Abstract
In this paper, we formulate a recursive relation for the marginal probabilities of a closed network with K customers in terms of the same network with K − 1 customers. Mean-value analysis (MVA) is an application of this relation, together with Little's formula. It is shown that the convolution method, too, can be based on the same recursive result. This leads to a new convolution algorithm called normalized convolution algorithm (NCA), which like MVA works entirely with probabilities and throughputs rather than with quantities such as normalization contacts. NCA avoids a difficult problem, the occurrence of floating-point over-flows in the original convolution algorithm. We shall also solve a numerical stability problem found in MVA. Finally, we show how MVA and the convolution algorithm can be combined in the same problem to yield a hybrid method retaining the best properties of both methods.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.