Linear system with only positive solutions

Hi,

I'm involved in the dimensioning of a markov chain.

In order to find its state probabilities I have constructed a system of equation, resulting in a sparse matrix of coefficients of the type Ax = b.

The problem is that when I solve the system (the solutions are correct, I already checked it), some states have negative solutions (which means that the probability of being in these states are negative (Headbang)).

Is there any rule/condition/property that the matrix A must have in order to obtain only Zero or Positive solutions?

Thanks in advance,

G.B.