Mathematical models of some evolutionary systems under the influence of stochastic factors
Rodríguez Said, Roberto D.
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As it is known, the problem of availability of information is normally addressed using a buffer. Most of the times it is required that the effectiveness or reliability of the system is calculated to optimize the amount of stored information according to the customers random requests and to the amount of incoming information from the supply line. In this thesis, we consider the case of single buffer connected to any number of customers with bursty demands. We model the variation of the level of stored information in the buffer as an evolution in a random media. We assume that the customers can be modeled as semi-Markov stochastic processes and we use the phase merging algorithm to reduce the evolution process in a semi-Markov to an approximated evolutions in a Markov media. Then we obtain a general solution to the stationary probability density of the level of the buffer and general results for the stationary efficiency of the system.