On the M/G/1 queue with heavy-tailed service time distributions

• Authors: J. W. Cohen
• Venue: On the M/G/1 queue with heavy-tailed service time distributions
• Year: 1997

In present teletraffic applications of queueing theory service time distributions $B(t)$ with a heavy tail occur, i.e. $1-B(t) \sim t^{-\nu}$ for $t \rightarrow \infty$ with $\nu \nu 2$. For $\nu =1\, \frac{1}{2}$ the explicit expression for $Q(t)$ is derived. For rational $\nu$ with $1 \nu 2$, an asymptotic series for the tail probabilities of $W(t)$ is derived.