Radon spectroscopy of inter-packet delay

    by Andre Broido, Ryan King, Evi Nemeth, kc claffy 

                   Abstract

We demonstrate the feasibility of Internet spectroscopy
techniques for analysis of rate limiting, packet
interarrival delay and passive bitrate estimation
of cell- or slot-based broadband connections.
Working with highly diverse packet trace data, we find
that delay's quantization in micro- and millisecond range
is ubiquitous in today's Internet and that different
providers have strong preferences for specific delay
quanta in their infrastructures. 

The paper consists of two parts. First part presents
an algorithm that evaluates interarrival delay quantum
(cell time) for rate-limited cell-based links.
The algorithm takes a joint 2D distribution of packet
sizes and interarrival times as its input. The 2D
distribution is then converted by a coarse-grained
Radon transform to a family of 1D marginals.
Each marginal has semantics of inter- and intra-packet
delay (i.e. link idle time) histogram that corresponds
to an assumed value of cell time. Our estimate of cell
time is the value that minimizes entropy of such a marginal,
i.e. makes it closest to a delta function.

As an application of Radon transform technique,
we determine the target cell time for the
rate limiting performed by the university commodity ISP 
to provide 20 Mbps connection over 155 Mbps link. This
allows to verify an under-fulfilment of the contract.
The knowledge of cell time enables us to compute
the distribution of inter-packet delay. We find that
it consists of two separate components overlapping
in time domain: a spike with a width of 
two cell times that corresponds to the 
rate limiter's fluctuations around target rate, 
and "true" link idle time, whose integral (ccdf)
closely follows a Weibull curve, while individual 
values are subject to a fine-grained delay quantization.
We also find that the link's high load makes the packet
arrival process to be very dissimilar with Poisson.
Combined with the rate limiter's long-term memory,
this deviation makes the byte counting process to be
strictly non-Gaussian over a very wide
range of aggregation intervals (up to 1 sec).

In the second part we analyze bitrates and other
properties of broadband mass-market connections.
We determine interarrival times for DSL and cable modem
sources by a simplified 1D version of the min-entropy
Radon algorithm applied to packets of fixed size
(40 or 1500 bytes). We find that delay quantization
in broadband access is dependent upon providers,
technologies and markets, even though the number
of choices appears to be rather limited. This suggests
that network spectroscopy has a potential for
source recognition, if a library of interarrival quanta
and inter-packet delay distributions is available.