Heavy traffic approximations for busy period in an M/G/\(\infty\) queue
Let B denote a typical busy period in an M/G/\(\infty\) queue with arrival rate \(\lambda\) and service-time distribution H having mean 1. It is shown that a necessary and sufficient condition for B/EB to have an asymptotic exponential distribution as \(\lambda\) \(\to \infty\) is (log x)\(\int^{\infty}_{x}\{1-H(y)\}dy\to 0\) as \(x\to \infty.\) When (log x)\(\sup_{u\geq x}u\{1-H(u)\}\to 0\) as \(x\to \infty\), it is further shown that B/\(\nu\) (\(\lambda)\) has an asymptotic exponential distribution, where \(\nu\) (\(\lambda)\) is an appropriate norming different from EB.
scientific article; zbMATH DE number 3905607