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FAX: 919 - 660 - 5293. Abstract. A number of analytical software reliabil- ity models have been proposed for estimat- ing the reliability growth of a software prod-.
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A Poisson{Hopf algebra of smooth functions on the (1+1) Cayley{Klein groups is constructed by using a classical r{matrix which is invariant under contraction.
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The Failure of Poisson Modeling. John Blesswin. Page 2. Outline. ⢠Introduction. ⢠Traces data. ⢠TCP connection i
The Failure of Poisson Modeling John Blesswin
Outline Introduction Traces data TCP connection interarrivals TELNET packet interarrivals Fully modeling TELNET originator traffic FTPDATA connection arrivals Large-scale correlations and possible connections to selfsimilarity • Implications • • • • • • •
1. Introduction (1) • In many studies, both local-area and wide-area network traffic, the distribution of packet interarrivals clearly differs from exponential. – [JR86,G90,FL91,DJCME92]
• For self-similar traffic, there is no natural length for a “burst”; traffic bursts appear on a wide range of time scales. • Poisson processes are valid only for modeling the arrival of user sessions – TELNET connections, FTP control connections – WAN packet arrival processes appear better modeled using selfsimilar process
1. Introduction (2) • This paper show that, in some cases commonly-used Poisson models seriously underestimate the burstiness of TCP traffic over a wide range of time scales. (time scales >= 0.1 sec) • Using the empirical TCPlib distribution for TELNET packet interarrivals instead results in packet arrival process significantly burstier than Poisson arrivals. • For small machine-generated bulk transfers such as SMTP(email) and NNTP(network news), connection arrivals are not well modeled as Poisson.
1. Introduction (3) • For large bulk transfer, FTPDATA traffic structure is quite different than suggested by Poisson models. – FTPDATA in bytes in each burst has a very heavy upper tail – A small fraction of the largest bursts carries almost all of the FTPDATA bytes. • Poisson arrival processes are quite limited in their burstiness, especially when multiplexed to a high degree. • Wide-area traffic is much burstier than Poisson models predict over many time scales.
