Geometrical Optics Approach to Markov-Modulated Fluid Models

Geometrical Optics Approach to Markov-Modulated Fluid Models

We analyze asymptotically a differential-difference equation, that arises in a Markovmodulated fluid model. Here there are N identical sources that turn on and off, and when on they generate fluid at unit rate into a buffer, which process the fluid at a rate c < N. In the steady state limit, the joint probability distribution of the buffer content and the number of active sources satisfies a sy...

Fast Simulation of Markov Modulated Fluid Models

We consider fluid models consisting of finite buffers, constant capacities and input processes modulated by continuous time Markov chains. These models are continuous flow approximations for describing the actually discrete traffic and buffer behaviour in ATM networks. A main issue is to find good estimates of buffer overflow and loss probabilities when they are (very) small, i.e. of the order ...

Markov Modulated Linear Fluid

Markov Modulated Linear Fluid

Markov-modulated Feedforward Fluid Networks

With the aim of studying a multi-station feedforward uid network with Markov modulated input and output rates we rst study a two dimensional parallel network having the property that the second station cannot be empty unless the rst station is. A method for computing the steady state characteristics of such a process is given and it is shown that this can be used to determine the steady state c...