Controlled stochastic model of a communication system with multiple sources

A stochastic model of buffering in a data communication system is considered, with source and sink transmission parameters depending on the number of active sources. For models in this control setting the authors analyze an effective numerical method for evaluating the equilibrium distribution of buffer content. The theoretical basis of the method is established first. Then, it is shown that the method has the same complexity, in terms of the total number of sources, as known analytical methods for the model with constant parameters. Asymptotics for tail probabilities at high buffer levels and under heavy load are also derived, and the complexity of their computation is compared with that of evaluating explicit formulas. In comparison to earlier results this approach reduces the complexity of computing the probability of overflow and its asymptotic estimates. The speed-up stems from the application of interpolation schemes