A Martingale-Envelope and Applications

ABSTRACT In the framework of stochastic network calculus we present a new envelope-based approach which uses martingales to characterize a queueing system. We show that this setting allows a simple handling of multiplexing and scheduling: whereas multiplexing of several sources results in multiplication of the corresponding martingales, per-flow analysis in a scheduled system can be done by shifting the martingales to a certain point in time. Applying this calculus to Markov Arrival Processes, it is shown that the performance bounds can become reasonably tight