Performance bounds for high-speed communications systems

Markov modulated Poisson processes (MMPP) with time-varying (possibly stochastic) rates are often used to model traffics in high-speed communications systems. For systems with MMPP arrivals, we obtain bounds for moment generating functions of the queue length processes and exponential bounds for the tail distributions. These bounds are useful for characterizing quality of service a system can provide to its users. An approach utilizing the theory of differential equations is adopted. The bounds given in this paper are tighter than those previously available for the same type of system. In fact, the bounds can be made arbitrarily tight given sufficient computational effort.