Expected flooding time in continuous edge-Markovian graphs

Abstract In this paper we study random Apollonian networks (RANs) and evolving Apollonian networks (EANs), in d dimensions for any d≥2, i.e. dynamically evolving random d-dimensional simplices, looked at as graphs inside an initial d-dimensional simplex. We determine the limiting degree distribution in RANs and show that it follows a power-law tail with exponent τ=(2d-1)/(d-1). We further show that the degree distribution in EANs converges to the same degree distribution if the simplex-occupation parameter in the nth step of the dynamics tends to 0 but is not summable in n. This result gives a rigorous proof for the conjecture of Zhang et al. (2006) that EANs tend to exhibit similar behaviour as RANs once the occupation parameter tends to 0. We also determine the asymptotic behaviour of the shortest paths in RANs and EANs for any d≥2. For RANs we show that the shortest path between two vertices chosen u.a.r. (typical distance), the flooding time of a vertex chosen uniformly at random, and the diameter of the graph after n steps all scale as a constant multiplied by log n. We determine the constants for all three cases and prove a central limit theorem for the typical distances. We prove a similar central limit theorem for typical distances in EANs.

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Performance Analysis of Time Synchronization Protocols in Wireless Sensor Networks

Sensors ◽

10.3390/s19133020 ◽

2019 ◽

Vol 19 (13) ◽

pp. 3020 ◽

Cited By ~ 3

Author(s):

Linh-An Phan ◽

Taejoon Kim ◽

Taehong Kim ◽

JaeSeang Lee ◽

Jae-Hyun Ham

Keyword(s):

Wireless Sensor Networks ◽

Sensor Networks ◽

Network Topology ◽

Time Synchronization ◽

Wireless Sensor ◽

Message Delay ◽

Delay Jitter ◽

Error Accumulation ◽

Flooding Time ◽

Synchronization Protocol

The time synchronization protocol is indispensable in various applications of wireless sensor networks, such as scheduling, monitoring, and tracking. Numerous protocols and algorithms have been proposed in recent decades, and many of them provide micro-scale resolutions. However, designing and implementing a time synchronization protocol in a practical wireless network is very challenging compared to implementation in a wired network; this is because its performance can be deteriorated significantly by many factors, including hardware quality, message delay jitter, ambient environment, and network topology. In this study, we measure the performance of the Flooding Time Synchronization Protocol (FTSP) and Gradient Time Synchronization Protocol (GTSP) in terms of practical network conditions, such as message delay jitter, synchronization period, network topology, and packet loss. This study provides insights into the operation and optimization of time synchronization protocols. In addition, the performance evaluation identifies that FTSP is highly affected by message delay jitter due to error accumulation over multi-hops. We demonstrate that the proposed extended version of the FTSP (E-FTSP) alleviates the effect of message delay jitter and enhances the overall performance of FTSP in terms of error, time, and other factors.

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Dynamic Flooding Time Synchronisation Protocol for WSNs

2012 IEEE Global Communications Conference (GLOBECOM) ◽

10.1109/glocom.2012.6503140 ◽

2012 ◽

Cited By ~ 3

Author(s):

Jonathan Shannon ◽

Hugh Melvin ◽

Antonio G. Ruzzelli

Keyword(s):

Flooding Time

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The Seed Bank Response of Five Pioneer Plants to Flooding – A Implication for Riverbank Vegetation Restoration

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.692.65 ◽

2014 ◽

Vol 692 ◽

pp. 65-69 ◽

Cited By ~ 1

Author(s):

Ji Wang ◽

Fang Qing Chen ◽

Lin Xiang ◽

Meng Ya Geng

Keyword(s):

Seed Germination ◽

Seed Bank ◽

Cynodon Dactylon ◽

Alternanthera Philoxeroides ◽

Setaria Viridis ◽

Amorpha Fruticosa ◽

Pioneer Plants ◽

Xanthium Sibiricum ◽

Flooding Time ◽

Riverbank Vegetation

Abstract. The seed bank response of five pioneer plants, including Cynodon dactylon, Setaria viridis, Amorpha fruticosa, Alternanthera Philoxeroides and Xanthium sibiricum, to flooding were tested through simulating the flooding experiments. The flooding treatments included 30d, 60d, 90d and the control. All of the treated seeds were germinated under an appropriate germinate condition. The results showed that seed germination rate and germination index of Amorpha fruticosa and Xanthium sibiricum increased with the increasing flooding time meanwhile that of Setaria viridis and Alternanthera Philoxeroides decreased, and Cynodon dactylon germination decreased firstly and then increased with the increasing flooding time. The results suggested that flooding influenced significantly seed germination, and implicated that Amorpha fruticosa, Cynodon dactylon and Amorpha fruticosa were appropriate species for the construction of artificial seed bank to restore riverbank vegetation in the Three Gorges reservoir area.

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