Abstract
We introduce a class of stochastic networks in which synchronization between nodes is modelled by a message passing mechanism with heterogeneous Markovian routing. We present a series of results about probability distributions related to steady states of such models.
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A. Manita, “Brownian particles interacting via synchronizations,” Commun. Stat.—Theor. Methods 40, 3440–3451 (2011).
A. Manita, “Intrinsic scales for high-dimensional Lévy-driven models with non-Markovian synchronizing updates,” arXiv:1409.2919 (2014).
A. Manita, “On behavior of stochastic synchronization models,” J. Phys.: Conf. Ser. 681, 012024 (2016).
S. P. Kumar and J. S. Kowalik, “On the Parallelization of Sequential Programs,” in Supercomputing, Ed. by J. S. Kowalik (Springer, Berlin, Heidelberg, 1989), pp. 173–188.
R. Fujimoto, Parallel and Distributed Simulation Systems (Wiley, Chichester, 2000).
L. N. Shchur and L. V. Shchur, “Parallel discrete event simulation as a paradigm for large scale modeling experiments,” in Proceedings of the Conference on Data Analytics and Management in Data Intensive Domains, DAMDID/RCDL’2015, Obninsk, Russia, 2015, pp. 107–113.
A. Manita and F. Simonot, “Clustering in stochastic asynchronous algorithms for distributed simulations,” in Stochastic Algorithms: Foundations and Applications, Lect. NotesComput. Sci. 3777, 26–37 (2005).
B. Sundararaman, U. Buy, and A. D. Kshemkalyani, “Clock synchronization for wireless sensor networks: a survey,” Ad Hoc Networks 3, 281–323 (2005).
A. Manita, “Clock synchronization in symmetric stochastic networks,” Queueing Syst. 76, 149–180 (2014).
M. Kijima, Markov Processes for Stochastic Modeling (Springer, New York, 1997).
L. Klebanov, G. Maniya, and I. Melamed, “A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a sheme for summing of a random number of random variables,” Theory Probab. Appl. 29, 791–794 (1985)
V. Bening and V. Korolev, Generalized PoissonModels and Their Applications in Insurance and Finance (VSP, London, 2002).
S. Kotz, T. Kozubowski, and K. Podgorski, The LaplaceDistribution and Generalizations: A RevisitWith Applications to Communications, Economics, Engineering, and Finance (Birkhäuser, Boston, 2001).
A. Manita, “Intrinsic space scales for multidimensional stochastic synchronization models,” in New Perspectives on Stochastic Modeling and Data Analysis (ISAST, 2014), pp. 271–282.
Yu. Linnik, “Linear forms and statistical criteria,” Ukrain. Math. J. 5, 207–290 (1953).
M. Bladt, L. J. R. Esparza, and B. F. Nielsen, “Bilateral matrix-exponential distributions,” in Matrix-Analytic Methods in StochasticModels (Springer, New York, 2013), pp. 41–56.
S. Bhalla, “The performance of an efficient distributed synchronization and recovery algorithm,” J. Supercomput. 19, 199–219 (2001).
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Submitted by A. M. Elizarov
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Manita, A. Probabilistic issues in the node synchronization problem for large distributed systems. Lobachevskii J Math 38, 948–953 (2017). https://doi.org/10.1134/S1995080217050250
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DOI: https://doi.org/10.1134/S1995080217050250