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Reference.org
Spectral expansion solution
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<p>In <a href="/facts/Probability_theory/mFBn51rE">probability theory</a>, the spectral expansion solution method is a technique for computing the stationary probability distribution of a <a href="/facts/Continuous-time_Markov_chain/h7ytJ6p3">continuous-time Markov chain</a> whose state space is a semi-infinite lattice strip. For example, an <a href="/facts/M%2fM%2fc_queue/MXB6lmQ1">M/M/c queue</a> where service nodes can breakdown and be repaired has a two-dimensional state space where one dimension has a finite limit and the other is unbounded. The stationary distribution vector is expressed directly (not as a transform) in terms of eigenvalues and eigenvectors of a matrix polynomial. </p>