Time-Dependent Behavior of Fluid Buffer Models with Markov Input and Constant Output Rates

Abstract

The authors study a method for the analysis of fluid buffer models with Markov input rate and constant output rate. In telecommunications applications, the constant output rate typically represents a fixed-rate transmission channel. Given the initial system state, the conditional (time-dependent) survivor function and moments of the buffer content are characterized as the solution of an integral equation. The method depends on the solution of a first passage time problem for the cumulative input process (an integrated Markov process) which is described by a Fredholm integral equation of the second kind. Under appropriate conditions, the integral equation has a Neumann series solution that can be found by successive approximations. Numerical results are presented for a specific example of a buffer shared by a number of input sources varying as independent Ornstein–Uhlenbeck diffusion processes, which may be used, for instance, as a model for statistically multiplexed variable bit-rate video.