Re: Telephone call time distribution

danheyman_at_yahoo.com
Date: 01/25/05 

Date: 25 Jan 2005 15:33:55 -0800

The exponential distribution was empirically verified by early
teletraffic engineers. A (circa) 1956 paper by R. Wilkenson the the
BELL SYSTEM TECHINICAL JOURNAL about traffic engineering in the USA
might give some details. Look at INTRO TO QUEUEING THEORY by R. B.
Cooper for an exact reference and for more discussion. These
measurements were done before computer messages and cell-phone calls.

The large amount of probability near 0 for the expo dst. was not a bad
fit to the calls that were incomplete because the caller abandoned
after dialing several digits. (The measurements were taken before
current electronic switching and the call holding time started when the
first digit was dialed and ended when the caller hung up.)

There is a paper by V. Bolotin in the 1997 Proc. of the International
Teletraffic Congress ( I think the year is correct, but I'm not sure)
claiming the the lognormal dst. fits data transmissions. I would use a
gamma dst. (which is close to the lognormal) because it's usually more
tractable.

If you know the first 3 moments of the holding times, there is a
graphical way to select a dst. from the following choices: exponential,
gamma, Weibull, hyper-exponential, Pareto and lognormal. All of these
dsts. can be parameterized by their coefficient of variation (=std.
dev./mean) and skewness (third central moment/ mean cubed). The idea of
the plot is by Cox and Oates, ANALYSIS OF SURVIVAL DATA, 1984. I
extended the idea and show an expanded figure in "Souce models for VBR
video conferences", IEEE/ACM Trans. Networking 4(1):40-48, Feb. 1996.
Dan Heyman