NDLI: Asymptotic buffer overflow probabilities in multiclass multiplexers: an optimal control approach

Content Provider	IEEE Xplore Digital Library
Author	Bertsimas, D. Paschalidis, I.C. Tsitsiklis, J.N.
Copyright Year	1963
Abstract	We consider a multiclass multiplexer with support for multiple service classes and dedicated buffers for each service class. Under specific scheduling policies for sharing bandwidth among these classes, we seek the asymptotic (as the buffer size goes to infinity) tail of the buffer overflow probability for each dedicated buffer. We assume dependent arrival and service processes as is usually the case in models of bursty traffic. In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper bound on the buffer overflow probabilities. We introduce a novel optimal control approach to address these problems. In particular, we relate the lower bound derivation to a deterministic optimal control problem, which we explicitly solve. Optimal state trajectories of the control problem correspond to typical congestion scenarios. We explicitly and in detail characterize the most likely modes of overflow. We specialize our results to the generalized processor sharing policy (GPS) and the generalized longest queue first policy (GLQF). The performance of strict priority policies is obtained as a corollary. We compare the GPS and GLQF policies and conclude that GLQF achieves smaller overflow probabilities than GPS for all arrival and service processes for which our analysis holds. Our results have important implications for traffic management of high-speed networks and can be used as a basis for an admission control mechanism which guarantees a different loss probability for each class.
Sponsorship	IEEE Control Systems Society
Starting Page	315
Ending Page	335
Page Count	21
File Size	1050839
File Format	PDF
ISSN	00189286
Volume Number	43
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1998-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Buffer overflow Optimal control Global Positioning System Traffic control Multiplexing Bandwidth H infinity control Tail Upper bound Communication system traffic control
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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