Statistical Traffic Envelopes for Markov-Modulated Poisson Packet Sources

In this paper, we develop a method for using traffic sources modelled as a Markov modulated Poisson processes (MMPP) in the framework of the recently developed theory of the statistical traffic and service envelopes, referred to as the statistical approach. The statistical approach is a powerful and general framework for providing straightforwardly an approximated evaluation of the delay and buffer tail distributions in network schedulers. However, the input of the statistical approach is the statistical traffic envelope, which is not available for generic MMPP sources. We provide two statistical traffic envelopes, named two-moments and upper-bounding bucket, for a generic MMPP source, so as to use the rich collection of MMPP models of voice, audio, data and video sources available in the literature within the framework of the statistical approach. In this way, we can avoid the computational complexity of traditional Markov analysis with MMPP traffic, due to the exploding number of states as the number of MMPP sources grows. The tighter approximation is provided by the two-moments envelope while with the upper-bounding bucket envelope we can obtain simple closed-form solutions.