A fundamental problem of Internet traffic engineering is bandwidth estimation: determining the bandwidth (bits per second) required to carry traffic with a specific bit rate (bits per second) offered to an Internet link and satisfy quality-of-service requirements. The traffic is packets of varying sizes that arrive for transmission on the link. Packets can queue up and are dropped if the queue size (bits) is bigger than the size of the buffer (bits) for the queue. For the predominant traffic on the Internet, best-effort traffic, quality metrics are the packet loss (fraction of lost packets), a queueing delay (seconds) and the delay probability (probability of a packet exceeding the delay). This article presents an introduction to bandwidth estimation and a solution to the problem of best-effort traffic for the case where the quality criteria specify negligible packet loss. The solution is a simple statistical model: (1) a formula for the bandwidth as a function of the delay, the delay probability, the traffic bit rate and the mean number of active host-pair connections of the traffic and (2) a random error term. The model is built and validated using queueing theory and extensive empirical study; it is valid for traffic with 64 host-pair connections or more, which is about 1 megabit/s of traffic. The model provides for Internet best-effort traffic what the Erlang delay formula provides for queueing systems with Poisson arrivals and i.i.d. exponential service times.
"Bandwidth Estimation for Best-Effort Internet Traffic." Statist. Sci. 19 (3) 518 - 543, August 2004. https://doi.org/10.1214/088342304000000260