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TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN M<sup>X</sup>/G/1 RETRIAL QUEUE
TAIL ASYMPTOTICS FOR THE QUEUE SIZE DISTRIBUTION IN AN MX/G/1 RETRIAL QUEUE
Journal of applied mathematics & informatics. 2015. May, 33(3_4): 343-350
  • Received : November 26, 2014
  • Published : May 30, 2015
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KIM JEONGSIM

Abstract
We consider an M<sup>X</sup>/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of <xref>Kim et al. (2007)</xref> to the M<sup>X</sup>/G/1 retrial queue.
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