The Internet of Things (IoT) has emerged as one of the key features of the next-generation wireless networks, where timely delivery of status update packets is essential for many real-time IoT applications. Age of Information (AoI) is a new metric to measure the freshness of update. The reduction of the violation probability that AoI of status updates exceeds a given age constraint is of great significance for guaranteeing the information freshness in IoT systems. By modeling the IoT networks as M/M/1 and M/D/1 queuing systems, this work focuses on characterizing the violation probability of peak AoI and AoI in IoT systems, where a sensor delivers updates to a monitor under M/M/1 and M/D/1 queues with first-come-first-served policy. From a time-domain perspective, we explore the correlation between interdeparture time and system time, by which the closed-form expressions of peak AoI distribution and the violation probability for any AoI constraint are derived. The obtained results induce accurate characterizations for probability distribution functions of peak AoI and AoI. Consequently, accurate characterizations of average AoI and the variance of AoI are obtained. Then, for peak AoI and AoI, the optimal generation rate of the status update that induces the minimal violation probability is also found. The numerical results show that the optimal update rate can significantly reduce the AoI violation probability for a wide range of AoI constraints. The theoretical findings and predictions are verified by numerical simulation results as well as provide guidance for the design of IoT networks.

We consider an Internet-of-Things (IoT) based sensing system, in which an energy harvesting powered sensor observes the phenomenon of interest and transmits its observations to a remote monitor through a Gaussian channel. Based on the received signals, the monitor makes estimations of source signals with some distortion requirement. We measure the timeliness of the recovered signals using age of information (AoI), which could be reduced by transmitting observations more frequently (i.e., with shorter intervals). We evaluate the recovery distortion with the mean-squared error (MSE) metric, which would be reduced if a larger transmit power and a larger source coding rate were used. Since the energy harvested by the sensor is quite limited, however, the frequency and power of transmissions cannot be increased at the same time. Thus, we shall investigate the timeliness-distortion trade-off of the system by minimizing the average weighted-sum AoI and distortion over all possible transmit powers and transmission intervals. First, we explicitly present the optimal transmit powers for the performance-limit achieving save-and-transmit policy and the easy-implementing fixed power transmission policy. Second, we investigate the offline optimization of the system and propose a backward water-filling based power allocation scheme, as well as a genetic based joint transmission scheduling and power control algorithm. Third, we formulate the online power control as an Markov Decision Process (MDP) and solve the problem with an iterative algorithm, which closely approaches the trade-off limit of the system. We show that the optimal transmit power is a monotonic and bi-valued function of current AoI and distortion. Finally, we present our results via simulations and extend the results on the save-and-transmit policy to fading sensing systems.

We consider an Internet of Things (IoT) system in which a sensor observes a phenomena of interest with exponentially distributed intervals and delivers the updates to a monitor with random service times. At the monitor, the received updates are used to make decisions with deterministic or random intervals. For this system, we investigate the freshness of the received updates at decision epochs using the age upon decisions (AuD) metric. With the First-come-First-served (FCFS) policy, theoretical results show that 1) when the decisions are made with exponentially distributed intervals, the average AuD of the system is smaller when the service time (e.g., transmission time) is uniformly distributed than when it is exponentially distributed, and would be the smallest if it is deterministic; 2)when the decisions are made periodically, the average AuD of the system is larger than, and decreases with decision rate to, the average AuD of the corresponding system with Poisson decision intervals; 3)the probability of missing to use a received update for any decisions is decreasing with the decision rate, and is the smallest if the service time is deterministic. When the Last-come-First-served (LCFS) policy with preemption is used, we observe that systems with Poisson service processes perform the best while systems with periodic service processes perform the worst. For IoT based monitoring systems, therefore, it is suggested to use deterministic monitoring schemes, deterministic transmitting schemes, and Poisson decision schemes, so that the received updates are as fresh as possible at the time they are used to make decisions.

Fog computing is attracting more and more attentions in next generation wireless communication systems. In this paper, we consider such a mobile edge scenario where a fog node and a mobile user exchange their data in a two-way manner and only the fog node has a constant power supply. In particular, the fog node performs energy transfer when it is not transmitting information and the mobile user has an energy harvesting capability. For this scenario, we investigate the timeliness of the two-way data exchange between the fog node and the mobile user in terms of age of information (AoI) and derive closed form average AoI for both directions, as well as the achievable data rate of the mobile user. We also discuss the achievable tradeoff on the average downlink/uplink AoIs and the achievable tradeoff on downlink/uplink data rates, which explicitly present the performance limit of the system in terms of timeliness and efficiency.

In this paper, we consider a two-way relay with multirelays. We first review the joint decoding (JD), decoding by parts (DP), bit-level exclusive-or (XOR), and superposition coding (SC) schemes for the two-way decode-and-forward relay (TWDR), and then propose a new TWDR selection scheme for the two mentioned coding methods. In particular, we focus on the outage performance analysis of the relay selection strategy using the aforementioned coding and decoding methods. Based on an approximate analysis of the outage performance in the high signal-to-noise ratio, we present the diversity-multiplexing tradeoff for the considered decoding and coding schemes. Moreover, we present an optimal power allocation for relays with the SC mechanism. Our simulation results show that our proposed relay selection strategy is outage optimal for all the coding and decoding methods mentioned in this paper. Our results also show that the outage performance under the JD-Xor and JD-SC schemes is more competitive for the case in which the channel statistical characteristics satisfy γ̅ _α σ _kα ² ≈ γ̅ _b σ _kb ² (γ̅i = P _i /N ₀ , i ∈ {α, b}, where a and b denote two sources exchanging information with each other, Pi is the average transmitting power from the i source, N ₀ is the variance of additive white Gaussian noise obtained by the relay k, and σ _ki ² is the variance of the Rayleigh fading channel between k and i). When γ̅ _α σ _kα ² ≫ γ̅ _b σ _kb ² or γ̅ _α σ _kα ² ≪ γ̅ _α σ _kα ² , the outage performance using DP-Xor or DP-SC mechanisms is much better.