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This paper studies the heavy-traffic asymptotics for the multiclass FIFOM${}^X$/G/1 queue. We first derive the probability generating function of thejoint queue length distribution. Using the probability generating function, wethen present heavy-traffic asymptotic formulas for the joint queue lengthdistribution and its joint moments (i.e., the joint queue length moments).These formulas are proved under weaker conditions on the service timedistributions, compared to the ones reported in the literature. This fact leadsus to conjectures that some of the conditions made in the literature arerelaxed.

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