computational procedures for a class of gi/d/k systems in discrete time

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ID: 255825
2009
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Abstract
A class of discrete time GI/D/k 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.
Reference Key
rahman2009journalcomputational Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Md. Mostafizur Rahman;Attahiru Sule Alfa
Journal nature protocols
Year 2009
DOI
10.1155/2009/716364
URL
http://dx.doi.org/10.1155/2009/716364
Keywords
probabilities mathematical statistics

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