Probability Analysis of Age of Information in Multi-Hop Networks

Ayan, Onur; Gürsu, H. Murat; Papa, Arled; Kellerer, Wolfgang

doi:10.1109/lnet.2020.2976991

Cited by 31 publications

(18 citation statements)

References 22 publications

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“…The authors of [25] characterized the distribution of peak AoI for a system having two M/M/1 FCFC queues in tandem. The distribution of AoI/peak AoI was also analyzed for multi-hop networks with/without priorities in [26], [27]. For multi-source single-server systems, the distributions of AoI and PAoI were characterized for various discrete time queues in [28], and the joint Laplace transform of the AoI values associated with different sources was derived in [29].…”

Section: A Related Workmentioning

confidence: 99%

Closed-form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems

Abd-Elmagid¹,

Dhillon²

2021

Preprint

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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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Section: A Related Workmentioning

confidence: 99%

Closed-form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems

Abd-Elmagid¹,

Dhillon²

2021

Preprint

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“…A practical age control protocol to improve AoI in multi-hop IP networks was proposed in [192]. The distribution of AoI for general networks with time-invariant erasure probabilities on each link was derived in [193].…”

Section: E General Wireless Networkmentioning

confidence: 99%

Age of Information: An Introduction and Survey

Yates¹,

Yin²,

Brown³

et al. 2020

Preprint

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We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications.

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“…In these situations, since a packet generated behind may be transmitted to destination via a short-delay path, it is possible that this packet arrives at the receiver before the packets generated before it. Recently, many papers have been launched considering the AoI of status updating networks with simple structures, such as the status updating system with multiple sources [ 19 , 20 , 21 , 22 , 23 , 24 , 25 ], the system with more than one hop transmission [ 26 , 27 , 28 , 29 , 30 ], and the system in which the packet transmission is assisted by a relay [ 31 , 32 , 33 , 34 , 35 ]. Recently, using the SHS method, the AoI of an arbitrarily connected network named the gossip network was discussed in [ 36 , 37 ].…”

Section: Introductionmentioning

confidence: 99%

Age Analysis of Status Updating System with Probabilistic Packet Preemption

Zhang

2022

Entropy

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The age of information (AoI) metric was proposed to measure the freshness of messages obtained at the terminal node of a status updating system. In this paper, the AoI of a discrete time status updating system with probabilistic packet preemption is investigated by analyzing the steady state of a three-dimensional discrete stochastic process. We assume that the queue used in the system is Ber/Geo/1/2*/η, which represents that the system size is 2 and the packet in the buffer can be preempted by a fresher packet with probability η. Instead of considering the system’s AoI separately, we use a three-dimensional state vector (n,m,l) to simultaneously track the real-time changes of the AoI, the age of a packet in the server, and the age of a packet waiting in the buffer. We give the explicit expression of the system’s average AoI and show that the average AoI of the system without packet preemption is obtained by letting η=0. When η is set to 1, the mean of the AoI of the system with a Ber/Geo/1/2* queue is obtained as well. Combining the results we have obtained and comparing them with corresponding average continuous AoIs, we propose a possible relationship between the average discrete AoI with the Ber/Geo/1/c queue and the average continuous AoI with the M/M/1/c queue. For each of two extreme cases where η=0 and η=1, we also determine the stationary distribution of AoI using the probability generation function (PGF) method. The relations between the average AoI and the packet preemption probability η, as well as the AoI’s distribution curves in two extreme cases, are illustrated by numerical simulations. Notice that the probabilistic packet preemption may occur, for example, in an energy harvest (EH) node of a wireless sensor network, where the packet in the buffer can be replaced only when the node collects enough energy. In particular, to exhibit the usefulness of our idea and methods and highlight the merits of considering discrete time systems, in this paper, we provide detailed discussions showing how the results about continuous AoI are derived by analyzing the corresponding discrete time system and how the discrete age analysis is generalized to the system with multiple sources. In terms of packet service process, we also propose an idea to analyze the AoI of a system when the service time distribution is arbitrary.

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Probability Analysis of Age of Information in Multi-Hop Networks

Cited by 31 publications

References 22 publications

Closed-form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems

Closed-form Characterization of the MGF of AoI in Energy Harvesting Status Update Systems

Age of Information: An Introduction and Survey

Age Analysis of Status Updating System with Probabilistic Packet Preemption

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