Clustering in Stochastic Asynchronous Algorithms for Distributed Simulations

Manita, Anatoly; Simonot, F.

doi:10.1007/11571155_3

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…Of course, in that case we cannot expect such short and explicit results as in Section 3. Successful examples of synchronization studies for some special nonhomogeneous (or weakly nonhomogeneous) systems can be found in [12,10,13,15].…”

Section: Discussionmentioning

confidence: 99%

“…Our probablistic technique is similar to that was recently used to study mathematical models of multi-processor parallel computing [21,1,14,13] and collective behavior in abstract particle systems with synchronization-like interaction [12,10,15,11,16,18,19]. Our stochastic models can be considered also as special classes of self-organizing systems [26,5,23,29].…”

Section: Introductionmentioning

confidence: 99%

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Time Scales in Probabilistic Models of Wireless Sensor Networks

Manita¹

2013

Preprint

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We consider a stochastic model of clock synchronization in a wireless network consisting of N sensors interacting with one dedicated accurate time server. For large N we find an estimate of the final time sychronization error for global and relative synchronization. Main results concern a behavior of the network on different time scales t N → ∞, N → ∞. We discuss existence of phase transitions and find exact time scales on which an effective clock synchronization of the system takes place.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time Scales in Probabilistic Models of Wireless Sensor Networks

Manita¹

2013

Preprint

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“…Note that |φ (s; λ)| 2 is the real symmetric characteristic function and λ) . Summing over j 1 < j 2 as in (41) we get (44).…”

Section: Lemmas Of Dynamicsmentioning

confidence: 99%

Intrinsic scales for high-dimensional LEVY-driven models with non-Markovian synchronizing updates

Manita

2014

Preprint

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We propose stochastic N -component synchronization models (x 1 (t), . . . , x N (t)), x j ∈ R d , t ∈ R + , whose dynamics is described by Lévy processes and synchronizing jumps. We prove that symmetric models reach synchronization in a stochastic sense: differences between components d (N ) kj (t) = x k (t)−x j (t) have limits in distribution as t → ∞. We give conditions of existence of natural (intrinsic) space scales for large synchronized systems, i.e., we are looking for such sequences {b N } that distribution of d (N ) kj (∞)/b N converges to some limit as N → ∞. It appears that such sequence exists if the Lévy process enters a domain of attraction of some stable law. For Markovian synchronization models based on α-stable Lévy processes this results holds for any finite N in the precise form with b N = (N − 1) 1/α . For non-Markovian models similar results hold only in the asymptotic sense. The class of limiting laws includes the Linnik distributions. We also discuss generalizations of these theorems to the case of non-uniform matrix-based intrinsic scales. The central point of our proofs is a representation of characteristic functions of d (N ) kj (t) via probability distribution of a superposition of N independent renewal processes.

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“…There can be many variants of exact formulation of such problem, see [4,7,10,2,15]. We will call the model considered here the basic model, because there are no restrictions on the jump process.…”

Section: The Modelmentioning

confidence: 99%

Asymptotic behaviour in the time synchronization model

Малышев¹,

Manita²

2011

Representation Theory, Dynamical Systems, and Asymptotic Combinatorics

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There are two types i = 1, 2 of particles on the line R, with N i particles of type i . Each particle of type i moves with constant velocity v i . Moreover, any particle of type i = 1, 2 jumps to any particle of type j = 1, 2 with rates N −1 j α ij . We discuss in details the initial desynchronization of this particle system, namely, we are interested in behaviour of the process when the total number of particles N 1 + N 2 tends to infinity, N 1 /N 2 → const and the time t > 0 is fixed.

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Clustering in Stochastic Asynchronous Algorithms for Distributed Simulations

Cited by 9 publications

References 10 publications

Time Scales in Probabilistic Models of Wireless Sensor Networks

Time Scales in Probabilistic Models of Wireless Sensor Networks

Intrinsic scales for high-dimensional LEVY-driven models with non-Markovian synchronizing updates

Asymptotic behaviour in the time synchronization model

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