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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Bibliographic Details
Published in:Applied mathematical modelling 2010-08, Vol.34 (8), p.2272-2278
Main Author: Do, Tien Van
Format: Article
Language:English
Subjects:
Applied sciences
Computational efficiency
Efficient Algorithm
Eigenvalues
Exact sciences and technology
Feedback
Feedback queue
Mathematical analysis
Mathematical models
Operational research and scientific management
Operational research. Management science
Queues
Queuing theory. Traffic theory
Steady state
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Summary: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.
ISSN:0307-904X
DOI:10.1016/j.apm.2009.10.025