The Multi-Source Preemptive M/PH/1/1 Queue with Packet Errors: Exact Distribution of the Age of Information and Its Peak

Doğan, Ozancan; Akar, Nail

doi:10.48550/arxiv.2007.11656

Cited by 2 publications

(2 citation statements)

References 37 publications

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“…Theorem 5 follows by selecting, k = n (32) for fixed λ e , λ s , λ ca and λ cb that do not depend on n. Theorem 5 implies that even though nodes in clusters do not gossip, by utilizing the information exchange at the cluster head level, the average version age scaling of an end user can be improved to O(n…”

Section: A Version Age In Clustered Disconnected Network With Connect...mentioning

confidence: 99%

Version Age of Information in Clustered Gossip Networks

Buyukates¹,

Bastopcu²,

Ulukuş³

2021

Preprint

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We consider a network consisting of a single source and n receiver nodes that are grouped into equal-sized clusters. Each cluster corresponds to a distinct community such that nodes that belong to different communities cannot exchange information. We use dedicated cluster heads in each cluster to facilitate communication between the source and the nodes within that cluster. Inside clusters, nodes are connected to each other according to a given network topology. Based on the connectivity among the nodes, each node relays its current stored version of the source update to its neighboring nodes by local gossiping. We use the version age metric to assess information freshness at the receiver nodes. We consider disconnected, ring, and fully connected network topologies for each cluster. For each of these network topologies, we characterize the average version age at each node and find the average version age scaling as a function of the network size n. Our results indicate that per node average version age scalings of O( √ n), O(n 1 3 ), and O(log n) are achievable in disconnected, ring, and fully connected cluster models, respectively. Next, we increase connectivity in the network and allow gossiping among the cluster heads to improve version age at the receiver nodes. With that, we show that when the cluster heads form a ring network among themselves, we obtain per node average version age scalings of O(n 1 3 ), O(n 1 4), and O(log n) in disconnected, ring, and fully connected cluster models, respectively.Next, focusing on a ring network topology in each cluster, we introduce hierarchy to the considered clustered gossip network model and show that when we employ two levels of hierarchy, we can achieve the same O(n 1 4 ) scaling without using dedicated cluster heads. We generalize this result for h levels of hierarchy and show that per user average version age scaling of O(n) is achievable in the case of a ring network in each cluster across all hierarchy levels. Finally, we find the version age-optimum cluster sizes as a function of the source, cluster head, and node update rates through numerical evaluations.

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Section: A Version Age In Clustered Disconnected Network With Connect...mentioning

confidence: 99%

Version Age of Information in Clustered Gossip Networks

Buyukates¹,

Bastopcu²,

Ulukuş³

2021

Preprint

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“…Provided these results, a general expression of the generation function of the AoI and peak was derived, which is equivalent to obtain their stationary distributions. Recently, using the queueing theory methods, the discrete time AoI and peak AoI distributions are numerically determined in series work [10]- [12]. In [13], the stationary distribution of continuous AoI is determined for single-server system with various queue models, and it seems that the ideas and methods used in [9] are from paper [13].…”

Section: Introductionmentioning

confidence: 99%

On Age of Information for Discrete Time Status Updating System With Ber/G/1/1 Queues

Zhang¹,

Xu²

2021

Preprint

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In this paper, we consider the age of information (AoI) of a discrete time status updating system, focusing on finding the stationary AoI distribution assuming that the Ber/G/1/1 queue is used. Following the standard queueing theory, we show that by invoking a two-dimensional state vector which tracks the AoI and packet age in system simultaneously, the stationary AoI distribution can be derived by analyzing the steady state of the constituted two-dimensional stochastic process. We give the general formula of the AoI distribution and calculate the explicit expression when the service time is also geometrically distributed. The discrete and continuous AoI are compared, we depict the mean of discrete AoI and that of continuous time AoI for system with M/M/1/1 queue. Although the stationary AoI distribution of some continuous time single-server system has been determined before, in this paper, we shall prove that the standard queueing theory is still appliable to analyze the discrete AoI, which is even stronger than the proposed methods handling the continuous AoI.

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The Multi-Source Preemptive M/PH/1/1 Queue with Packet Errors: Exact Distribution of the Age of Information and Its Peak

Cited by 2 publications

References 37 publications

Version Age of Information in Clustered Gossip Networks

Version Age of Information in Clustered Gossip Networks

On Age of Information for Discrete Time Status Updating System With Ber/G/1/1 Queues

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