Computational Probability pp 153-203 | Cite as

# Matrix Analytic Methods

## Abstract

This chapter shows how to find the equilibrium probabilities in processes of GI/M/1 type, and M/G/1 type, and GI/G/1 type by matrix analytic methods. GI/M/1-type processes are Markov chains with transition matrices having the same structure as the imbedded Markov chain of a GI/M/1 queue, except that the entries are matrices rather than scalars. Similarly, M/G/1 type processes have transition matrices of the same form as the imbedded Markov chain of the M/G/1 queue, except that the entries are matrices. In the imbedded Markov chain of the GI/M/1 queue, all columns but the first have the same entries, except that they are displaced so that the diagonal block entry is common to all. Similarly, in the M/G/1 queue, all rows except the first one are equal after proper centering.

## Keywords

Markov Chain Transition Matrix Type Process Computational Probability Naval Research Logistics## Preview

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