[e2e] Re: Where can I find statistics data on traffic over current high speed internet?

W. S. Cleveland wsc at research.bell-labs.com
Sun Jul 21 11:52:24 PDT 2002

The old but still relevant query below made its way to me.

Conventional wisdom until recently had it that the LRD of Internet traffic
occurred from the edges to the core. The conventional is false in the sense that 
is relevant for network engineering of the core.

We showed that packet inter-arrival times tend from LRD toward Poisson and the 
packet size process tends from LRD toward independent  as the traffic load
increases, both due to increased statistical multiplexing. There is always an 
LRD component in the inter-arrivals and the sizes, but the contribution of the 
component to the variability of each time process gets less and less. 

Packet and byte counts in fixed intervals maintain their LRD but their standard 
deviation relative to the mean decreases toward zero, so the LRD becomes 
irrelevant because the long excursions due to LRD above and below the mean 
traffic rate are so small that the excursions are irrelevant for traffic 

One might immediately question this on the basis that there is a contradiction.
The counts maintain their LRD but the sizes and inter-arrivals do not, even 
though the former two come from the latter two. The explanation is this. As the 
traffic load increases, the  smaller and smaller LRD components in the sizes and 
inter-arrivals are magnified more and more in forming the counts because going 
from sizes and inter-arrivals to counts is an aggregation process across traffic 
sources, which gets greater as the load increases, and magnifies more.

Should we care? The answer is yes. The queueing on links tends to that of 
Poisson and independent as the load increases. We are in the process of a 
careful study of queueing and of the utilization (as a function of load) that a 
link can bear and drop only a very small fraction of packets. We have found
so far that for very high traffic rates, say 200 mbps 3-minute average and above 
(from OC48 traffic measurement), the queueing results (1) for the real data, (2) 
for our FSD models which fit the real data very well, and (3) for a 
Poisson/independent model, give identical results for practical purposes.
Utilizations can be quite high, around 90%, going higher or lower depending on 
the strictness of the QoS criterion.

The traffic results can be found at 
The latest paper (to be published in a Springer book) is the most readable on 
this because we are getting better at explaining results. The 
queueing/utilization results will be available in a few weeks.

William S. Cleveland  http://www.stat.bell-labs.com/wsc
Bell Labs, 600 Mountain Av., Murray Hill, NJ 07974
908-582-6861 (phone)  908-582-3340  (fax)

> From: "Jing Shen" <jshen at cad.zju.edu.cn>
> To: <te-wg at UU.NET>
> Cc: <mpls at UU.NET>, <ippm at advanced.org>, <irtf-rr at puck.nether.net>,
>   <end2end-interest at postel.org>
> Date: Sun, 17 Mar 2002 15:26:05 +0800
> Subject: [ippm] Where can I find statistics data on traffic over current high 
> speed internet?
> Precedence: bulk

> Hi,

> I've read some books and papers on network traffic characteristics . But, all 
> of them seem to be measured before 1999 when
> internet is not such a high speed one. (  As I know, from 1996 to 2001
> ChinaNet  has involved from 45Mbps to 10Gbps, the subdomain of
> it involved from 2Mbps to 2.Gbps , more and more people start to enjoy stream 
> media, multiuser game
> other than only static web pages) .  

> I'm sure the self-similar character of internet traffic mainteins with the   
> network speed improvement,  
> But the distribution of these traffic between different protocols,  the size  
> distribution must have changed
> much.  ( It seems to no measurement done with ChinaNet)

> So, I want  to know where I can  find statistics data on current high speed   
> internet?  

> Thank you very much.

> Jing Shen

> State Key Lab of CAD&CG
> ZheJiang University 
> P.R.China

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