Heavy-traffic asymptotic formulas for the multiclass M^X/G/1 queue

2013/12/25 by Hiroshi Miyawaki, Miyawaki, Hiroshi, Hiroyuki Masuyama +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1312.6970

This paper has been withdrawn by the author because Conjecture 4.1 has turned out to be not true

arxiv created 2014/04/24 · arxiv updated 2014/04/25

Abstract

This paper studies the heavy-traffic asymptotics for the multiclass FIFO M^X/G/1 queue. We first derive the probability generating function of the joint queue length distribution. Using the probability generating function, we then present heavy-traffic asymptotic formulas for the joint queue length distribution and its joint moments (i.e., the joint queue length moments). These formulas are proved under weaker conditions on the service time distributions, compared to the ones reported in the literature. This fact leads us to conjectures that some of the conditions made in the literature are relaxed.

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