The Effect of Statistical Multiplexing on the Long-Range Dependence of Internet Packet Traffic

As the number of active connections (NAC) on an Internet link increases, the long-range dependence of packet traffic changes due to increased statistical multiplexing of packets from different connections. Four packet traffic variables are studied as time series — inter-arrival times, sizes, packet counts in 100 ms intervals, and byte counts in 100 ms intervals. Results are based on the following: (1) the mathematical theory of marked point processes; (2) empirical study of 2526 packet traces, 5 min or 90 sec in duration, from 6 Internet monitors measuring 15 interfaces ranging from 100 mbps to 622 mbps; (3) simple statistical models for the traffic variables; and (4) network simulation with NS. All variables have components of long-range dependence at all levels of the NAC. But the variances of the long-range dependent components of the sizes and of the inter-arrivals decrease to zero as the NAC increases; the sizes tend toward independent, and the inter-arrivals tend toward independent or very short range dependent. These changes in the sizes and inter-arrivals are not arrested by the increased upstream queueing that eventually occurs as the NAC increases. The long-range dependence of the count variables does not change with the NAC, but their standard deviations relative to the means decrease like one over the square root of the NAC, making the counts smooth relative to the mean. Theory suggests that once the NAC is large enough, increased upstream queueing should alter these properties of the counts, but in the empirical study and in the simulation study the NAC was not large enough to observe an alteration for 100 ms counts. The change in the long-range dependence of the sizes and inter-arrivals does not contradict the constancy of the long-range dependence of the counts because the summation operations that produce counts from the arrivals and sizes act on an increasing number of packets as the NAC increases.