the helper node and the victim node by formulating an optimization problem. Using non-trivial results, we first analyse the objective function and then, based on the analytical results, propose a low-complexity algorithm to synthesize the fast-forwarded constellations. Through simulations, we show that the error performance of the victim improves after employing our countermeasure.
In this work, we derive optimal transmission policies in an energy harvesting status update system. The system monitors a stochastic process which can be either in a normal or in an alarm state of operation. We capture the freshness of status updates for each state of the stochastic process by introducing two Age of Information (AoI) variables and extend the definition of AoI to account for the state changes of the stochastic process. We formulate the problem at hand as a Markov Decision Process which, under the assumption that the demand for status updates is higher when the stochastic process is in the alarm state, utilizes a transition cost function that applies linear and non-linear penalties based on AoI and the state of the stochastic process. Finally, we evaluate numerically the derived policies and illustrate their effectiveness for reserving energy in anticipation of future alarm states.