Characterization of the stationary distribution of the batch-transfer networks as a product of biased geometric distributions

Consideration was given to the class of exponential queuing networks with batch arrivals and batch servicing. The messages arriving to the network nodes form random-size batches of customers associated with these nodes. Upon completion of servicing a current batch, it discharges the network and send...

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Bibliographic Details
Published inAutomation and remote control Vol. 71; no. 12; pp. 2534 - 2546
Main Authors Malinkovskii, Yu. V., Korobeinikova, E. V.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.12.2010
Subjects
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Computer-Aided Engineering (CAD
Control
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Robotics
Stochastic Systems
Systems Theory
Geometric Distribution
Stationary Distribution
Terminal Node
Network Node
Remote Control
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Summary:Consideration was given to the class of exponential queuing networks with batch arrivals and batch servicing. The messages arriving to the network nodes form random-size batches of customers associated with these nodes. Upon completion of servicing a current batch, it discharges the network and sends a message, if any, to the rest of the nodes according to some routing matrix. The necessary and sufficient conditions under which the stationary distribution of the network states is multiplicative were established in terms of the isolated nodes placed in a dummy random medium. These conditions underlie characterization of the stationary distribution in the form of biased geometric distributions.
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117910120040