Ultrametric hierarchical resource utilization model using p-adic numbers

Computer Engineering, cognitive science, telecommunication, mathematical

We present a new model of resource utilization which we call the ultrametric model. It is based on a modeling of hierarchical resource utilization by p-adic numbers. This model can be used on a system with several resources which can be classified in order of importance. The state of such a system is a p-adic number. We define an elementary resource utilization as this state of the system, and a representation of the uses in the form of balls in the set of p-adic numbers has been advanced. From these models, and using state transitions at each change in resource utilization whether it is the arrival of a new customer, or a departure, we can demonstrate that the probability of resource utilization is governed by a Cauchy problem: a fractional differential equation, and more particularly, with the Vladimirov operator.

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