Optimal flow control of a stochastic fluid-flow system

This paper is concerned with the optimal flow control of an ATM switching element in a broadband-integrated services digital network. We model the switching element as a stochastic fluid-flow system with a finite buffer, a constant output rate, and Markov-modulated fluid input. There is a cost of holding fluid and a reward for admitting the fluid to the buffer. We study the optimal flow control policies that minimize the fetal expected discounted cost. We analyze the problem by two different approaches and show that the optimal policy is of the turnpike type with the turnpike levels dependent on the states of the Markov-modulated source. We also state sufficient conditions under which the optimal turnpike levels are monotonic functions of the states of the Markov-modulated source