## The Window Distribution of Idealized TCP Congestion Avoidance with Variable Packet Loss (1999)

Citations: | 49 - 4 self |

### BibTeX

@INPROCEEDINGS{Misra99thewindow,

author = {Archan Misra and Teunis J. Ott},

title = {The Window Distribution of Idealized TCP Congestion Avoidance with Variable Packet Loss},

booktitle = {},

year = {1999},

pages = {1564--1572}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper analyzes the stationary behavior of the TCP congestion window performing ideal congestion avoidance when the packet loss probability is not constant, but varies as a function of the window size. By neglecting the detailed window behavior during fast recovery, we are able to derive a Markov process that is then approximated by a continuous-time, continuous state-space process. The stationary distribution of this process is analyzed and derived numerically and then extrapolated to obtain the stationary distribution of the TCP window. This numerical analysis enables us to predict the behavior of the TCP congestion window when interacting with a router port performing Early Random Drop (or Random Early Detection) where the loss probability varies with the queue occupancy. Keywords---TCP, distribution, variable, loss. I. INTRODUCTION In this paper, we present a quantitative analysis of the stationary behavior of the evolution of the TCP congestion window (cwnd) ([1]) when the ...

### Citations

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(Show Context)
Citation Context ...m Bell Communications Research 445 South Street Morristown, NJ 07960 In this paper, we present a quantitative analysis of the stationary behavior of the evolution of the TCP congestion window (cwnd) (=-=[1]-=-) when the packet loss probability is variable and depends on the (instantaneous) window of the TCP connection. It can, thus, be viewed as a generalization of the analysis in ([2]) where the drop prob... |

2344 | Random Early Detection Gateways for Congestion Avoidance
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Citation Context ... observed very good agreement between simulations results and analytical predictions. We also investigated the applicability of this model when the router port performed Random Early Detection (RED) (=-=[11]-=-), so that the loss probability is a function of the average queue length. Although our memoryless state-dependent Markovian loss model does not accurately reflect the complicated effect of queue aver... |

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Citation Context ... time and p(Wn) is the loss probability associated with the value of the window Wn at ack time n. In other words, for a process defined under this 1 Readers familiar with Weighted Fair Queuing (WFQ) (=-=[12]-=-) may benefit from realizing that our subjective time formulation is analogous to that the definition of virtual time in WFQ; both attempt a state-dependent rescaling of time so that the process of in... |

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Citation Context ...increase of dt in the time We would also like to add a few words about the range of index t of X(t) corresponds to an increment of (X(t))dt in loss probabilities over which our analysis applies. Both =-=[3]-=- and the time index of Y ( ). A realization of the process Y will [4] have noted the importance of timeouts in analyzing the per- thus assume the same state-space values as the corresponding formance ... |

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Citation Context ...ng given by W (t) = p pW b t p c. (The time index generated by the rescaling is called subjective time in this paper.) The resulting analysis derived the well-known ‘square-root’ behavior of TCP (=-=[2],[9]-=-): the average window of a persistent TCP 1 connection is of the order of p . We shall also engage in simp ilar rescalings in this paper. While our space rescaling is still linear, the variable loss p... |

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Citation Context ...robabilities. The squareroot formula, which ignores the effects of TCP timeouts and fast recovery, has been rigorously derived in [2] and has also been separately reported through simpler analyses in =-=[6]-=- and [5] (the last publication also considers modifications to the formula resulting from losses of acknowledgement packets). Ott [8] stated that the throughput of persistent TCP (but not necessarily ... |

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Citation Context ...lity was assumed constant. The mathematical model abstracts TCP behavior into a continuous cycle of “congestion avoidance”, packet loss and “fast recovery”. We disregard the details of fast re=-=covery ([7]-=-) of TCP and assume an idealized behavior, whereby a packet loss that occurs when the congestion window is n MSSs instantaneously reduces the congestion window (and the number of unacknowledged packet... |

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Citation Context ...ty. We also applied this model to predict the window distributionof a persistent TCP connection that interacts with a router port, which handles this single flow and performs Early Random Drop (ERD) (=-=[10]-=-)). In an ERD port, the drop probability is a function of the instantaneous buffer occupancy (which we related to the instantaneous congestion window); we observed very good agreement between simulati... |

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Citation Context ...ties. The squareroot formula, which ignores the effects of TCP timeouts and fast recovery, has been rigorously derived in [2] and has also been separately reported through simpler analyses in [6] and =-=[5]-=- (the last publication also considers modifications to the formula resulting from losses of acknowledgement packets). Ott [8] stated that the throughput of persistent TCP (but not necessarily the cong... |

8 |
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Citation Context ...stion window (cwnd) ([1]) when the packet loss probability is variable and depends on the (instantaneous) window of the TCP connection. It can, thus, be viewed as a generalization of the analysis in (=-=[2]) where -=-the drop probability was assumed constant. The mathematical model abstracts TCP behavior into a continuous cycle of “congestion avoidance”, packet loss and “fast recovery”. We disregard the de... |

1 |
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Citation Context ... and has also been separately reported through simpler analyses in [6] and [5] (the last publication also considers modifications to the formula resulting from losses of acknowledgement packets). Ott =-=[8]-=- stated that the throughput of persistent TCP (but not necessarily the congestion window) starts behaving like 1 , when timeouts bep come significant. The recent work by Padhye et al [3] provides a be... |