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Internet traffic tends toward Poisson and independent as the load increases, 2002. 14 Additional figures Mean results of the legitimate connection completion rates when using the fixedthreshold strategy and when using threshold timeout and linear timeout
"... Abstract — Network devices put packets on an Internet link, and multiplex, or superpose, the packets from different active connections. Extensive empirical and theoretical studies of packet traffic variables — arrivals, sizes, and packet counts — demonstrate that the number of active connections has ..."
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Abstract — Network devices put packets on an Internet link, and multiplex, or superpose, the packets from different active connections. Extensive empirical and theoretical studies of packet traffic variables — arrivals, sizes, and packet counts — demonstrate that the number of active connections has a dramatic effect on traffic characteristics. At low connection loads on an uncongested link — that is, with little or no queueing on the linkinput router — the traffic variables are longrange dependent, creating burstiness: large variation in the traffic bit rate. As the load increases, the laws of superposition of marked point processes push the arrivals toward Poisson, the sizes toward independence, and reduces the variability of the counts relative to the mean. This begins a reduction in the burstiness; in network parlance, there are multiplexing gains. Once the connection load is sufficiently large, the network begins pushing back on the attraction to Poisson and independence by causing queueing on the linkinput router. But if the link speed is high enough, the traffic can get quite close to Poisson and independence before the pushback begins in force; while some of the statistical properties are changed in this highspeed case, the pushback does not resurrect the burstiness. These results reverse the commonlyheld presumption that Internet traffic is everywhere bursty and that multiplexing gains do not occur. Very simple statistical time series models — fractional sumdifference (FSD) models — describe the statistical variability of the traffic variables and their change toward Poisson and independence before significant queueing sets in, and can be used to generate openloop packet arrivals and sizes for simulation studies. Both science and engineering are affected. The magnitude of multiplexing needs to become part of the fundamental scientific framework that guides the study of Internet
Random Scale Effects
"... Data sets with random location effects can have random scale effects as well and often do. This paper describes an approach to modeling data with both effects. We treat the case where there is a normal error distribution, but the methodology could be extended to other cases. The scale effects are mo ..."
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Cited by 5 (2 self)
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Data sets with random location effects can have random scale effects as well and often do. This paper describes an approach to modeling data with both effects. We treat the case where there is a normal error distribution, but the methodology could be extended to other cases. The scale effects are modeled by mixing the normal error variable with a random scale variable. Tools are provided for model building: (1) methods for identifying the location distributions and the scale distributions; (2) methods for checking specifications that are fundamental to the model such as independence of the location and scale effects and the normality of the errors.