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November, 1994 Phase Transition in a Load Sharing Loss Model
Vadim Malyshev, Philippe Robert
Ann. Appl. Probab. 4(4): 1161-1176 (November, 1994). DOI: 10.1214/aoap/1177004909


In this paper we analyze the following loss network: When a customer arrives at a node of the network, it is served by this node if the node is not occupied; otherwise it is transmitted to some empty node where it will be served at a different rate. For the simplest systems of this type with a very large number of nodes and with global sharing, we show the existence of second order phase transitions and present explicit formulas for probability characteristics. For local sharing, we study the case of an infinite network and present some convergence results. Formulas for small and large loads are obtained.


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Vadim Malyshev. Philippe Robert. "Phase Transition in a Load Sharing Loss Model." Ann. Appl. Probab. 4 (4) 1161 - 1176, November, 1994.


Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0812.60083
MathSciNet: MR1304779
Digital Object Identifier: 10.1214/aoap/1177004909

Primary: 60K25
Secondary: 60K20

Keywords: Loss network , loss probabilities , Stationary measures , thermodynamic limit

Rights: Copyright © 1994 Institute of Mathematical Statistics


Vol.4 • No. 4 • November, 1994
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