Spectral expansion solution

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.^[1] 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.^[2]^[3]

References

^ Chakka, R. (1998). "Spectral expansion solution for some finite capacity queues". Annals of Operations Research. 79: 27–44. doi:10.1023/A:1018974722301.
^ 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.
^ 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.

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[1] Chakka, R. (1998). "Spectral expansion solution for some finite capacity queues". Annals of Operations Research. 79: 27–44. doi:10.1023/A:1018974722301.

[2] 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.

[3] 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.

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