An Upper Bound on Overflow Probability in Transient Source Systems

In this paper we consider a single buffer fluid model where sources arrive according to a Poisson process, and stay in the system for independent and identically distributed (iid) exponential amounts of time and then depart. While they are in the system, they generate fluid traffic that is modulated by iid finite state continuous time Markov chains (CTMC). The fluid in the buffer is drained at a constant rate. We study stability of the buffer content process, and then derive an exponential upper bound for the tail of the buffer content process in steady state. The results have applications in design and operation of ATM switches: we use them to develop call admission policies, and also for capacity design. Numerical results are presented to demonstrate the methodology. ∗Air Force Institute of Technology †University of North Carolina at Chapel Hill