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期刊名称: Problems of Information Transmission
Volume:55    Issue:2        Page:174-200
ISSN:0032-9460

The Geometry of Big Queues期刊论文

作者: Puhalskii A A
DOI:10.1134/S0032946019020054

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页码: 174-200
被引频次: 0
出版者: Pleiades Publishing,MAIK NAUKA/INTERPERIODICA/SPRINGER,Springer
期刊名称: Problems of Information Transmission
ISSN: 0032-9460
卷期: Volume:55    Issue:2
语言: English
摘要: We use Hamilton equations to identify most likely scenarios of long queues being formed in ergodic Jackson networks. Since the associated Hamiltonians are discontinuous and piecewise Lipschitz, one has to invoke methods of nonsmooth analysis. Time reversal of the Hamilton equations yields fluid equations for the dual network. Accordingly, the optimal trajectories are time reversals of the fluid trajectories of the dual network. Those trajectories are shown to belong to domains that satisfy a certain condition of being “essential.” As an illustration, we consider a two-station Jackson network. In addition, we prove certain properties of substochastic matrices, which may be of interest in their own right.
相关主题: large deviations, Jackson networks, queueing theory, Hamilton equations, dual Markov processes, Systems Theory, Control, Information Storage and Retrieval, fluid dynamics, Engineering, optimal trajectories, Communications Engineering, Networks, large deviation principle, Electrical Engineering, MATHEMATICS, APPLIED, COMPUTER SCIENCE, THEORY & METHODS, Fluid dynamics, Markov processes, Information management,

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