1997

# Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions

## Publication

### Publication

We consider a $GI/G/1$ queue in which the service time distribution and/or the interarrival time distribution has a heavy tail, i.e., a tail behaviour like $t^{-nu$ with $1<nu leq 2$, so that the mean is finite but the variance is infinite. We prove a heavy-traffic limit theorem for the distribution of the stationary waiting time ${bf W$. If the tail of the service time distribution is heavier than that of the interarrival time distribution, and the traffic load $a rightarrow 1$, then ${bf W$, multiplied by an appropriate `coefficient of contraction' that is a function of $a$, converges in distribution to the Kovalenko distribution. If the tail of the interarrival time distribution is heavier than that of the service time distribution, and the traffic load $a rightarrow 1$, then ${bf W$, multiplied by another appropriate `coefficient of contraction' that is a function of $a$, converges in distribution to the negative exponential distribution.

Additional Metadata | |
---|---|

Queueing theory (msc 60K25), Queues and service (msc 90B22) | |

Logistics (theme 3), Energy (theme 4) | |

CWI | |

CWI. Probability, Networks and Algorithms [PNA] | |

Organisation | Stochastics |

Boxma, O.J, & Cohen, J.W. (1997).
Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions. CWI. Probability, Networks and Algorithms [PNA]. CWI. |