
In other words:



Resulting state equations:
p_{0} = p_{0} (1  λΔt) + p_{1} μΔt p_{1} = p_{0} λΔt + p_{1} (1  λΔt  μΔt) + p_{2} μΔt p_{2} = p_{1} λΔt + p_{2} (1  λΔt  μΔt) + p_{3} μΔt p_{3} = p_{2} λΔt + p_{3} (1  λΔt  μΔt) + p_{4} μΔt ... 
And so on....
Final set of equations:
p_{0} λ = p_{1} μ p_{1} λ = p_{2} μ p_{2} λ = p_{3} μ p_{3} λ = p_{4} μ ... 
We can express every p_{i}, i = 1, 2, 3, ... in terms on p_{0}
Unfortunately, we do not (yet) know the value of p_{0}...
p_{0} + p_{1} + p_{2} + p_{3} + ... = 1 .... (5) 
Substituting p_{i} in equation (5) and we get:
p_{0} + (λ/μ)^{1} × p_{0} + (λ/μ)^{2} × p_{0} + (λ/μ)^{3} × p_{0} + .... = 1
1 p_{0} ×  = 1 1(λ/μ) p_{0} = 1  (λ/μ) = 1  ρ ...... (6) 
Notation:

p_{0} = (λ/μ)^{0} × (1(λ/μ)) p_{1} = (λ/μ)^{1} × (1(λ/μ)) p_{2} = (λ/μ)^{2} × (1(λ/μ)) p_{3} = (λ/μ)^{3} × (1(λ/μ)) ....




Example:
Equilibrium equation:


p_{0} λ = p_{1} μ p_{1} λ = p_{2} μ p_{2} λ = p_{3} μ p_{3} λ = p_{4} μ ... 
This is the same set of equation as before... (see: click here)