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Original Articles

The Waiting Time Distribution of a Type k Customer in a Discrete-Time MMAP[K]/PH[K]/c (c = 1, 2) Queue Using QBDs

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Pages 55-69 | Received 27 Feb 2003, Accepted 01 Jul 2003, Published online: 16 Feb 2007

References

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  • Van Houdt , B. and Blondia , C. 2002 . The waiting time distribution of a type k customer in a FCFS MMAP[K]/PH[K]/2 queue. Technical Report
  • #B. Van Houdt is a postdoctoral Fellow of the FWO Flanders.
  • aHere, the delay is defined as the waiting time plus the service time. One can obtain the waiting time distribution from d k by means of a deconvolution, as the service time is independent from the waiting time.
  • bNotice, we do not know which customer occupies which server. We can easily add this information to the MC by stating that the type k i customer occupies server i. However, this would imply that the condition k 1 ≥ k 2 is lost, hence, the number of states that are part of each level increases (up to a factor 2). Adding this additional info would however simplify the description of the transition probabilities.
  • cOf course, both systems, have a different R matrix.

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