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Queueing Theory - Series and Recursive Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67624] Queueing Theory - Series and Recursive Functions
  • From: "passwd9" <david at carter-hitchin.clara.co.uk>
  • Date: Sun, 2 Jul 2006 06:28:16 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I want to plot a 3d graph of the probability of the queue length of a
M/D/1 queue - the height of the surface will be the probability and
we'll have 'queue length' x and 'traffic intensity' rho in the 'x' and
'y' directions.  The problem is that there is no closed form for the
queue length probability function (at least as far as I know).  This is
a recursive function definition and has x+1 terms for each queue length
x probability.  It is defined as:

Px = e^(-rho) ( ( Po + P1) (1/x!) * rho^x + P2 * (1 / (x-1)!) *
rho^(x-1) + ... + Px * rho + Px+1 )

Some initial condition say Po = 1 - rho is used to start things off.

So can this function be coded up in Mathematica?  I looked through the
master index for 'recursive' and
'series' but I didn't find anything which looked applicable.  If this
is too difficult, then I have computed a few values by hand (so I have
a 4 x 3 matrix of Px's for different x's and rho's) and I would like to
graph those, but again, all the information I found on Plot3D suggests
it only takes functions as inputs.

Thanks for any help.

David.


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