The continuous development of modern communication and computation gives rise to a large number of applications based on Internet of Things (IoT) technology. Considering the diverse uses and various service requirements, the information freshness of IoT data, which is measured by Age of Information (AoI), is crucial for latency-sensitive IoT applications, such as industrial automation and intelligent transportation, because outdated information can lead to delayed and inaccurate response. Under the assumptions of bufferless and no service preemption, in this article we consider the scenario where multiple sources transmit packets through a common server and analyze the discrete AoI corresponding to each source. To facilitate the description of random AoI evolutions, we assign priorities to the sources and assume that when multiple sources generate new packets in one time slot, the packet with the highest priority is selected and served. We obtain the explicit expression of average AoI and calculate the general formula in several cases, where the relationships between average AoI and other system parameters are investigated detailly. Also, under a constraint imposed on average service time over all the sources, we consider minimizing average AoI of one source by finding the optimal service rates for the packet from each source. In particular, for minimizing one source’s average AoI in two-source systems, the pair of optimal service rates are determined completely. The results show that if the probability that one source’s packet obtains the service is large enough, then to minimize average AoI of this source, maximizing the service rate for its own packets is not the optimal. Some discussions on source priorities are given and finally we provide the numerical simulations for the obtained results.

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is $Ber/Geo/1/2^{*}/\eta$, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability $\eta$. Instead of considering the system’s AoI separately, we use a three-dimensional state vector $(n,m,l)$ to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting $\eta =0$. When $\eta$ is set to 1, the mean of the AoI of the system with a $Ber/Geo/1/2^{*}$ queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the $Ber/Geo/1/c$ queue and the average continuous AoI with the $M/M/1/c$ queue. For each of two extreme cases where $\eta =0$ and $\eta =1$, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability $\eta$, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.

The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. Assuming the queue used in system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in buffer can be preempted by fresher packet with probability η. Instead of considering system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real time changes of the AoI, the age of packet in server, and the age of packet waiting in buffer. We give the explicit expression of system’s average AoI, and show that the average AoI of system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of AoI of system having Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between average discrete AoI with Ber/Geo/1/c queue and the average continuous AoI with M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between average AoI and the packet preemption probability η, as well as AoI’s distribution curves in two extreme cases are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of wireless sensor network, where the packet in buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper we give much more explanations showing that how the results about continuous AoI is derived by analyzing the corresponding discrete time system, and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose our idea to analyze system’s AoI when the service time distribution is relaxed to be arbitrary.

Low-latency information transmission is required in 5G communication networks, where the cache is commonly used to speed up the data access. Meanwhile, a large number of IoT applications need real-time information exchange, resulting in the information freshness more important. In this article, under the discrete-time model, we consider the average age of all files in a cached-files-updating system. To keep the cached files fresh, in each time slot the server refreshes files with certain probabilities. The age of one file or its age of information (AoI) is defined as the time the file stays in cache since it was sent to cache last time. Assume that each file in cache has its own request popularity, we determine the probability distribution of the popularity-weighted average file age. For the random age of single file, both the mean and its probability distribution can be obtained by establishing a simple Markov chain. Following the same line of thinking, we show that an $N$ -dimensional stochastic process can be constituted to characterize the changes of $N$ file ages simultaneously. By solving the steady state of the resulting process, we obtain the explicit expression of stationary probability for an arbitrary state vector. Then, the distribution of the popularity-weighted average file age can be found by mergering a proper set of stationary probabilities, which gives the complete description of the average age. We also provide the numerical results of the distribution for some simple cases. The age-distribution can be utilized to compute certain stochastic performance indices, such as the AoI violation probability of some status updating systems.

We consider the scenario in which the source sends status updates, or packets, to the receiver through an infinite capacity transmitter, where the transmitted packets are subject to potential illegal eavesdropping. Time is discretized into identical time slots. In recent years, the age of information (AoI) metric, which was defined as the time has elapsed since the generation instant of the latest received packet, has been widely applied to characterize the freshness of obtained packets. Due to the presence of eavesdroppers, some packets may be eavesdropped during their transmissions, causing information leakages. To assess an infinite-capacity system’s performance of securely transmitting status updates, in this paper, we define an AoI-related metric called the freshness advantage of the legitimate receiver, F, to be average instantaneous gap between eavesdropper’s and legitimate receiver’s AoI. For arbitrarily distributed packet interarrival times, and assuming that in each time slot with probabilities ${\gamma }_d$, ${\gamma }_E$, the transmitted packet is received by the legitimate receiver and the eavesdropper, we derive the explicit formula of F. The concise expression shows that F is fully determined by the average interarrival time and the ratio of ${\gamma }_d$ to ${\gamma }_E$. For special cases where the interarrival time follows geometric distributions, we first determine the explicit distribution of instantaneous AoI gap. Then, given ${\gamma }_d$ and ${\gamma }_E$, we derive the optimal packet generation rate $p^{\ast }$ that minimizes the combined performance Q, which is constructed as the average AoI minus the freshness advantage F. When imposing timeliness and security constraints at the same time, the feasible regions of p and ${\gamma }_d$ such that both two required performances can be satisfied are depicted and discussed. Finally, we investigate the impacts of different parameters on F and show the tradeoffs between timeliness performance and security performance through numerical simulations.

We consider that the source sends packets to the receiver through a Ber/Geo/1/2 queue modeled status updating system, where the transmitted packets are subject to potential eavesdropping. Time is discretized into identical time slots. This paper studies the tradeoffs between the information freshness and transmission security of a system, where freshness is characterized by the age of information (AoI) metric and transmission security is represented by the proportion of obtained insecure packets over a long period of time. We assume that in a time slot, the source generates a new packet with probability p, and a packet arrives at the receiver with probability ${\gamma }_d$. With probability ${\gamma }_E$, a transmitted packet is eavesdropped. At the receiver, AoI is defined as the elapsed time since the generation instant of the latest obtained packet. A packet is defined to be insecure if it is obtained by the eavesdropper earlier than the receiver. To control the proportion of insecure packets obtained in the receiver, we propose using the probabilistic deletion/retaining scheme. More specifically, when a packet is eavesdropped before arriving at the receiver, this packet is deleted with probability $\delta$ or retained with probability $1-\delta$. Under this transmission policy, we derive the system’s average AoI which we call the average $\delta -$secure AoI, and investigate its relations with the insecure packet proportion, which is denoted as $\eta \left(\delta \right)$. The obtained formulas are then calculated in three special cases, including ${\gamma }_E=0$, ${\gamma }_E=1$, and $\delta =1$. We explain that these cases correspond to the average AoI of a basic status updating system with Ber/Geo/1/2 queue, packet with random geometric deadline in service process, and average age of secure information (AoSI), respectively. Numerical simulations of obtained results are provided. In particular, the tradeoffs between average $\delta -$secure AoI and $\eta \left(\delta \right)$ are analyzed in detail. We demonstrate that depending on the value of the eavesdropping probability ${\gamma }_E$, average $\delta -$secure AoI varies in different trends with $\eta \left(\delta \right)$, and in most cases the average $\delta -$secure AoI and $\eta \left(\delta \right)$ can be minimized simultaneously.