Non-skip-free M/G/1 and G/M/1 type Markov chains

Non-skip-free M/G/1 and G/M/1 type Markov chains

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Article ID: iaor19982944
Country: United Kingdom
Volume: 29
Issue: 3
Start Page Number: 733
End Page Number: 758
Publication Date: Sep 1997
Journal: Advances in Applied Probability
Authors: , ,
Keywords: queues: theory
Abstract:

For Markov chains of M/G/1 type that are not skip-free to the left, the corresponding G matrix is shown to have special structure and be determined by its first block row. An algorithm that takes advantage of this structure is developed for computing G. For non-skip-free M/G/1 type Markov chains, the algorithm significantly reduces the computational complexity of calculating the G matrix, when compared with reblocking to a system that is skip-free to the left and then applying usual iteration schemes to find G. A similar algorithm to calculate the R matrix for G/M/1 type Markov chains that are not skip-free to the right is also described.

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