A feedback fluid queue with two congestion control thresholds

R. Malhotra, M.R.H. Mandjes, Willem R.W. Scheinhardt, Hans Leo van den Berg

Research output: Contribution to journalArticle

  • 10 Citations

Abstract

Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.
LanguageUndefined
Pages149-169
Number of pages21
JournalMathematical methods of operations research
Volume70
Issue number1
DOIs
StatePublished - 2009

Keywords

  • Feedback regulation
  • Spectral expansion
  • EWI-20933
  • Congestion control
  • METIS-292501
  • Fluid queues
  • IR-80266

Cite this

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title = "A feedback fluid queue with two congestion control thresholds",
abstract = "Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.",
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A feedback fluid queue with two congestion control thresholds. / Malhotra, R.; Mandjes, M.R.H. ; Scheinhardt, Willem R.W.; van den Berg, Hans Leo.

In: Mathematical methods of operations research, Vol. 70, No. 1, 2009, p. 149-169.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A feedback fluid queue with two congestion control thresholds

AU - Malhotra,R.

AU - Mandjes,M.R.H.

AU - Scheinhardt,Willem R.W.

AU - van den Berg,Hans Leo

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N2 - Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.

AB - Feedback fluid queues play an important role in modeling congestion control mechanisms for packet networks. In this paper we present and analyze a fluid queue with a feedback-based traffic rate adaptation scheme which uses two thresholds. The higher threshold $B_1$ is used to signal the beginning of congestion while the lower threshold $B_2$ signals the end of congestion. These two parameters together allow to make the trade-off between maximizing throughput performance and minimizing delay. The difference between the two thresholds helps to control the amount of feedback signals sent to the traffic source. In our model the input source can behave like either of two Markov fluid processes. The first applies as long as the upper threshold $B_1$ has not been hit from below. As soon as that happens, the traffic source adapts and switches to the second process, until $B_2$ (smaller than $B_1$) is hit from above. We analyze the model by setting up the Kolmogorov forward equations, then solving the corresponding balance equations using a spectral expansion, and finally identifying sufficient constraints to solve for the unknowns in the solution. In particular, our analysis yields expressions for the stationary distribution of the buffer occupancy, the buffer delay distribution, and the throughput.

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