Heavy‐traffic asymptotics for stationary GI/G/1‐type Markov chains

Asmussen (1987) proved a heavy‐traffic limit theorem for the GI/G/1‐type Markov chain. As a corollary, the theorem shows that in the heavy‐traffic limit, the stationary distribution of the properly scaled level variable is geometric and independent of the phase variable. In this paper, the heavy‐traffic asymptotics of the stationary distribution is proved under a weaker condition than Asmussen’s, by the characteristic function approach.