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Abstruet This paper is concerned with geometric decay properties of the joint queue length distributiori p(ni,n2) in two-stage tandem queueing system Pll'fPff/ci-)v IPfflc2. We prove that, under some conditions, p(ni,n2) N C(n2)n"i as nico and p(ni,n2)-C(ni)ii'i' as n2oo. We also obtain the asymptoeic form of state probabilities whell ni is large or when n2 is large. These results prove a part of the conjectllre of a previolls paper [1]. The proof is a direct application of a theorem i] [7] which proves geometric decay property of the st,ationary distribution in a quasi-birth-and-death process with a countable number of phases in each level.

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