Buzen's algorithm: Difference between revisions

Revision as of 22:49, 17 January 2013

Revision as of 22:49, 17 January 2013

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Write g(''N'',''M'') for the normalising constant of a closed queueing network with ''N'' circulating customers and ''M'' service stations. The algorithm starts by noting<ref name="buzen-1973" />

: :<math>g(0, m) = 1 \text{ for }m=1,2,\cdots,M</math>

: :<math>g(n, 1) = (X_1)^n \text{ for }n=0,1,\cdots,N</math>

and solving for the ''X''_''i''. The recurrence relation<ref name="buzen-1973" />

: :<math>g(n, m) = g(n,m-1)+X_m g(n-1,m).</math>

is used to compute a grid of values. The sought for value G(''N'')&nbsp;=&nbsp;g(''N'',''M'').<ref name="buzen-1973" />