On the tail of the arrival process
Presented in the proceedings of ITCOM in October 2004

Khushboo Shah
Department of Electrical Engineering
University of Southern California

Stephan Bohacek
Department of Electrical and Computer Engineering
University of Delaware

Andre Broido
Cooperative Association for Internet Data Analysis - CAIDA
San Diego Supercomputer Center,
University of California, San Diego

We examine the cause of the tail of the distribution of the number of packet and byte arrivals at backbone routers. One possible cause is that sometimes there are a large number of active connections resulting in a large number of arrivals in a short period of time. Another possibility is that the tail is due to one or a few very fast connections. By examining time-stamped packet headers from several backbone links, we find that the tail is neither strictly from many users nor strictly from fast connections. Rather, at some times and some time-scales, we find that the tail (the skewness of the distribution in particular) is strongly influenced by the tail of the distribution of the number of active connections, while at other times, the tail of the number of arrivals is due to the tail of the distribution of the connection bit-rates.