MATLAB: Help with differential equation Kolmogorov in queuing theory

differential equationode45

Hi everybody,
I have a problem with differential equation Kolmogorov in queuing theory. Now I need to write a code to solve the equation system (1) with the condition (2) and (3) according to Euler method. I wrote the code but the output didn't seem right (please see images). Any one can see my code and give me some advices. Thanks so much
clear all
tspan = [0:0.01:5];
n=6;
ic=zeros(1,n+1);
for ii=1:n+1
    ic(1,1)=1;
end
[t, p] = ode45(@odeFun, tspan, ic);
figure ('name','xac suat theo time')
plot(t, p)
legend({'p7'})
function dpdt = odeFun(t, p)
lambda = 4.8;
mu = 2;
A=[-1 0 0 0 0 0 0;
  1 -1 0 0 0 0 0;
  0 1 -1 0 0 0 0;
  0 0 1 -1 0 0 0;
  0 0 0 1 -1 0 0;
  0 0 0 0 1 -1 0;
  0 0 0 0 0 1 0];
B=[0 1 0 0 0 0 0;
   0 -1 0 0 0 0 0;
   0 0 -2 2 0 0 0;
   0 0 0 -2 2 0 0;
   0 0 0 0 -2 2 0;
   0 0 0 0 0 -2 2;
   0 0 0 0 0 0 -2];
dpdt = (lambda.*A + mu.*B)*p;
end
.

Best Answer

Your code doesn't maintain condition (2) for all times. You should eliminate p6 from equations (1) using condition (2), then use the ode solver to solve for the others. You can subsequently calculate p6 for each timestep.
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