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.