A Stochastic Hybrid Systems Approach to the Joint Distribution of Ages of Information in Networks

Abd-Elmagid, Mohamed A.; Dhillon, Harpreet S.

doi:10.48550/arxiv.2205.07448

Cited by 1 publication

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References 19 publications

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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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Section: Introductionmentioning

confidence: 99%

Age Analysis of Status Updating System with Probabilistic Packet Preemption

Zhang

2022

Entropy

View full text Add to dashboard Cite

show abstract

A Stochastic Hybrid Systems Approach to the Joint Distribution of Ages of Information in Networks

Cited by 1 publication

References 19 publications

Age Analysis of Status Updating System with Probabilistic Packet Preemption

Age Analysis of Status Updating System with Probabilistic Packet Preemption

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