Summary: 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 packetcounts – 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 link-input router – the traffic variables are long-range 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 link-input router. But if the link speed is high enough, the traffic can get quite close to Poisson and independence before the push-back begins in force; while some of the statistical properties are changed in this high-speed case, the push-back does not resurrect the burstiness. These results reverse the commonly-held presumption that Internet traffic is everywhere bursty and that multiplexing gains do not occur. Very simple statistical time series models – fractional sum-difference (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 open-loop 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 traffic. The engineering of Internet devices and Internet networks needs to reflect the multiplexing gains.
For the entire collection see [Zbl 1005.00018].