NetRule was the first tool to be based on analytical methods. The Poisson distribution for packet arrivals is a basis for several of the methods. A concise definition of the Poisson distribution can be found at wikipedia.org, Poisson Distribution. Since early 1998, when NetRule was offered on the market, other applications have come to market which also use analytical methods. None of them have the breadth and depth that NetRule does in producing results.
Using analytical methods results in run times that are small fractions of the time to run discrete event simulations. Scaling up to very large networks with thousands of nodes in NetRule incurs a cost of additional seconds in run time; you won't have to wait for hours, or days for the model to run.
One run of an analytically based evaluation in NetRule is sufficient to obtain mathematically valid steady-state results. One run is not sufficient for discrete simulation events, unless the simulation runs long enough for the network to reach a steady-state condition. Most users of discrete event simulations ignore, or don't know, that multiple discrete runs of the same options in the model should be made. This mathematical requirement exists because discrete event simulators use statistical traffic generators. They produce a sample of traffic; along with typical samples, they can produce "rare" samples. An analysis of variance on repeated runs of a discrete event simulation tells you whether you have a set of "typical" runs or not. While analytical methods also use statistical traffic generators, the mathematics are applied via the calculations in NetRule to arrive quickly and unerringly at the steady-state.
During the mid-1990's articles appeared in the academic world claiming that the Poisson distribution, which NetRule uses to describe traffic arrival, did not describe Internet traffic well and adjustments were required for self-similar and long range dependency in Internet traffic. As often happens, further investigation by researchers yielded causes for these incorrect conclusions. Traffic measurement that could not distinguish partial packets from whole ones led to anomalies in the data being analyzed and a misfit to the Poisson distribution for small packets occurred in the earlier studies. The paper below provides technical notes about this:
Grout, V., Cunningham, S., Oram, D. & Hebblewhite, R.,
A Note on the Distribution of Packet Arrivals in High-Speed Data Networks, Proceedings of IADIS International Conference WWW/Internet 2004, Madrid, Spain, 6th-9th October 2004, pp889-892.
A more detailed study with the following conclusions about Internet traffic characteristics was published in "Nonlinear Estimation and Classification,"
eds. C. Holmes, D. Denison, M. Hansen, B. Yu, and B. Mallick, Springer, New York, 2002.
"Starting at low connection loads on an uncongested link, packet arrivals tend toward Poisson and packet sizes tend toward independence as the load increases. ...On a link with a sufficiently large speed that the increasing connection load can bring the traffic to Poisson and independence before substantial upstream queueing occurs, the onset of queueing does not resurrect the long range dependence. All this means that the burstiness of traffic, once thought to pervade the whole Internet, dissipates with the connection load."
The authors are in the Computing and Mathematical Sciences Research Division, Bell Labs, Murray Hill, NJ. This paper can be viewed at
Internet Traffic Tends toward Poisson ....
The conclusions in this paper are consistent with the results of NetRule customers who have tested NetRule's predictions against real networks.