Problem trying to solve queuing equations with dsolve

Hi,

I'm trying to solve the set of equations defined in page 63 of http://www.eecs.harvard.edu/~michaelm/postscripts/mythesis.pdf (in the internal numbering it's page 52). Two pages down you can see the solution. I'd like to reach something similar.

I've tried different modelings for dsolve. I assume there's no real way to model an infinite set of equation, but getting a close solution for a finite set would be good enough. I also tried decoupling into two different problems.... no success...

Here's one approach I used:

syms x0(t)

syms x1(t)

syms x2(t)

syms x3(t)

syms x4(t)

syms x5(t)

syms x6(t)

syms x7(t)

syms a

syms d

dsolve(diff(x1)==a*((x0^2)-(x1^2))-(x1-x2), diff(x2)==a*((x1^2)-(x2^2))-(x2-x3), diff(x3)==a*((x2^2)-(x3^2))-(x3-x4), diff(x4)==a*((x3^2)-(x4^2))-(x4-x5), diff(x5)==a*((x4^2)-(x5^2))-(x5-x6), diff(x6)==a*((x5^2)-(x6^2))-(x6-x7), x0(0)==1)

Can anyone help? any idea how to solve those equations???

Thanks!

   Amir

[Amir]

(In the above, I tried setting d to 2, to see if it simplifies things)