Bell Labs Internet Traffic Research

Inter-Arrival Time Plot



This is a trellis display with one page and two panels; it displays the HTTP start times for 2 of 10704 blocks of data. It was immensely informative for modeling the start times to see such displays for hundreds of blocks. And the only practical medium to communicate these MPMP displays is our medium of study, the Internet.

The left panel of the figure, an inter-arrival plot , displays the 2515 HTTP start times for one block, 7:45 a.m. to 8:00 a.m. on 12/11/98. Let s(k) for k = 1 to 2515 be the start times, and let t(k) = s(k) - s(k-1) for k = 2 to 2515 be the inter-arrival times. On the plot, l(k) = log base 2 t(k) is graphed against s(k). The log on the vertical scale is vital because inter-arrivals can vary over 16 powers of 2, a factor of about 64000, and small intervals are as important as large ones; so the vertical scale provides the requisite resolution to see this variation. The horizontal scale, however, conveys arrivals and inter-arrivals on the original scale. The connection rate over this block is 2.8 connections per second (c/s). The right panel of Figure 1 is an inter-arrival plot for the block 12:15 p.m. to 12:30 p.m. on the same day; the connection rate is 20.1 c/s.

Both panels show discreteness on the vertical scale, inter-arrivals piling up at a few values. This is a network effect, a small delay; each accumulation point is a time equal to the time it takes to process a packet in the network. For example, suppose two SYN packets are back to back, which happens a small fraction of the time. The inter-arrival time is the time it takes to read the first packet, which is the packet size times the wire speed; at the time of collection the speed was 10 megabits/sec.

Here is a collection of inter-arrival time plots (compressed postscript, pdf) used in the paper "On the Nonstationarity of Internet Traffic". Inter-arrival times of packets flowing from web servers to clients. Each page displays the packet inter-arrival times for one 5-minute interval. Due to large file size of the original plots, only a subset of 25 intervals out of 500 intervals is available for download here.