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Joint Queue-Length Distribution for the Non-Preemptive Multi-Server Multi-Level Markovian Priority Queue
  • Josef Zuk ,
  • David Kirszenblat
Josef Zuk
Defence Science and Technology Group (DSTG)

Corresponding Author:[email protected]

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David Kirszenblat
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Explicit results are obtained using simple and exact methods for the joint queue-length distribution of the M/M/c queue with an arbitrary number of non-preemptive priority levels. This work is the first to provide explicit results for the joint probability generating function and joint probability mass function for a general number of priority levels. A fixed-point iteration is developed for the stationary balance equations, which enables direct computation of the joint queue-length distribution. A multi-variate probability generating function is also derived, from which the joint probability mass function can be computed by means of a multi-dimensional fast Fourier transform method.