Felix Poloczek
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.
- E. Buffet and N. G. Duffield. Exponential upper bounds via martingales for multiplexers with Markovian arrivals. Journal of Applied Probability, 31(4):1049--1060, 1994.Google Scholar
Cross Ref
- G. Choudhury, D. Lucantoni, and W. Whitt. Squeezing the most out of ATM. IEEE Transactions on Communications, 44(2):203--217, Feb. 1996.Google ScholarCross Ref
- F. Ciucu, F. Poloczek, and J. Schmitt. Sharp Bounds in Stochastic Network Calculus. ArXiv e-prints, Mar. 2013.Google Scholar
- F. Ciucu and J. Schmitt. Perspectives on network calculus: no free lunch, but still good value. SIGCOMM Comput. Commun. Rev., 42(4):311--322, Aug. 2012. Google ScholarDigital Library
- N. G. Duffield. Exponential bounds for queues with Markovian arrivals. Queueing Systems, 17(3-4):413--430, Sept. 1994.Google ScholarCross Ref
Index Terms
- A martingale-envelope and applications
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