NDLI: Exponential bounds for the waiting time distribution in Markovian queues, with applications to TES/GI/1 systems

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Exponential bounds for the waiting time distribution in Markovian queues, with applications to TES/GI/1 systems

Content Provider	ACM Digital Library
Author	Devetsikiotis, Michael Lambadaris, Ioannis Fang, Youjian Kaye, A. Roger
Abstract	Several services to be supported by emerging high-speed networks are expected to result in highly bursty (autocorrelated) traffic streams. A typical example is variable bit-rate (VBR) compressed video. Therefore, traffic modeling and performance evaluation techniques geared towards autocorrelated streams are extremely important for the design of practical networks.The TES (Transform - Expand - Sample) technique has emerged as a general methodology for modeling autocorrelated random processes with arbitrary marginal distributions. Because of their generality and practical applicability, TES models can be readily used to accurately characterize bursty traffic streams in ATM networks.Although TES models can be easily implemented for simulation studies, the need still exists for analytical results on the performance of queueing systems driven by autocorrelated traffic. Of particular interest are the tails of the waiting time distribution in queues driven by TES-modeled bursty traffic. Such tail probabilities, when they become exceedingly small, may be difficult to obtain via conventional simulation.In order to extend existing results, based on Large Deviations theory, to TES processes, the main difficulty is posed by the continuous state-space of the TES time-series. In this paper, we develop a general result concerning exponential bounds for the waiting time under continuous state-space Markov arrivals. We apply this result to TES/GI/1 queues, show numerical examples, and compare our bound with simulation results. Accurate estimates of extremely low probabilities are obtained by employing fast simulation techniques based on importance sampling.
Starting Page	108
Ending Page	115
Page Count	8
File Format	PDF
ISBN	0897916956
DOI	10.1145/223587.223600
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1995-05-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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