Computational Procedures for a Class of GI/D/k Systems in Discrete Time

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dc.contributor.authorRahman, Md. Mostafizur
dc.contributor.authorAlfa, Attahiru Sule
dc.date.accessioned2015-04-01T18:00:22Z
dc.date.available2015-04-01T18:00:22Z
dc.date.issued2009-11-5
dc.date.updated2015-03-29T13:40:17Z
dc.description.abstractA class of discrete time GI/D/ systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD) type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures.
dc.description.versionPeer Reviewed
dc.identifier.citationMd. Mostafizur Rahman and Attahiru Sule Alfa, “Computational Procedures for a Class of GI/D/k Systems in Discrete Time,” Journal of Probability and Statistics, vol. 2009, Article ID 716364, 18 pages, 2009. doi:10.1155/2009/716364
dc.identifier.urihttp://dx.doi.org/10.1155/2009/716364
dc.identifier.urihttp://hdl.handle.net/1993/30334
dc.language.rfc3066en
dc.rightsopen accessen_US
dc.rights.holderCopyright © 2009 Md. Mostafizur Rahman and Attahiru Sule Alfa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.titleComputational Procedures for a Class of GI/D/k Systems in Discrete Time
dc.typeJournal Article
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