Age-Minimal Transmission for Energy Harvesting Sensors With Finite Batteries: Online Policies

An energy-harvesting sensor node that is sending status updates to a destination is considered. The sensor is equipped with a battery of finite size to save its incoming energy, and consumes one unit of energy per status update transmission, which is delivered to the destination instantly over an er...

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Published in:	IEEE transactions on information theory Vol. 66; no. 1; pp. 534 - 556
Main Authors:	Arafa, Ahmed, Yang, Jing, Ulukus, Sennur, Poor, H. Vincent
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.01.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Age-of-information (AoI) Batteries Battery charge measurement Energy Energy conservation Energy harvesting Energy policy finite battery Long term online scheduling Optimization Rechargeable batteries Sensor phenomena and characterization Sensors Stochastic processes Thresholds
ISSN:	0018-9448, 1557-9654
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Abstract	An energy-harvesting sensor node that is sending status updates to a destination is considered. The sensor is equipped with a battery of finite size to save its incoming energy, and consumes one unit of energy per status update transmission, which is delivered to the destination instantly over an error-free channel. The setting is online in which the harvested energy is revealed to the sensor causally over time after it arrives, and the goal is to design status update transmission times (policy) such that the long term average age of information (AoI) is minimized. The AoI is defined as the time elapsed since the latest update has reached at the destination. Two energy arrival models are considered: a random battery recharge (RBR) model, and an incremental battery recharge (IBR) model. In both models, energy arrives according to a Poisson process with unit rate, with values that completely fill up the battery in the RBR model, and with values that fill up the battery incrementally in a unit-by-unit fashion in the IBR model. The key approach to characterizing the optimal status update policy for both models is showing the optimality of renewal policies , in which the inter-update times follow a renewal process in a certain manner that depends on the energy arrival model and the battery size. It is then shown that the optimal renewal policy has an energy-dependent threshold structure, in which the sensor sends a status update only if the AoI grows above a certain threshold that depends on the energy available in its battery. For both the random and the incremental battery recharge models, the optimal energy-dependent thresholds are characterized explicitly , i.e., in closed-form, in terms of the optimal long term average AoI. It is also shown that the optimal thresholds are monotonically decreasing in the energy available in the battery, and that the smallest threshold, which comes in effect when the battery is full, is equal to the optimal long term average AoI.
AbstractList	An energy-harvesting sensor node that is sending status updates to a destination is considered. The sensor is equipped with a battery of finite size to save its incoming energy, and consumes one unit of energy per status update transmission, which is delivered to the destination instantly over an error-free channel. The setting is online in which the harvested energy is revealed to the sensor causally over time after it arrives, and the goal is to design status update transmission times (policy) such that the long term average age of information (AoI) is minimized. The AoI is defined as the time elapsed since the latest update has reached at the destination. Two energy arrival models are considered: a random battery recharge (RBR) model, and an incremental battery recharge (IBR) model. In both models, energy arrives according to a Poisson process with unit rate, with values that completely fill up the battery in the RBR model, and with values that fill up the battery incrementally in a unit-by-unit fashion in the IBR model. The key approach to characterizing the optimal status update policy for both models is showing the optimality of renewal policies , in which the inter-update times follow a renewal process in a certain manner that depends on the energy arrival model and the battery size. It is then shown that the optimal renewal policy has an energy-dependent threshold structure, in which the sensor sends a status update only if the AoI grows above a certain threshold that depends on the energy available in its battery. For both the random and the incremental battery recharge models, the optimal energy-dependent thresholds are characterized explicitly , i.e., in closed-form, in terms of the optimal long term average AoI. It is also shown that the optimal thresholds are monotonically decreasing in the energy available in the battery, and that the smallest threshold, which comes in effect when the battery is full, is equal to the optimal long term average AoI.
Author	Arafa, Ahmed Yang, Jing Poor, H. Vincent Ulukus, Sennur
Author_xml	– sequence: 1 givenname: Ahmed orcidid: 0000-0003-2032-1840 surname: Arafa fullname: Arafa, Ahmed email: aarafa@uncc.edu organization: Electrical Engineering Department, Princeton University, Princeton, NJ, USA – sequence: 2 givenname: Jing orcidid: 0000-0002-6009-864X surname: Yang fullname: Yang, Jing email: yangjing@psu.edu organization: School of Electrical Engineering and Computer Science, The Pennsylvania State University, State College, PA, USA – sequence: 3 givenname: Sennur orcidid: 0000-0002-8219-8190 surname: Ulukus fullname: Ulukus, Sennur email: ulukus@umd.edu organization: Department of Electrical and Computer Engineering, University of Maryland at College Park, College Park, MD, USA – sequence: 4 givenname: H. Vincent orcidid: 0000-0002-2062-131X surname: Poor fullname: Poor, H. Vincent email: poor@princeton.edu organization: Electrical Engineering Department, Princeton University, Princeton, NJ, USA
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SubjectTerms	Age-of-information (AoI) Batteries Battery charge measurement Energy Energy conservation Energy harvesting Energy policy finite battery Long term online scheduling Optimization Rechargeable batteries Sensor phenomena and characterization Sensors Stochastic processes Thresholds
Title	Age-Minimal Transmission for Energy Harvesting Sensors With Finite Batteries: Online Policies
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