Finite Horizon Online Lazy Scheduling with Energy Harvesting Transmitters over Fading Channels

Lazy scheduling, i.e. setting transmit power and rate in response to data traffic as low as possible so as to satisfy delay constraints, is a known method for energy efficient transmission.This paper addresses an online lazy scheduling problem over finite time-slotted transmission window and introduces low-complexity heuristics which attain near-optimal performance.Particularly, this paper generalizes lazy scheduling problem for energy harvesting systems to deal with packet arrival, energy harvesting and time-varying channel processes simultaneously. The time-slotted formulation of the problem and depiction of its offline optimal solution provide explicit expressions allowing to derive good online policies and algorithms

Age-Optimal Updates of Multiple Information Flows

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

Optimal Packet Scheduling on an Energy Harvesting Broadcast Link

The minimization of transmission completion time for a given number of bits per user in an energy harvesting communication system, where energy harvesting instants are known in an offline manner is considered. An achievable rate region with structural properties satisfied by the 2-user AWGN Broadcast Channel capacity region is assumed. It is shown that even though all data are available at the beginning, a non-negative amount of energy from each energy harvest is deferred for later use such that the transmit power starts at its lowest value and rises as time progresses. The optimal scheduler ends the transmission to both users at the same time. Exploiting the special structure in the problem, the iterative offline algorithm, FlowRight, from earlier literature, is adapted and proved to solve this problem. The solution has polynomial complexity in the number of harvests used, and is observed to converge quickly on numerical examples.Comment: 25 pages, 6 figures, added lemma and theorems, added reference, corrected typo

Peak-Age Violation Guarantees for the Transmission of Short Packets over Fading Channels

We investigate the probability that the peak age of information in a point-to-point communication system operating over a multiantenna wireless fading channel exceeds a predetermined value. The packets are scheduled according to a last-come first-serve policy with preemption in service, and are transmitted over the channel using a simple automatic repetition request protocol. We consider quadrature phase shift keying modulation, pilot-assisted transmission, maximum-likelihood channel estimation, and mismatched scaled nearest-neighbor decoding. Our analysis, which exploits nonasymptotic tools in information theory, allows one to determine, for a given information packet size, the physical layer parameters such as the SNR, the number of transmit and receive antennas, the amount of frequency diversity to exploit, and the number of pilot symbols, to ensure that the system operates below a target peak-age violation probability.Comment: 6 pages, 6 figures. To be presented at Infocom 201

Optimal Status Updating with a Finite-Battery Energy Harvesting Source

We consider an energy harvesting source equipped with a finite battery, which needs to send timely status updates to a remote destination. The timeliness of status updates is measured by a non-decreasing penalty function of the Age of Information (AoI). The problem is to find a policy for generating updates that achieves the lowest possible time-average expected age penalty among all online policies. We prove that one optimal solution of this problem is a monotone threshold policy, which satisfies (i) each new update is sent out only when the age is higher than a threshold and (ii) the threshold is a non-increasing function of the instantaneous battery level. Let $\tau_B$ denote the optimal threshold corresponding to the full battery level $B$, and $p(\cdot)$ denote the age-penalty function, then we can show that $p(\tau_B)$ is equal to the optimum objective value, i.e., the minimum achievable time-average expected age penalty. These structural properties are used to develop an algorithm to compute the optimal thresholds. Our numerical analysis indicates that the improvement in average age with added battery capacity is largest at small battery sizes; specifically, more than half the total possible reduction in age is attained when battery storage increases from one transmission's worth of energy to two. This encourages further study of status update policies for sensors with small battery storage.Comment: 15 pages, 6 figure

Analysis of Slotted ALOHA with an Age Threshold

We present a comprehensive steady-state analysis of threshold-ALOHA, a distributed age-aware modification of slotted ALOHA proposed in recent literature. In threshold-ALOHA, each terminal suspends its transmissions until the Age of Information (AoI) of the status update flow it is sending reaches a certain threshold $\Gamma$. Once the age exceeds $\Gamma$, the terminal attempts transmission with constant probability $\tau$ in each slot, as in standard slotted ALOHA. We analyze the time-average expected AoI attained by this policy, and explore its scaling with network size, $n$. We derive the probability distribution of the number of active users at steady state, and show that as network size increases the policy converges to one that runs slotted ALOHA with fewer sources: on average about one fifth of the users is active at any time. We obtain an expression for steady-state expected AoI and use this to optimize the parameters $\Gamma$ and $\tau$, resolving the conjectures in \cite{doga} by confirming that the optimal age threshold and transmission probability are $2.2n$ and $4.69/n$, respectively. We find that the optimal AoI scales with the network size as $1.4169n$, which is almost half the minimum AoI achievable with slotted ALOHA, while the loss from the maximum throughput of $e^{-1}$ remains below $1\%$. We compare the performance of this rudimentary algorithm to that of the SAT policy that dynamically adapts its transmission probabilities