A circle of interacting servers; spontaneous collective behavior in case of large fluctuations

Details A circle of interacting servers; spontaneous collective behavior in case of large fluctuations A circle of interacting servers; spontaneous collective behavior in case of large fluctuations

2008-03-18

arxiv.org/abs/0803.2576v1

Mathematics

Probability

22 pages

Scientific paper

We consider large fluctuations, namely overload of servers, in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers, the messages of any flow are distributed between two neighboring servers, upon its arrival a message is directed to the least loaded of these servers. Under the condition that at least two servers are overloaded the number of overloaded servers in such network depends on the rate of input flows. In particular there exists critical level of input rate that in case of higher rate most probable that all servers are overloaded.

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