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Age-Optimal Multi-Channel-Scheduling under Energy and Tolerance Constraints
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Abstract
We study the optimal scheduling problem where n source nodes attempt to transmit updates over L shared wireless on/off fading channels to optimize their age performance under energy and age-violation tolerance constraints. Specifically, we provide a generic formulation of age-optimization in the form of a constrained Markov Decision Processes (CMDP), and obtain the optimal scheduler as the solution of an associated Linear Programming problem. We investigate the characteristics of the optimal single-user multi-channel scheduler for the important special cases of average-age and violation-rate minimization. This leads to several key insights on the nature of the optimal allocation of the limited energy, where a usual threshold-based policy does not apply and will be useful in guiding scheduler designers. We then investigate the stability region of the optimal scheduler for the multi-user case. We also develop an online scheduler using Lyapunov-drift-minimization methods that do not require the knowledge of channel statistics. Our numerical studies compare the stability region of our online scheduler to the optimal scheduler to reveal that it performs closely with unknown channel statistics.
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In this paper, we study how to take samples at a data source for improving the freshness of received data samples at a remote receiver. We use non-linear functions of the age of information to measure data freshness, and provide a survey of non-linear age functions and their applications. The sampler design problem is studied to optimize these data freshness metrics, even when there is a sampling rate constraint. This sampling problem is formulated as a constrained Markov decision process (MDP) with a possibly uncountable state space. We present a complete characterization of the optimal solution to this MDP: The optimal sampling policy is a deterministic or randomized threshold policy, where the threshold and the randomization probabilities are characterized based on the optimal objective value of the MDP and the sampling rate constraint. The optimal sampling policy can be computed by bisection search, and the curse of dimensionality is circumvented. These age optimality results hold for (i) general data freshness metrics represented by monotonic functions of the age of information, (ii) general service time distributions of the queueing server, (iii) both continuous-time and discrete-time sampling problems, and (iv) sampling problems both with and without the sampling rate constraint. Numerical results suggest that the optimal sampling policies can be much better than zero-wait sampling and the classic uniform sampling.
In this paper, we study the interplay between delay violation probability and average Age-of-Information (AoI) in a two-user wireless multiple access channel with multi-packet reception capability. The users have heterogeneous traffic characteristics: the first has stringent delay constraints, while the second measures a source and transmits status updates in order to keep the AoI low. We show the effect of the sensor sampling rate to the delay violation probability and of the service rate of the first user to the information freshness.
Age of Information (AoI) measures the freshness of the information at a remote location. AoI reflects the time that is elapsed since the generation of the packet by a transmitter. In this paper, we consider a remote monitoring problem (e.g., remote factory) in which a number of sensor nodes are transmitting time sensitive measurements to a remote monitoring site. We consider minimizing a metric that strikes a trade-off between minimizing the sum of the expected AoI of all sensors and minimizing an Ultra Reliable Low Latency Communication (URLLC) term. The URLLC term minimization is represented by ensuring that the probability the AoI of each sensor exceeds a predefined threshold should be at its minimum. Moreover, we assume that sensors require different threshold values and generate different packet sizes. Motivated by the success of machine learning in solving large networking problems at low complexity, we develop a low complexity reinforcement learning based algorithm to solve the proposed formulation. We trained our algorithm using the state-of-the-art actor-critic algorithm over a set of public bandwidth traces. Simulation results show that the proposed algorithm outperforms the considered baselines in terms of minimizing the expected AoI and the threshold violation of each sensor.
We study the task of scheduling in a multi-source system where sources report their time-varying information to a central monitoring station via multiple orthogonal channels. The Age-of-Information of a source is defined as the amount of time elapsed since the latest update from that source was received at the monitoring station. At each time instant, the system pays a cost that is a function of the current Ages-of-Information of the sources. Our goal is to design scheduling policies to minimize this cost.
We draw a novel parallel between our scheduling problem and the minimum mean cost cycle problem in weighted graphs and use this insight to design optimal scheduling policies for a very general class of cost functions. In addition, we compare the performance of our policy with naive greedy policies. We show that while greedy policies can be optimal if the cost function is symmetric with respect to the sources, our policy strictly outperforms greedy policies when the cost function is asymmetric across sources.
Emerging applications rely on wireless broadcast to disseminate time-critical information. For example, vehicular networks may exchange vehicle position and velocity information to enable safety applications. The number of nodes in one-hop communication range in such networks can be very large, leading to congestion and undesirable levels of packet collisions. Earlier work has examined such broadcasting protocols primarily from a MAC perspective and focused on selective aspects such as packet error rate. In this work, we propose a more comprehensive metric, the average system information age, which captures the requirement of such applications to maintain current state information from all other nearby nodes. We show that information age is minimized at an optimal operating point that lies between the extremes of maximum throughput and minimum delay. Further, while age can be minimized by saturating the MAC and setting the CW size to its throughput-optimal value, the same cannot be achieved without changes in existing hardware. Also, via simulations we show that simple contention window size adaptations like increasing or decreasing the window size are unsuitable for reducing age. This motivates our design of an application-layer broadcast rate adaptation algorithm. It uses local decisions at nodes in the network to adapt their messaging rate to keep the system age to a minimum. Our simulations and experiments with 300 ORBIT nodes show that the algorithm effectively adapts the messaging rates and minimizes the system age.
Future generation wireless technologies are expected to serve an increasingly dense and dynamic population of users that generate short bundles of information to be transferred over the shared spectrum. This calls for new distributed and low-overhead Multiple-Access-Control (MAC) strategies to serve such dynamic demands with spectral efficiency characteristics. In this work, we address this need by identifying and developing two fundamentally different MAC paradigms: (i) congestion-based paradigm that estimates the congestion level in the system and adapts to it; and (ii) age-based paradigm that prioritizes demands based on their ages. Despite their apparent differences, we develop policies under each paradigm in a generic multi-channel access scenario that are provably throughput-optimal when they employ any asymptotically-efficient channel encoding/decoding mechanism. We also characterize the stability regions of the two designs, and investigate the conditions under which one design outperforms the other. We perform extensive simulations to validate the theoretical claims and investigate the non-asymptotic performances of our designs.
We introduce a framework and provably-efficient schemes for ‘fresh’ caching at the (front-end) local cache of content that is subject to ‘dynamic’ updates at the (back-end) database. We start by formulating the hard-cache-constrained problem for this setting, which quickly becomes intractable due to the limited cache. To bypass this challenge, we first propose a flexible time-based-eviction model to derive the average system cost function that measures the system’s cost due to the service of aging content in addition to the regular cache miss cost. Next, we solve the cache-unconstrained case, which reveals how the refresh dynamics and popularity of content affect optimal caching. Then, we extend our approach to a soft-cache-constrained version, where we can guarantee that the cache use is limited with arbitrarily high probability. The corresponding solution reveals the interesting insight that ‘whether to cache an item or not in the local cache?’ depends primarily on its popularity level and channel reliability, whereas ‘how long the cached item should be held in the cache before eviction?’ depends primarily on its refresh rate. Moreover, we investigate the cost-cache saving trade-offs and prove that substantial cache gains can be obtained while also asymptotically achieving the minimum cost as the database size grows.
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. 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 (FCFS) policy. From a time-domain perspective, we explore the correlation between inter-departure 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. 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.
Industrial wireless networks (IWNs) have attracted significant attention for providing time-critical delivery services, which can benefit from device-to-device (D2D) communication for low transmission delay. In this paper, a distributed scheduling issue is investigated for D2D-enabled IWNs, where D2D links have age-of-information (AoI) constraints for information freshness. This is formulated as a constrained optimization problem to optimize D2D packet delivery over limited spectrum resources, which is intractable since D2D users have no prior knowledge of the operating environment. To tackle it, an AoI-aware scheduling algorithm (AoIS) is proposed based on primal-dual optimization and actor-critic reinforcement learning. In specific, multiple local actors for D2D devices learn AoI-aware scheduling policies to make on-site decisions with their stochastic AoI constraints addressed in dual domain. An edge based critic estimates the performance of all actors' policies from a global view, which effectively addresses the non-stationary environment caused by concurrent learning of multiple local actors.
Due to the ever-increasing time-sensitive industrial applications, critical-machine type communication (C-MTC) is a promising technique for timely delivery services in industrial wireless networks (IWNs), where vicinal devices can benefit from device-to-device (D2D) communication for low power consumption and latency. For real-time applications, age of information (AoI) is an essential metric that represents the freshness of data from the perspective of destinations. Thus, an AoI orchestration agent for link scheduling in D2D-enabled IWNs is needed. Most existing works on AoI deal with this scheduling in a centralized manner, which cannot afford timely packet delivery requirements for numerous D2D devices. Different from the existing works, a learning-based autonomous AoI and power orchestration agent, namely L-AoI, is proposed for D2D-enabled IWNs in this paper, where D2D devices adaptively compete for wireless resources in a distributed manner. As a result, the global channel state information as well as the actions of other D2D devices are unknown. Hence, D2D devices deal with this uncertainty under the guidance of L-AoI so that AoI constraints can be respected. By leveraging from the belief-based Bayesian Reinforcement Learning, L-AoI learns the scheduling action profile with strategies of other D2D devices considered so that the spectrum sharing coalitions can be intelligently formed. Both theoretical analysis and simulation are provided to validate the performance of L-AoI in terms of AoI stability and violation ratio.
Network traffic of delay-sensitive services has become a dominant part in the network. Proactive caching with the aid of predictive information has been proposed as a promising method to enhance the delay performance, which is one of the principal concerns of such services. In this paper, we analytically investigate the problem of how to efficiently utilize uncertain predictive information to design proactive caching strategies with provably good access-delay characteristics. First, we derive an upper bound for the average amount of proactive service per request that the system can support. Then we analyze the behavior of a family of threshold-based proactive strategies with a Markov chain, which shows that the average amount of proactive service per request can be maximized by properly selecting the threshold. Finally, we propose the UNIFORM strategy, which is the threshold-based strategy with the optimal threshold, and show that it outperforms the commonly used Earliest-Deadline-First (EDF) type proactive strategies in terms of delay. We perform extensive numerical experiments to demonstrate the influence of thresholds on delay performance under the threshold-based strategies, and specifically compare the EDF strategy and the UNIFORM strategy to verify our results.
Timely message delivery is a key enabler for Internet of Things (IoT) and cyber-physical systems to support wide range of context-dependent applications. Conventional time-related metrics (e.g. delay and jitter) fails to characterize the timeliness of the system update. Age of information (AoI) is a time-evolving metric that accounts for the packet inter-arrival and waiting times to assess the freshness of information. In the foreseen large-scale IoT networks, mutual interference imposes a delicate relation between traffic generation patterns and transmission delays. To this end, we provide a spatiotemporal framework that captures the peak AoI (PAoI) for large scale IoT uplink network under time-triggered (TT) and event triggered (ET) traffic. Tools from stochastic geometry and queueing theory are utilized to account for the macroscopic and microscopic network scales. Simulations are conducted to validate the proposed mathematical framework and assess the effect of traffic load on the PAoI. The results unveil a counter-intuitive superiority of the ET traffic over the TT in terms of PAoI, which is due to the involved temporal interference correlations. Insights regarding the network stability frontiers and the location-dependent performance are presented. Key design recommendations regarding the traffic load and decoding thresholds are highlighted.
This work is motivated by the need of collecting fresh data from power-constrained sensors in the industrial Internet of Things (IIoT) network. A recently proposed metric, the
Age of Information
(AoI) is adopted to measure data freshness from the perspective of the central controller in the IIoT network. We wonder what is the minimum average AoI the network can achieve and how to design scheduling algorithms to approach it. To answer these questions when the channel states of the network are time-varying and scheduling decisions are restricted to both bandwidth and power consumption constraint, we first decouple the multi-sensor scheduling problem into a single-sensor constrained Markov decision process (CMDP) by relaxing the hard bandwidth constraint. Next we exploit the threshold structure of the optimal policy for the decoupled single sensor CMDP and obtain the optimum solution through linear programming (LP). Finally, an asymptotically optimal truncated policy that can satisfy the hard bandwidth constraint is built upon the optimal solution to each of the decoupled single-sensor. Our investigation shows that to obtain a small average AoI over the network: (1) The scheduler exploits good channels to schedule sensors supported by limited power; (2) Sensors equipped with enough transmission power are updated in a timely manner such that the bandwidth constraint can be satisfied.
Mobile edge computing (MEC) is a promising technique to improve the quality of computation experience for mobile devices by providing computation resources in close proximity. However, the design of scheduling policies for MEC systems inevitably encounters a challenging optimization problem that should take both transmissions and computations into consideration. In particular, how to jointly schedule transmissions and the computations should adapt to the cross-layer system dynamics, i.e., random task arrivals and channel state variations. We formulate this scheduling problem as a joint optimization problem for both transmissions and computations in order to minimize the power consumption of mobile devices, while meeting the latency requirement. With given distributions of the system dynamics, Markov decision process (MDP) is used to model the system operations. Based on this model, the power-optimal scheduling policy can be obtained by converting the joint optimization problem to linear programming (LP) by using variable substitutions and thus the optimal power-latency tradeoff can be achieved. When the distribution information of the system dynamics is unknown, we exploit the Lyapunov optimization to present a low complexity scheduling policy. Our theoretical analysis and extensive simulation studies show that our approach can offer a good tradeoff between power consumption and latency.
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 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 making process. Theoretical results show that 1) when the decisions are made according to a Poisson process, the average AuD is independent of decision rate and would be minimized if the arrival process is periodic (i.e., deterministic); 2) when both the decision process and the arrive process are periodic, the average AuD is larger than, but decreases with decision rate to, the average AuD of the corresponding system with Poisson decisions (i.e., random); 3) when both the decision process and the arrive process are periodic, the average AuD can be further decreased by optimally controlling the offset between the two processes. For practical IoT systems, therefore, it is suggested to employ periodic arrival processes and random decision processes. Nevertheless, making periodical updates and decisions with properly controlled offset also is a promising solution if the timing information of the two processes can be accessed by the monitor.
We consider a system consisting of multiple sensors, a central monitoring station, and multiple orthogonal frequency channels. The sensors measure heterogeneous time-varying signals and report their measurements to the central monitoring station which uses them to make control decisions. Due to limited communication capacity, not all sensors can send updates to the monitoring station at all times. The cost of the system pays at any time is a weighted sum of the ages-of-information of the various sensors at that time. The goal is to design scheduling policies which minimize the time-average of this cost. We propose a policy called SQRT-Weight which schedules updates from sensors at a frequency proportional to the square-root of the corresponding weights and show that this policy is asymptotically 8--optimal. In addition, we compare the performance of the SQRT-Weight policy with other natural scheduling policies via simulations.
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 that a base-station updates many users on stochastic information arrivals over a wireless broadcast network, where 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 derive the Whittle index in a closed form and establish the indexability, by introducing a post-action age. Based on the Whittle index, we propose a scheduling algorithm, while experimentally showing that it closely approximates an age-optimal scheduling algorithm.
Age of information (AoI) was introduced in the early 2010s as a notion to characterize the freshness of the knowledge a system has about a process observed remotely. AoI was shown to be a fundamentally novel metric of timeliness, significantly different, to existing ones such as delay and latency. The importance of such a tool is paramount, especially in contexts other than transport of information, since communication takes place also to control, or to compute, or to infer, and not just to reproduce messages of a source. This volume comes to present and discuss the first body of works on AoI and discuss future directions that could yield more challenging and interesting research.
Round robin and its variants are well known scheduling policies that are popular in wireline networks due to their throughput optimality, delay insensitivity to file size distributions and short-term fairness. The latter two properties are also extremely important for emerging wireless applications, such as Internet of Things and cyber-physical systems. However, there is no direct wireless analog of round robin with all the desirable properties in wireless networks, where wireless interference and channel fading are predominant. The main reason is due to the fact that it is very difficult to even define what round robin means in wireless networks. This motivates us to develop a round-robin-like algorithm in wireless networks that has nice properties as round robin in wireline networks. To that end, we utilize a counter called the Time-Since-Last-Service (TSLS) that keeps track of the time of each file since its last service, and observe that scheduling a file with maximum TSLS in a single server is equivalent to serving files in a round robin fashion. Based on this key observation, we develop a TSLS-based algorithm that balances the tradeoff between the TSLS value and the channel rate for each link and show that the proposed algorithm achieves maximum system throughput, which demands a nontraditional approach due to the abrupt dynamics of the TSLS metrics. Numerous simulations are provided to validate its desired properties such as delay insensitivity and excellent short-term fairness performance as in the case of round robin algorithms of wireline networks.
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