Matrix Analytic Methods

  • Winfried K. Grassmann
  • David A. Stanford
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 24)


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.


Markov Chain Transition Matrix Type Process Computational Probability Naval Research Logistics 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Winfried K. Grassmann
    • 1
  • David A. Stanford
    • 2
  1. 1.Department of Computer ScienceThe University of SaskatchewanSaskatoonCanada
  2. 2.Department of Statistical & Actuarial SciencesThe University of Western OntarioLondonCanada

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