Spectral expansion solution

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Means of solving M/M/c queue models in queueing theory

In probability theory, the spectral expansion solution method is a technique for computing the stationary probability distribution of a continuous-time Markov chain whose state space is a semi-infinite lattice strip. For example, an M/M/c queue 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.

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References

Chakka, R. (1998). "Spectral expansion solution for some finite capacity queues". Annals of Operations Research. 79: 27–44. doi:10.1023/A:1018974722301. /wiki/Doi_(identifier) ↩
Mitrani, I.; Chakka, R. (1995). "Spectral expansion solution for a class of Markov models: Application and comparison with the matrix-geometric method". Performance Evaluation. 23 (3): 241. doi:10.1016/0166-5316(94)00025-F. /wiki/Performance_Evaluation ↩
Daigle, J.; Lucantoni, D. (1991). "Queueing systems having phase-dependent arrival and service rates". In Stewart, William J. (ed.). Numerical Solutions of Markov Chains. pp. 161–202. ISBN 9780824784058. 9780824784058 ↩