We study the information freshness under three different source aware packet management policies in a status update system consisting of two independent sources and one server. The packets of each source are generated according to the Poisson process and the packets are served according to an exponentially distributed service time. We derive the average age of information (AoI) of each source using the stochastic hybrid systems (SHS) technique for each packet management policy. In Policy 1, the queue can contain at most two waiting packets at the same time (in addition to the packet under service), one packet of source 1 and one packet of source 2. When the server is busy at an arrival of a packet, the possible packet of the same source waiting in the queue (hence, source-aware) is replaced by the arrived fresh packet. In Policy 2, the system (i.e., the waiting queue and the server) can contain at most two packets, one from each source. When the server is busy at an arrival of a packet, the possible packet of the same source in the system is replaced by the fresh packet. Policy 3 is similar to Policy 2 but it does not permit preemption in service, i.e., while a packet is under service all new arrivals from the same source are blocked and cleared. Numerical results are provided to assess the fairness between sources and the sum average AoI of the proposed policies.
In this paper, we consider performing packet managements in discrete time status updating system, focusing on determining the stationary AoI-distribution of the system. Firstly, let the queue model be Ber/G/1/1, we obtain the AoI-distribution by introducing a two-dimensional AoI-stochastic process and solving its steady state, which describes the random evolutions of AoI and age of packet in system simultaneously. In this case, actually we analyze a more general queue called probabilistic preemption Ber/G/1/1, where the packet service is allowed to be preempted with certain probabilities. As a…
This paper investigates the tradeoff between the average age of information (AoI) and the transmission cost for networks with stochastic packet arrival and random erasure channel. Specifically, we model the resource-constrained AoI minimization problem as a constrained Markov decision process (CMDP) and propose a low-complexity single threshold packet scheduling policy for it. The key advantage of the proposed policy is its tractability and convenience for implementation. The AoI distribution and long-term average transmission cost of the proposed policy are derived as closed-form functions of…
We consider a status update system consisting of two independent sources and one server in which packets of each source are generated according to the Poisson process and packets are served according to an exponentially distributed service time. We derive the moment generating function (MGF) of the age of information (AoI) for each source in the system by using the stochastic hybrid systems (SHS) under two existing source-aware packet management policies which we term self-preemptive and non-preemptive policies. In the both policies, the system (i.e., the waiting queue and the server) can cont…
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…
We investigate the age-of-information (AoI) in the context of random access networks, in which transmitters need to send a sequence of information packets to intended receivers over shared spectrum. We establish an analytical framework that accounts for the key features of a wireless system, including the fading, path loss, network topology, as well as the spatial interactions amongst the queues. A closed-form expression is derived to quantify the network average AoI and its accuracy is verified via simulations. Our analysis unveils several unconventional behaviors of AoI in such a setting. Fo…
We consider a multi-source status update system in which status updates are transmitted as packets containing the measured value of the monitored process and a time stamp representing the time when the sample was generated. The packets of each source are generated according to the Poisson process and the packets are served according to an exponentially distributed service time. We assume that the received status update packets needs further processing before being used (hence, computation-intensive). This is mathematically modeled by introducing an additional server at the sink node. The sink …
We consider a multi-source status update system, where each source generates status update packets according to a Poisson process which are then served according to a generally distributed service time. For this multi-source M/G/1/1 queueing model, we introduce a source-aware preemptive packet management policy and derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI of each source. According to the policy, an arriving fresh packet preempts the possible packet of the same source in the system. Furthermore, we derive the MGFs of the AoI and peak AoI for the…
This paper investigates the average age of information (AoI) minimization in status update systems in which the update packets are transmitted with fixed rate. It is assumed that the source avoids queue-induced delay by generating and sending a new status update packet in each time slot. Assuming that the transmit power can be adapted based on the number of successive NACKs (negative acknowledgements) received, a closed-form expression for the average AoI is derived considering transmissions over block fading channel models. An optimization problem for minimizing the average AoI under average …
We consider a wireless communication network with an adaptive scheme to select the number of packets to be admitted and encoded for each transmission, and characterize the information timeliness. For a network of erasure channels and discrete time, we provide closed form expressions for the Average and Peak Age of Information (AoI) as functions of admission control and adaptive coding parameters, the feedback delay, and the maximum feasible end-to-end rate that depends on channel conditions and network topology. These new results guide the system design for robust improvements of the AoI when …
We investigate the age-of-information (AoI) in the context of random access networks, in which transmitters need to send a sequence of information packets to the intended receivers over a shared spectrum. Due to interference, the dynamics at the link pairs will interact with each other over both space and time, and the effects of these spatiotemporal interactions on the AoI are not well understood. In this paper, we straddle queueing theory and stochastic geometry to establish an analytical framework, that accounts for the interplay between the temporal traffic attributes and spatial network t…
In this paper, we explore the potential of server waiting before packet transmission in improving the Age of Information (AoI) in status update systems. We consider a non-preemptive queue with Poisson arrivals and independent general service distribution and we incorporate waiting before serving in two packet management schemes: M/GI/1/1 and M/GI/1/$2^*$. In M/GI/1/1 scheme, the server waits for a deterministic time immediately after a packet enters the server. In M/GI/1/$2^*$ scheme, depending on idle or busy system state, the server waits for a deterministic time before starting service of t…
In this paper, we consider a point-to-point wireless communication system. The source monitors a physical process and generates status update packets according to a Poisson process. The packets are transmitted to the destination by using finite blocklength coding to update the status (e.g., temperature, speed, position) of the monitored process. In some applications, such as real-time monitoring and tracking, the timeliness of the status updates is critical since the users are interested in the latest condition of the process. The timeliness of the status updates can be reflected by a recently…
In this letter, we investigate the impact of channel memory on the average age of information (AoI) for networks with various packet arrival models under first-come-first-served (FCFS) and preemptive last-generated-first-served (pLGFS) policies over Gilbert-Elliott (GE) erasure channel. For networks with Bernoulli arrival model, we first derive the average AoI under the pLGFS queuing policy, and then characterize the AoI gap between the FCFS and pLGFS policies. For networks with Bernoulli arrival and generate-at-will arrival models, the AoI performances under the FCFS and pLGFS policies are de…
In this paper, we analyze the non-linear age of information (AoI) performance in a point-to-point short packet communication system, where a transmitter generates packets based on status updates and transmits the packets to a receiver. Specifically, we investigate three packet management strategies, namely, the non-preemption with no buffer strategy, the non-preemption with one buffer strategy, and the preemption strategy. To characterize the level of the receiver's dissatisfaction on outdated data, we adopt a generalized α-βAoI penalty function into the analysis and derive closed-form express…
Age-of-information (AoI) is a metric quantifying information freshness at the receiver. It captures the delay together with packet loss and packet generation rate. However, the existing literature focuses on average or peak AoI and neglects the complete distribution. In this work, we consider a N-hop network with time-invariant packet loss probabilities on each link. We derive closed form equations for the probability mass function of AoI. We verify our findings with simulations. Our results show that the performance indicators considered in the literature such as average or peak AoI may give …
Age of information (AoI) is an effective performance metric measuring the freshness of information and is popular for applications involving status update. Most of the existing works have adopted average AoI as the metric, which cannot provide strict performance guarantees. In this work, the outage probability of the peak AoI exceeding a given threshold is analyzed in a multi-source system under round robin scheduling. Two queueing disciplines are considered, namely the first-come-first-serve (FCFS) queue and the single packet queue. For FCFS, upper and lower bounds on the outage probability a…
Timeliness is an emerging requirement for many Internet of Things (IoT) applications. In IoT networks, where a large-number of nodes are distributed, severe interference may incur during the transmission phase which causes age of information (AoI) degradation. It is therefore important to study the performance limit of AoI as well as how to achieve such limit. In this paper, we aim to optimize the AoI in random access Poisson networks. By taking into account the spatio-temporal interactions amongst the transmitters, an expression of the peak AoI is derived, based on explicit expressions of the…
This paper investigates the information freshness of two-way relay networks (TWRN) operated with physical-layer network coding (PNC). Information freshness is quantified by age of information (AoI), defined as the time elapsed since the generation time of the latest received information update. PNC reduces communication latency of TWRNs by turning superimposed electromagnetic waves into network-coded messages so that end users can send update packets to each other via the relay more frequently. Although sending update packets more frequently is potential to reduce AoI, how to deal with packet …
We investigate the age of information (AoI) of a relay-assisted cooperative communication system, where a source node sends status update packets to the destination node as timely as possible with the aid of a relay node. For time-slotted systems without relaying, prior works have shown that the source should generate and send a new packet to the destination every time slot to minimize the average AoI, regardless of whether the destination has successfully decoded the packet in the previous slot. However, when a dedicated relay is involved, whether the relay can improve the AoI performance req…
In this work, we consider the problem of jointly minimizing the average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information (AoI) constraints. Errors in the transmission may occur and a scheduling policy has to decide if the users sample a new packet or attempt for retransmission of the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost on the system. We formulate a stochastic optimization problem with the average cost in…
In this paper, we consider N information streams sharing a common service facility. The streams are supposed to have different priorities based on their sensitivity. A higher priority stream will always preempt the service of a lower priority packet. By leveraging the notion of Stochastic Hybrid Systems (SHS), we investigate the Age of Information (AoI) in the case where each stream has its own waiting room; when preempted by a higher priority stream, the packet is stored in the waiting room for future resume. Interestingly, it will be shown that a "no waiting room" scenario, and consequently …
Freshness of status update packets is essential for enabling services where a destination needs the most recent measurements of various sensors. In this paper, we study the information freshness of single-server multi-source queueing models under a first-come first-served (FCFS) serving policy. In the considered model, each source independently generates status update packets according to a Poisson process. The information freshness of the status updates of each source is evaluated by the average age of information (AoI). We derive an exact expression for the average AoI for the case with expo…
We study the probability distribution of age of information (AoI) in arbitrary networks with memoryless service times. A source node generates packets following a Poisson process, and then the packets are forwarded across the network in such a way that newer updates preempt older ones. This model is equivalent to gossip networks that was recently studied by Yates, and for which he obtained a recursive formula allowing the computation for the average AoI. In this paper, we obtain a very simple characterization of the stationary distribution of AoI at every node in the network. This allows for t…
In an Internet-of-Things system where status data are collected from sensors and actuators for time-critical applications, the freshness of data is vital and can be quantified by the recently proposed age-of-information (AoI) metric. In this paper, we first consider a general scenario where multiple terminals share a common channel to transmit or receive randomly generated status packets. The optimal scheduling problem to minimize AoI is formulated as a restless multi-armed bandit problem. To solve the problem efficiently, we derive the Whittle's index in closed-form and establish the indexabi…
Age of Information (AoI), which measures the time elapsed since the generation of the last received packet at the destination, is a new metric for real-time status update tracking applications. In this paper, we consider a status-update system in which a source node samples updates and sends them to an edge server over a delay channel. The received updates are processed by the server with an infinite buffer and then delivered to a destination. The channel can send only one update at a time, and the server can process one at a time as well. The source node applies generate-at-will model accordi…
Towards Autonomous Driving with Short-Packet Rate Splitting: Age of Information Analysis and Optimization
College of Information Science and Technology, Jinan University（暨南大学信息科学技术学院）；School of Computer Science and Engineering, Northeastern University（东北大学计算机科学与工程学院）；College of Cyber Security, Jinan University（暨南大学网络空间安全学院）；Department of Informatics and Telecommunications, University of Thessaly（色萨利大学信息与电信系）；School of Electronic and Information Engineering, South China University of Technology（华南理工大学电子与信息工程学院）；Key Laboratory of Information Coding and Transmission, Southwest Jiaotong University（西南交通大学信息编码与传输重点实验室）
We study age-agnostic scheduling in a non-preemptive status update system with two sources sending time-stamped information packets at random instances to a common monitor through a single server. The server is equipped with a waiting room holding the freshest packet from each source called "single-buffer per-source queueing". The server is assumed to be work-conserving and when the waiting room has two waiting packets (one from each source), a probabilistic scheduling policy is applied so as to provide Age of Information (AoI) differentiation for the two sources of interest. Assuming Poisson …
In this work, we combine the two notions of timely delivery of information in order to study their interplay; namely, deadline-constrained packet delivery due to latency constraints and freshness of information at the destination. More specifically, we consider a two-user multiple access setup with random access, in which user 1 is a wireless device with a queue and has external bursty traffic which is deadline-constrained, while user 2 monitors a sensor and transmits status updates to the destination. For this simple, yet meaningful setup, we provide analytical expressions for the throughput …
Age-of-information (AoI) is a metric quantifying information freshness at the receiver. Since AoI combines packet generation frequency, packet loss, and delay into a single metric, it has received a lot of research attention as an interface between communication network and application. In this work, we apply AoI to the problem of wireless scheduling for multi-loop networked control systems (NCS), i.e., feedback control loops closed over a shared wireless network. We model the scheduling problem as a Markov decision process (MDP) with AoI as its observable states and derive a relation of contr…
In a typical Internet of Things (IoT) application where a central controller collects status updates from multiple terminals, e.g., sensors and monitors, through a wireless multiaccess uplink, an important problem is how to attain timely status updates autonomously. In this paper, the timeliness of the status is measured by the recently proposed age-of-information (AoI) metric; both the theoretical and practical aspects of the problem are investigated: we aim to obtain a scheduling policy with minimum AoI and, meanwhile, still suitable for decentralized implementation on account of signalling …
An optimal control problem with heterogeneous servers to minimize the average age of information (AoI) is considered. Each server maintains a separate queue, and each packet arriving to the system is randomly routed to one of the servers. Assuming Poisson arrivals and exponentially distributed service times, we first derive an exact expression of the average AoI for two heterogeneous servers. Next, to solve for the optimal average AoI, a close approximation is derived, called the approximate AoI, this is shown to be useful for multi-server systems as well. We show that for the optimal approxim…
We consider the problem of minimizing the time average cost of sampling and transmitting status updates by users over a wireless channel subject to average Age of Information constraints (AoI). Errors in the transmission may occur and the scheduling algorithm has to decide if the users sample a new packet or attempt for retransmission of the packet sampled previously. The cost consists of both sampling and transmission costs. The sampling of a new packet after a failure imposes an additional cost in the system. We formulate a stochastic optimization problem with time average cost in the object…
Information freshness and low latency communication is important to many emerging applications. While Age of Information (AoI) serves as a metric of information freshness, packet delay is a traditional metric of communication latency. We prove that there is a natural tradeoff between the AoI and packet delay. We consider a single server system, in which at most one update packet can be serviced at a time. The system designer controls the order in which the packets get serviced and the service time distribution, with a given service rate. We analyze two tradeoff problems that minimize packet de…
In this paper, the minimization of the weighted sum average age of information (AoI) in a multi-source status update communication system is studied. Multiple independent sources send update packets to a common destination node in a time-slotted manner under the limit of maximum retransmission rounds. Different multiple access schemes, i.e., orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are exploited here over a block-fading multiple access channel (MAC). Constrained Markov decision process (CMDP) problems are formulated to describe the AoI minimization problems co…
We consider a single source-destination pair, where information updates arrive at the source at arbitrary time instants. For each update, its size, i.e. the service time required for complete transmission to the destination, is also arbitrary. At any time, age of information (AoI) is equal to the difference between the current time, and the arrival time of the latest update (at the source) that has been completely transmitted (to the destination). AoI quantifies the staleness of the update (information) at the destination. The goal is to find a causal scheduling policy that minimizes the time …
This paper is motivated by emerging edge computing applications in which generated data are pre-processed at the source and then transmitted to an edge server. In such a scenario, there is typically a tradeoff between the amount of pre-processing and the amount of data to be transmitted. We model such a system by considering two non-preemptive queues in tandem whose service times are independent over time but the transmission service time is dependent on the computation service time in mean value. The first queue is in M/GI/1/1 form with a single server, memoryless exponential arrivals, genera…
We consider a status updating system where having timely knowledge about the information source at the destination (monitor) is of utmost importance. By utilizing the age of information (AoI) metric, the freshness of status update over an erasure channel is investigated. Due to the erasure nature of the update transmission, an error-free feedback channel from the monitor to the source is necessary for reducing AoI. Each status update contains $K$ packets which can be sent through the channel one at a time. At each channel use, one status update is available from the information source. Dependi…
The notion of age-of-information (AoI) is investigated in the context of large-scale wireless networks, in which transmitters need to send a sequence of information packets, which are generated as independent Bernoulli processes, to their intended receivers over a shared spectrum. Due to interference, the rate of packet depletion at any given node is entangled with both the spatial configurations, which determine the path loss, and temporal dynamics, which influence the active states, of the other transmitters, resulting in the queues to interact with each other in both space and time over the…
Edge computing applications typically require generated data to be preprocessed at the source and then transmitted to an edge server. In such cases, transmission time and preprocessing time are coupled, yielding a tradeoff between them to achieve the targeted objective. This paper presents analysis of such a system with the objective of optimizing freshness of received data at the edge server. We model this system as two queues in tandem whose service times are independent over time but the transmission service time is monotonically dependent on the computation service time in mean value. This…
Age of information (AoI) is a recently proposed metric for measuring information freshness. AoI measures the time that elapsed since the last received update was generated. We consider the problem of minimizing average and peak AoI in a wireless networks, consisting of a set of source-destination links, under general interference constraints. When fresh information is always available for transmission, we show that a stationary scheduling policy is peak age optimal. We also prove that this policy achieves average age that is within a factor of two of the optimal average age. In the case where …
Device-to-device (D2D) links scheduling for avoiding excessive interference is critical to the success of wireless D2D communications. Most of the traditional scheduling schemes only consider the maximum throughput or fairness of the system and do not consider the freshness of information. In this paper, we propose a novel D2D links scheduling scheme to optimize an age of information (AoI) and throughput jointly scheduling problem when D2D links transmit packets under the last-come-first-serve policy with packet-replacement (LCFS-PR). It is motivated by the fact that the maximum throughput sch…
In this paper, we analyze the average age of information (AoI) and the average peak AoI (PAoI) of a multiuser mobile edge computing (MEC) system where a base station (BS) generates and transmits computation-intensive packets to user equipments (UEs). In this MEC system, we focus on three computing schemes: (i) The local computing scheme where all computational tasks are computed by the local server at the UE, (ii) The edge computing scheme where all computational tasks are computed by the edge server at the BS, and (iii) The partial computing scheme where computational tasks are partially allo…
