Re: Every time ..., was Re: General formula

[Ed Gerck <egerck@xxxxxxxxxx>]

Alan Lloyd wrote:

> Ed - this is all too hard for me ... I cannot even predict how long my
> wife will be on the phone tonight

Alan:

Theory says that "how long your wife will be on the phone" does NOT
depend when you first noted that she was on the phone -- if this is
of any use to you, though it may already relate to your experience ;-)

This also means that if you call someone and it is busy, you could call
right afterwards (just add the round-trip total delay time -- say, 5 sec)
and your sucess rate should be the same as if you would wait some
minutes (as people normally do).

The reason in both cases is simple -- since phone statistics is given by
a Poison distribution and you don't know when the conversation actually
*started*, its end does not depend on the duration of your observation.

So, theory is nice -- when it corresponds to reality (as the above two
examples do). It allows us to use elevators, credit and rely on chemistry.


> or the number of times my mobile will drop out when using it (hands free
> of course) in the car.

I might be tempted to model it ;-)

> As to certificate usage and lifetime - theory is useful - but practice
> makes perfect.

Oh, not the cliche again! Don't have anything better down there?

> What is the lifetime of a Bus or Train ticket... It depends on the
> attitude and hunger of the damn machines that read them...QED

No -- their lifetime is actually the expected duration of their existence as
tickets, ie, the expected duration of time that you can still use them. Well,
I do have a metro ticket for Washington DC that I use for three months
now... and I sure expect them to be valid this whole year, their lifetime.

> PS - This person that predicted phone calls and phone connections - gee
> he must be "one from on high" - can you ask him how big my next month's
> bill will be :-)

His name was Agner Krarup Erlang -- Eralng for short. And his name is also
the unit for phone traffic.

 A.K. Erlang was the first person to study the problem of telephone networks.
 By studying a village telephone exchange he worked out a formula, now known
 as Erlang's formula, to calculate the fraction of callers attempting to call someone
 outside the village that must wait because all of the lines are in use. Although
 Erlang's model is a simple one, the mathematics underlying today's complex
 telephone networks is still based on his work.

Check in
 http://pass.maths.org.uk/issue2/erlang/index.html


> PPS good luck with the paper - is it signed - and how many
> attributes does it have.?

That is why long postings must be very carefully written; the more
you write the less it tends to live without at least one correction. I hope
this may be a good enough excuse for my long postings.... I risk more
when they are long ;-)

Cheers,

Ed Gerck
______________________________________________________________________
Dr.rer.nat. E. Gerck                                 egerck@mcg.org.br
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