Matrix geometric method: Difference between revisions

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\end{pmatrix}</math>
 
where each of ''B''<sub>00</sub>, ''B''<sub>01</sub>, ''B''<sub>10</sub>, ''A''<sub>0</sub>, ''A''<sub>1</sub> and ''A''<sub>2</sub> are matrices. To compute the stationary distribution ''π'' writing ''π''&nbsp;''Q''&nbsp;=&nbsp;0 the [[balance equation]]s are considered for sub-vectors ''π''<sub>''i''</sub>
 
To compute the stationary distribution ''π'' writing ''π''&nbsp;''Q''&nbsp;=&nbsp;0 the [[balance equation]]s are considered for sub-vectors ''π''<sub>''i''</sub>
 
::<math>\begin{align}
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which can be solve to find ''π''<sub>0</sub> and ''π''<sub>1</sub> and therefore iteratively all the ''π''<sub>''i''</sub>.
 
==Matrix analytic method==
 
{{Main|Ramaswami’s formula}}
The '''matrix analytic method''' is a more complicated version of the matrix geometric solution method used to analyse models with block [[M/G/1 queue|M/G/1]] matrices.<ref>{{cite doi|10.1002/9780470400531.eorms0631}}</ref> Such models are harder because no relationship like ''π''<sub>''i''</sub>&nbsp;=&nbsp;''π''<sub>1</sub>&nbsp;R<sup>''i''&nbsp;&ndash;&nbsp;1</sup> used above holds.
 
==External links==