We can obtain the equilibrium solutions for this system by setting

and obtaining the state distribution p_i∀ i such that the normalization condition

is satisfied.

Note that the first condition amounts to saying that for a system at equilibrium, the rate of change of all the state probabilities must be zero (this is as per the definition of a system at equilibrium). The second condition is also logical as that amounts to saying that the system has to be in some state or the other at all times and that this condition would also hold at equilibrium.

This yields the following equations to be solved for the state probabilities under equilibrium conditions-

The solution is -			(2.2)
			(2.3)

Note that the equation given by (2.3) arises directly from the normalization condition mentioned earlier, given that the individual state probabilities are given by (2.2)

The state probabilities given by (2.2) are in the form of a continued product. This is an interesting form as equilibrium solutions of this form will arise naturally in many queueuing analysis. Solutions of this form are referred to as Product Form Solutions.