Closed-Form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems
This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form of status updates to a destination node. The status update and harvested energy packets are assumed to arriv...
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| Published in | IEEE transactions on information theory Vol. 68; no. 6; pp. 3896 - 3919 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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IEEE
01.06.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form of status updates to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI) . Unlike most of the existing analyses of AoI focusing on the evaluation of its average value when the transmitter is not subject to energy constraints, our analysis is focused on understanding the distributional properties of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and preemptive in service/waiting strategies. Using these MGF results, we further obtain closed-form expressions for the first and second moments of AoI in each queueing discipline. We demonstrate the generality of this analysis by recovering several existing results for the corresponding system with no energy constraints as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the necessity of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value. |
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| AbstractList | This paper considers a real-time status update system in which an energy harvesting (EH)-powered transmitter node observes some physical process, and sends its sensed measurements in the form of status updates to a destination node. The status update and harvested energy packets are assumed to arrive at the transmitter according to independent Poisson processes, and the service time of each status update is assumed to be exponentially distributed. We quantify the freshness of status updates when they reach the destination using the concept of Age of Information (AoI) . Unlike most of the existing analyses of AoI focusing on the evaluation of its average value when the transmitter is not subject to energy constraints, our analysis is focused on understanding the distributional properties of AoI through the characterization of its moment generating function (MGF). In particular, we use the stochastic hybrid systems (SHS) framework to derive closed-form expressions of the MGF of AoI under several queueing disciplines at the transmitter, including non-preemptive and preemptive in service/waiting strategies. Using these MGF results, we further obtain closed-form expressions for the first and second moments of AoI in each queueing discipline. We demonstrate the generality of this analysis by recovering several existing results for the corresponding system with no energy constraints as special cases of the new results. Our numerical results verify the analytical findings, and demonstrate the necessity of incorporating the higher moments of AoI in the implementation/optimization of real-time status update systems rather than just relying on its average value. |
| Author | Dhillon, Harpreet S. Abd-Elmagid, Mohamed A. |
| Author_xml | – sequence: 1 givenname: Mohamed A. orcidid: 0000-0002-8853-8168 surname: Abd-Elmagid fullname: Abd-Elmagid, Mohamed A. email: maelaziz@vt.edu organization: Department of Electrical and Computer Engineering, Wireless@VT, Virginia Tech, Blacksburg, VA, USA – sequence: 2 givenname: Harpreet S. orcidid: 0000-0003-2829-9449 surname: Dhillon fullname: Dhillon, Harpreet S. email: hdhillon@vt.edu organization: Department of Electrical and Computer Engineering, Wireless@VT, Virginia Tech, Blacksburg, VA, USA |
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| SubjectTerms | Age of information Closed form solutions communication networks Energy harvesting Exact solutions Hybrid systems Markov processes Mathematical analysis Optimization Preempting Queueing Queueing analysis queueing systems Real time Real-time systems Servers stochastic hybrid systems Transmitters |
| Title | Closed-Form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems |
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