## Wide-Area Traffic: The Failure of Poisson Modeling (1995)

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Venue: | IEEE/ACM Transactions on Networking |

Citations: | 1493 - 21 self |

### BibTeX

@ARTICLE{Paxson95wide-areatraffic:,

author = {Vern Paxson and Sally Floyd},

title = {Wide-Area Traffic: The Failure of Poisson Modeling},

journal = {IEEE/ACM Transactions on Networking},

year = {1995},

volume = {3},

pages = {226--244}

}

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### Abstract

Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remote-login and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into "c...

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Citation Context ...of packet interarrivals clearly differs from exponential [JR86, G90, FL91, DJCME92]. Recent work argues convincingly that LAN traffic is much better modeled using statisticallysself-similar processes =-=[LTWW94], which ha-=-ve much different theoretical properties than Poisson processes. For self-similar traffic, there is no natural length for a "burst"; traffic bursts appear on a wide range of time scales. In ... |

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Citation Context ...sumes that each TELNET originator packet conveys one byte of user data, corresponding to a keystroke. Often, however, a packet carries more than one byte, either due to effects of the Nagle algorithm =-=[N84]-=- or because the TELNET connection is operating in “line mode” [B90] or “line-at-a-time mode” [PR83, S94]. For example, the LBL PKT-2 TELNET originator traffic comprised about 85,000 packets carrying 1... |

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Citation Context ...ects the burstiness found in actual TELNET traffic. (We do not model the TELNET response, only the user side.) The success with this model of using Tcplib packet interarrivals confirms the finding in =-=[DJCME92]-=- that the arrival pattern of user-generated TELNET packets has an invariant distribution, independent of network details. For small machine-generated bulk transfers such as SMTP (email) and NNTP (netw... |

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Citation Context ... bytes transferred in each direction. The BC and UCB traces are analyzed in depth in [DJCME92], and also in [P94a], and the UCB trace forms the basis of the connection characteristics used for Tcplib =-=[DJ91]. The NC, UK, a-=-nd DEC traces are analyzed in [P94a], and the LBL traces are analyzed in [P94a, P94b]. The "DEC 1-3" rows represents three wide-area TCP SYN/FIN traces, each spanning 1 day, and the "LB... |

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Citation Context ...1:05 ! fi ! 1:25 is a good model for the amount of CPU time consumed by an arbitrary process [LO86]. In communications, heavy-tailed distributions have been used to model telephone call holding times =-=[DMRW94]-=- and frame sizes for variable-bit-rate video [GW94]. The discrete Pareto (Zipf) distribution [A83, p.95]: P [x = n] = 1=((n + 1)(n + 2)) for ns0: arises in connection with platoon lengths for cars at ... |

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Citation Context ... more precise notion of sustained correlation is that of “long-range dependence.” A stationary process is long-range dependent if its autocorrelation function r(k) is nonsummable (i.e., ∑ k r(k) = ∞) =-=[C84]-=-. Thus, the definition of long-range dependence applies only to infinite time series. The simplest models with long-range dependence are selfsimilar processes, which are characterized by hyperbolicall... |

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Citation Context ...d mixture of distributions), and because this is true of no other distribution, this invariance could in some respects explain the widespread observance of Pareto distributions in the social sciences =-=[M63]-=- [M83, p.344]. C Pareto interpacket times In this section we give some intuition for the observed long-range dependence of traces of TELNET traffic. Recall that the main body of the distribution of TE... |

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Citation Context ... traffic parameters of individual connections [CSZ92]. As has been shown by numerous researchers, such admissions control procedures could lead to a much more effective use of the available bandwidth =-=[YKTH93]-=-. Nevertheless, if the measured class has high burstiness consisting of both a high variance and significant long-range dependence, then an admissions control procedure that considers only recent traf... |

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Citation Context ... more precise notion of sustained correlation is that of "long-range dependence." A stationary process is long-range dependentsif its autocorrelation function r(k) is nonsummable (i.e., P k =-=r(k) = 1) [C84]-=-. Thus, the definition of long-range dependence applies only to infinite time series. The simplest models with long-range dependence are self-similar processes, which are characterized by hyperbolical... |

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Citation Context ...with location parameter a and shape parameter fi, for 1 ! fi ! 2. From Equation 4, the autocorrelation function r(k) is as follows: r(k) = ae Z 1 k i a x j fi dx: = aea fi fi 0 1 k (10fi) : Following =-=[BSTW94]-=-, the process fX t g t=0;1;2;::: is asymptotically self-similar if r(k)sk 0D L(k) as k !1; (5) for 0 ! D ! 1 and L a slowly-varying function. 2 Thus, for as0 and 1 ! fi ! 2, the count process of the M... |

33 |
On Traffic Phase Effects
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Citation Context ...n. In addition, TCP’s window flow control contributes a shorter-term periodicity to the traffic pattern, as each packet is transmitted in response to an acknowledgement returned for an earlier packet =-=[FJ92]-=-. It is particularly important to take into account these effects in simulations investigating changes to either TCP, the gateway scheduling algorithms, or the network’s packet-dropping algorithms. 8 ... |

24 |
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Citation Context ... we note that our source model of TELNET connections presented in x 5 in some respects matches the M/G/1 model described in the previous section. TELNET connection sizes in packets have a long-tailed =-=[WT92]-=- distribution, in that the tail function of a log-normal distribution decreases more slowly than any exponential function. While we show in Appendix E that the M/G/1 queue with log-normal service time... |

22 |
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Citation Context ...so occur due to the presence of non-stationarity. In addition to looking at variance-time plots of the TELNET traffic, we also used Whittle's procedure [GW94, LTWW94] and Beran's goodness-of-fit test =-=[B92a]-=- to gauge the agreement between the traffic and the simplest type of self-similar process, fractional Gaussian noise [B92b]. All of the results are consistent with selfsimilarity on scales of tens of ... |

21 |
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Citation Context ... do not fit a Poisson model, since earlier work looking at many different components of interactive traffic failed to find any statistically significant exponential fits to the observed distributions =-=[FJ70]-=-. This leaves the question: What are the consequences of using Poisson packet arrivals rather than the Tcplib distribution for TELNET traffic? (Row 1: Tcplib Interarrivals. Row 2: Exponential Interarr... |

13 |
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Citation Context ...ata, corresponding to a keystroke. Often, however, a packet carries more than one byte, either due to effects of the Nagle algorithm [N84] or because the TELNET connection is operating in "line m=-=ode" [B90] or "-=-line-at-a-time mode" [PR83, S94]. For example, the LBL PKT-2 TELNET originator traffic comprised about 85,000 packets carrying 139,000 user data bytes. Given these difficulties, we attempted to f... |

12 |
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Citation Context ...islands, cities and extinction events [K93, M63]. Leland and Ott also found that a Pareto distribution with 1.05 < β < 1.25 is a good model for the amount of CPU time consumed by an arbitrary process =-=[LO86]-=-. In communications, heavy-tailed distributions have been used to model telephone call holding times [DMRW94] and frame sizes for variable-bit-rate video [GW94]. The discrete Pareto (Zipf) distributio... |

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8 |
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Citation Context ...isson fit somewhat, but still falls short of statistical consistency. The finding that TELNET connection arrivals are well-modeled as a Poisson process with fixed hourly rates is at odds with that of =-=[MM85], who foun-=-d that user interarrival times looked "roughly log-normal". We believe the discrepancy is due to characterizing the distribution of all of the interarrivals lumped together, rather than post... |

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Citation Context ...discusses the Pareto distribution and its occurrence in the physical world. The classical Pareto distribution with shape parameter fi and location parameter a has the cumulative distribution function =-=[HK80]-=-: F (x) = P [Xsx] = 1 0 (a=x) fi ; a; fis0; xsa; with the corresponding probability density function: f(x) = fia fi x 0fi01 : 13 If fis2, then the distribution has infinite variance, and if fis1, then... |

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4 |
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Citation Context ...oisson fit somewhat, but still falls short of statistical consistency. The finding that TELNET connection arrivals are wellmodeled as a Poisson process with fixed hourly rates is at odds with that of =-=[MM85]-=-, who found that user interarrival times looked “roughly log-normal”. We believe the discrepancy is due to characterizing the distribution of all of the interarrivals lumped together, rather than post... |

1 |
gordoni@netcom.com), "ufs'93 [Updated file size survey results]," USENET newsgroup comp.os.research, message 2ddp3b$jn5@darkstar.UCSC.EDU
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Citation Context ... bursts will vary considerably from one time to another; but they will be present. We also note that our finding that the size of an FTPDATA burst has a heavy tail matches a survey conducted by Irlam =-=[I93]-=- of the sizes of files in 1,000 file systems comprising 12 million files and 250 GB of data: 1.9% of the files accounted for 71% of the bytes, and 0.5% accounted for 54% of the bytes. We performed fit... |

1 |
gordoni@netcom.com), “ufs’93 [Updated file size survey results],” USENET newsgroup comp.os.research, message 2ddp3b$jn5@darkstar.UCSC.EDU
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(Show Context)
Citation Context ... bursts will vary considerably from one time to another; but they will be present. We also note that our finding that the size of an FTPDATA burst has a heavy tail matches a survey conducted by Irlam =-=[I93]-=- of the sizes of files in 1,000 file systems comprising 12 million files and 250 GB of data: 1.9% of the files accounted for 71% of the bytes, and 0.5% accounted for 54% of the bytes. We performed fit... |

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