Abstract

Random walks with additive increase and multiplicative decrease are widely used for performance control and modeling in telecommunication, smart spaces and some biological systems as well. There exists in the literature two mainstream approaches which apply discrete stepwise and piecewise linear random processes. Meanwhile most real implementations of the algorithms used by the networking applications support discrete arithmetics for its key variables. Therefore piecewise linear models provide approximate results and the applicability of these results needs further studies. In the paper we consider the connection between discrete stepwise and piecewise linear models and provide the boundary estimation for the important characteristic of the stepwise random process in terms of the piecewise linear random process.