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 average of AoI, where the possible decisions at any time are i) whether to preempt the update under transmission upon arrival of a new update, and ii) if no update is under transmission, then choose which update to transmit (among the available updates).
In this paper, we propose a causal policy called SRPT$^+$ that at each time, i) preempts the update under transmission if a new update arrives with a smaller size, and ii) if no update is under transmission, then begins to transmit the update for which the ratio of the reduction in AoI upon complete transmission (if not preempted in future) and the remaining size, is maximum. We characterize the performance of SRPT$^+$ using the metric called the competitive ratio, i.e. the ratio of the average AoI of causal policy and the average AoI of an optimal offline policy (that knows the entire input in advance), maximized over all possible inputs. We show that the competitive ratio of SRPT$^+$ is at most $4$. Further, we propose a simpler policy called SRPT$^L$, that i) preempts the update under transmission if a new update arrives with a smaller size, and ii) if no update is under transmission, then begins to transmit the update with the latest arrival time. We show that the competitive ratio of SRPT$^L$ is at most $29$.
The problem of online packet scheduling to minimize the required conventional grid energy for transmitting a fixed number of packets given a common deadline is considered. The total number of packets arriving within the deadline is known, but the packet arrival times are unknown, and can be arbitrary. The proposed algorithm tries to finish the transmission of each packet assuming all future packets are going to arrive at equal time intervals within the left-over time. The proposed online algorithm is shown to have competitive ratio that is logarithmic in the number of packet arrivals. The hybr…
We consider a time slotted communication system consisting of a base station (BS) and a user. At each time slot an update packet arrives at the BS with probability $p$, and the BS successfully transmits the update packet with probability $q$ over an erasure channel. We assume that the BS has a unit size buffer where it can store an update packet upon paying a storage cost $c$. There is a trade-off between the age of information and the storage cost. We formulate this trade-off as a Markov decision process and find an optimal switching type storage policy.
This paper deals with the delay-throughput analysis of a single-hop wireless network with $n$ transmitter/receiver pairs. All channels are assumed to be block Rayleigh fading with shadowing, described by parameters $(α,\varpi)$, where $α$ denotes the probability of shadowing and $\varpi$ represents the average cross-link gains. The analysis relies on the distributed on-off power allocation strategy (i.e., links with a direct channel gain above a certain threshold transmit at full power and the rest remain silent) for the deterministic and stochastic packet arrival processes. It is also assumed…
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 serv…
A multiple access system with bursty data arrivals to the terminals is considered. The users are frame-synchronized, with variable sized packets independently arriving in each slot at every transmitter. Each packet needs to be delivered to a common receiver within a certain number of slots specified by a maximum delay constraint. The key assumption is that the terminals know only their own packet arrival process, i.e. the arrivals at the rest of the terminals are unknown to each transmitter, except for their statistics. For this interesting distributed multiple access model, we design novel on…
We consider a node-monitor pair, where updates are generated stochastically (according to a known distribution) at the node that it wishes to send to the monitor. The node is assumed to incur a fixed cost for each transmission, and the objective of the node is to find the update instants so as to minimize a linear combination of AoI of information and average transmission cost. First, we consider the Poisson arrivals case, where updates have an exponential inter-arrival time for which we derive an explicit optimal online policy. Next, for arbitrary distributions of inter-arrival time of update…
We consider the optimal packet scheduling problem in a single-user energy harvesting wireless communication system. In this system, both the data packets and the harvested energy are modeled to arrive at the source node randomly. Our goal is to adaptively change the transmission rate according to the traffic load and available energy, such that the time by which all packets are delivered is minimized. Under a deterministic system setting, we assume that the energy harvesting times and harvested energy amounts are known before the transmission starts. For the data traffic arrivals, we consider …
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…
In this paper, we investigate scheduling policies that minimize the age of information in single-hop queueing systems. We propose a Last-Generated, First-Serve (LGFS) scheduling policy, in which the packet with the earliest generation time is processed with the highest priority. If the service times are i.i.d. exponentially distributed, the preemptive LGFS policy is proven to be age-optimal in a stochastic ordering sense. If the service times are i.i.d. and satisfy a New-Better-than-Used (NBU) distributional property, the non-preemptive LGFS policy is shown to be within a constant gap from the…
We consider the resource allocation problem in cooperative wireless networks wherein nodes perform mutual information accumulation. We consider a unicast setting and arbitrary arrival processes at the source node. Source arrivals can be broken down into numerous packets to better exploit the spatial and temporal diversity of the routes available in the network. We devise a linear-program-based algorithm which allocates network resource to meet a certain transmission objective. Given a network, a source with multiple arriving packets and a destination, our algorithm generates a policy that regu…
This paper describes a low-complexity approach for reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process. Assuming that the rate vector of this Poisson process is sparse or approximately sparse, the goal is to maintain a compressed summary of the process sample paths using a small number of counters, such that at any time it is possible to reconstruct both the total number of packets in each flow and the underlying rate vector. We show that these tasks can be accomp…
We consider a setting in which a sender wishes to broadcast a block of K data packets to a set of wireless receivers, where each of the receivers has a subset of the data packets already available to it (e.g., from prior transmissions) and wants the rest of the packets. Our goal is to find a linear network coding scheme that yields the minimum average packet decoding delay (APDD), i.e., the average time it takes for a receiver to decode a data packet. Our contributions can be summarized as follows. First, we prove that this problem is NP-hard by presenting a reduction from the hypergraph color…
The offline problem of transmission completion time minimization for an energy harvesting transmitter under fading is extended to allow packet arrivals during transmission. A method for computing an optimal power and rate allocation (i.e., an optimal offline schedule) is developed and studied.
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…
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 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…
We consider a wireless network with a base station serving multiple traffic streams to different destinations. Packets from each stream arrive to the base station according to a stochastic process and are enqueued in a separate (per stream) queue. The queueing discipline controls which packet within each queue is available for transmission. The base station decides, at every time t, which stream to serve to the corresponding destination. The goal of scheduling decisions is to keep the information at the destinations fresh. Information freshness is captured by the Age of Information (AoI) metri…
Age of information is a new network performance metric that captures the freshness of information at end-users. This paper studies the age of information from a scheduling perspective. To that end, we consider a wireless broadcast network where a base-station (BS) is updating many users on random information arrivals under a transmission capacity constraint. For the offline case when the arrival statistics are known to the BS, we develop a structural MDP scheduling algorithm and an index scheduling algorithm, leveraging Markov decision process (MDP) techniques and the Whittle's methodology for…
In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. This work proposes distributed age-efficient transmission policies for random access channels with $M$ transmitters. In the first part of this work, we analyze the age performance of stationary randomized policies by relating the problem of finding age to the absorption time of a related Markov chain. In the second part of this work, we propose the notion of \emph{age-gain} of a packet to quantify how much the packet will reduce the instantaneous age of information…
In this paper, we analyze binary-tree algorithms in a setup in which the receiver can perform multi-packet reception (MPR) of up to and including K packets simultaneously. The analysis addresses both traffic-independent performance as well as performance under Poisson arrivals. For the former case, we show that the throughput, when normalized with respect to the assumed linear increase in resources required to achieve K-MPR capability, tends to the same value that holds for the single-reception setup. However, when coupled with Poisson arrivals in the windowed access scheme, the normalized thr…
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…
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, a network comprising wireless devices equipped with buffers transmitting deadline-constrained data packets over a slotted-ALOHA random-access channel is studied. Although communication protocols facilitating retransmissions increase reliability, packet transmission from the queue experiences delays and thus, packets with time constraints might be dropped before being successfully transmitted, while at the same time causing the queue size of the buffer to increase. Towards understanding the trade-off between reliability and delays that might lead to packet drops due to the deadli…
Some Machine-to-Machine (M2M) communication links particularly those in a industrial automation plant have stringent latency requirements. In this paper, we study the delay-performance for the M2M uplink from the sensors to a Programmable Logic Controller (PLC) in a industrial automation scenario. The uplink traffic can be broadly classified as either Periodic Update (PU) and Event Driven (ED). The PU arrivals from different sensors are periodic, synchronized by the PLC and need to be processed by a prespecified firm latency deadline. On the other hand, the ED arrivals are random, have low-arr…
In this work, we investigate the design of information-update systems, where incoming update packets are forwarded to a remote destination through multiple servers (each server can be viewed as a wireless channel). One important performance metric of these systems is the age-of-information or simply age, which is defined as the time elapsed since the freshest packet at the destination was generated. Recent studies on information-update systems have shown that the age-of-information can be reduced by intelligently dropping stale packets. However, packet dropping may not be appropriate in many 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…
This paper investigates the problem of energy-efficient packet transmission with arbitrary arrival instants and deadline constraints over a point-to-point Additive White Gaussian Noise (AWGN) channel. This is different from previous work where it is assumed that the packets follow a First-In-First-Out (FIFO) order in that the packets that arrive earlier will have a deadline that is also earlier. We first investigate the necessary and sufficient conditions of the optimal transmission scheduler. We then propose an algorithm which finds the transmission schedule of each packet in the order of the…
This paper studies data aggregation in large-scale regularly deployed Internet of Things (IoT) networks, where devices generate synchronized time-triggered traffic (e.g., measurements or updates). The data granularity, in terms of information content and temporal resolution, is parameterized by the sizes of the generated packets and the duty cycle of packet generation. The generated data packets at the devices are aggregated through static terrestrial gateways. Universal frequency reuse is adopted across all gateways and randomized scheduling is utilized for the IoT devices associated with eac…
This paper analyzes the asymptotic behavior of a multiple-access network comprising a large number of selfish transmitters competing for access to a common wireless communication channel, and having different utility functions for determining their strategies. A necessary and sufficient condition is given for the total number of packet arrivals from selfish transmitters to converge in distribution. The asymptotic packet arrival distribution at Nash equilibrium is shown to be a mixture of a Poisson distribution and finitely many Bernoulli distributions.
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 aim to obtain the optimal delay-power tradeoff and the corresponding optimal scheduling policy for an arbitrary i.i.d. arrival process and adaptive transmissions. The number of backlogged packets at the transmitter is known to a scheduler, who has to determine how many backlogged packets to transmit during each time slot. The power consumption is assumed to be convex in transmission rates. Hence, if the scheduler transmits faster, the delay will be reduced but with higher power consumption. To obtain the optimal delay-power tradeoff and the corresponding optimal policy, we mo…
This paper investigates the Age of Information (AoI) performance of Frame Slotted ALOHA with Reservation and Data slots (FSA-RD). We consider a symmetric multi-access network where each user transmits its randomly generated status updates to an access point in a framed manner. Each frame consists of one reservation slot and several data slots. The reservation slot is made up of some mini-slots. In each reservation slot, users, with a status update packet to transmit, randomly send short reservation packets in one of the mini-slots to contend for data slots of the frame. The data slots are assi…
We consider the optimal online packet scheduling problem in a single-user energy harvesting wireless communication system, where energy is harvested from natural renewable sources, making future energy arrivals instants and amounts random in nature. The most general case of arbitrary energy arrivals is considered where neither the future energy arrival instants or amount, nor their distribution is known. The problem considered is to adaptively change the transmission rate according to the causal energy arrival information, such that the time by which all packets are delivered is minimized. We …
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…
We develop an analytical framework for the perfor- mance comparison of small cell networks operating under static time division duplexing (S-TDD) and dynamic TDD (D-TDD). While in S-TDD downlink/uplink (DL/UL) cell transmissions are synchronized, in D-TDD each cell dynamically allocates resources to the most demanding direction. By leveraging stochastic geom- etry and queuing theory, we derive closed-form expressions for the UL and DL packet throughput, also capturing the impact of random traffic arrivals and packet retransmissions. Through our analysis, which is validated via simulations, we …
In this paper, we study an age of information minimization problem, where multiple flows of update packets are sent over multiple servers to their destinations. Two online scheduling policies are proposed. When the packet generation and arrival times are synchronized across the flows, the proposed policies are shown to be (near) optimal for minimizing any time-dependent, symmetric, and non-decreasing penalty function of the ages of the flows over time in a stochastic ordering sense.
This paper develops a novel approach to obtaining energy-efficient transmission schedules for delay-limited bursty data arrivals under non-ideal circuit power consumption. Assuming a-prior knowledge of packet arrivals, deadlines and channel realizations, we show that the problem can be formulated as a convex program. For both time-invariant and time-varying fading channels, it is revealed that the optimal transmission between any two consecutive channel or data state changing instants, termed epoch, can only take one of the three strategies: (i) no transmission, (ii) transmission with an energ…
We consider an Internet of Things (IoT) system in which a sensor delivers updates to a monitor with exponential service time and first-come-first-served (FCFS) discipline. We investigate the freshness of the received updates and propose a new metric termed as \textit{Age upon Decisions (AuD)}, which is defined as the time elapsed from the generation of each update to the epoch it is used to make decisions (e.g., estimations, inferences, controls). Within this framework, we aim at improving the freshness of updates at decision epochs by scheduling the update arrival process and the decision mak…
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 …
In this work we examine the operation of a node relaying packets from a number of users to a destination node. We assume multi-packet reception capabilities for the relay and the destination node. The relay node can transmit and receive at the same time, so the problem of self interference arises. The relay does not have packets of its own and the traffic at the source nodes is considered saturated. The relay node stores a source packet that it receives successfully in its queue when the transmission to the destination node has failed. We obtain analytical expressions for the characteristics o…
This paper considers the slotted ALOHA protocol in a communication channel shared by N users. It is assumed that the channel has the multiple-packet reception (MPR) capability that allows the correct reception of up to M ($1 \leq M < N$) time-overlapping packets. To evaluate the reliability in the scenario that a packet needs to be transmitted within a strict delivery deadline D ($D \geq 1$) (in unit of slot) since its arrival at the head of queue, we consider the successful delivery probability (SDP) of a packet as performance metric of interest. We derive the optimal transmission probability…
This paper provides proofs of the rate stability, Harris recurrence, and epsilon-optimality of CSMA algorithms where the backoff parameter of each node is based on its backlog. These algorithms require only local information and are easy to implement. The setup is a network of wireless nodes with a fixed conflict graph that identifies pairs of nodes whose simultaneous transmissions conflict. The paper studies two algorithms. The first algorithm schedules transmissions to keep up with given arrival rates of packets. The second algorithm controls the arrivals in addition to the scheduling and at…
Wireless devices need to adapt their transmission power according to the fluctuating wireless channel in order to meet constraints of delay sensitive applications. In this paper, we consider delay sensitivity in the form of strict packet deadlines arriving in a transmission queue. Packets missing the deadline while in the queue are dropped from the system. We aim at minimizing the packet drop rate under average power constraints. We utilize tools from Lyapunov optimization to find an approximate solution by selecting power allocation. We evaluate the performance of the proposed algorithm and s…
We consider a line of terminals which is connected by packet erasure channels and where random linear network coding is carried out at each node prior to transmission. In particular, we address an online approach in which each terminal has local information to be conveyed to the base station at the end of the line and provide a queueing theoretic analysis of this scenario. First, a genie-aided scenario is considered and the average delay and average transmission energy depending on the link erasure probabilities and the Poisson arrival rates at each node are analyzed. We then assume that all n…
Security and privacy are major concerns in modern communication networks. In recent years, the information theory of covert communications, where the very presence of the communication is undetectable to a watchful and determined adversary, has been of great interest. This emerging body of work has focused on additive white Gaussian noise (AWGN), discrete memoryless channels (DMCs), and optical channels. In contrast, our recent work introduced the information-theoretic limits for covert communications over packet channels whose packet timings are governed by a Poisson point process. However, a…
Age of Information (AoI) has proven to be a useful metric in networked systems where timely information updates are of importance. In the literature, minimizing "average age" has received considerable attention. However, various applications pose stricter age requirements on the updates which demand knowledge of the AoI distribution. Furthermore, the analysis of AoI distribution in a multi-hop setting, which is important for the study of Wireless Networked Control Systems (WNCS), has not been addressed before. Toward this end, we study the distribution of AoI in a WNCS with two hops and devise…
Age of information is a new concept that characterizes the freshness of information at end devices. This paper studies the age of information from a scheduling perspective. We consider a wireless broadcast network where a base-station updates many users on stochastic information arrivals. Suppose that only one user can be updated for each time. In this context, we aim at developing a transmission scheduling algorithm for minimizing the long-run average age. To develop a low-complexity transmission scheduling algorithm, we apply the Whittle's framework for restless bandits. We successfully deri…
We consider a wireless broadcast network with a base station sending time-sensitive information to a number of clients through unreliable channels. The Age of Information (AoI), namely the amount of time that elapsed since the most recently delivered packet was generated, captures the freshness of the information. We formulate a discrete-time decision problem to find a transmission scheduling policy that minimizes the expected weighted sum AoI of the clients in the network. We first show that in symmetric networks a Greedy policy, which transmits the packet with highest current age, is optimal…
We consider the problem of in-order packet transmission over a cascade of packet-erasure links with acknowledgment (ACK) signals, interconnected by relays. We treat first the case of transmitting a single packet, in which ACKs are unnecessary, over links with independent identically distributed erasures. For this case, we derive tight upper and lower bounds on the probability of arrive failure within an allowed end-to-end communication delay over a given number of links. When the number of links is commensurate with the allowed delay, we determine the maximal ratio between the two -- coined in…
MIT Lincoln Laboratory（麻省理工学院林肯实验室）；MIT Laboratory for Information and Decision Systems（麻省理工学院信息与决策系统实验室）
We consider a system consisting of a single transmitter/receiver pair and $N$ channels over which they may communicate. Packets randomly arrive to the transmitter's queue and wait to be successfully sent to the receiver. The transmitter may attempt a frame transmission on one channel at a time, where each frame includes a packet if one is in the queue. For each channel, an attempted transmission is successful with an unknown probability. The transmitter's objective is to quickly identify the best channel to minimize the number of packets in the queue over $T$ time slots. To analyze system perf…
We consider a single-hop wireless network with sources transmitting time-sensitive information to the destination over multiple unreliable channels. Packets from each source are generated according to a stochastic process with known statistics and the state of each wireless channel (ON/OFF) varies according to a stochastic process with unknown statistics. The reliability of the wireless channels is to be learned through observation. At every time slot, the learning algorithm selects a single pair (source, channel) and the selected source attempts to transmit its packet via the selected channel…
