An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity
Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate [1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when N + c is...
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Veröffentlicht in: | Applied mathematical modelling 2010-08, Vol.34 (8), p.2272-2278 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate
[1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when
N
+
c
is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is
⌊
(
N
+
c
+
2
)
/
2
⌋
. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way. |
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ISSN: | 0307-904X |
DOI: | 10.1016/j.apm.2009.10.025 |