We show that in the stationary M/G/1 queue, if the service time distribution is with increasing (decreasing) failure rate (IFR (DFR)), then (a) The distribution of the number of customers in the system is also IFR (DFR), (b) The conditional distribution of the remaining service time given the number of customers in the system is also IFR (DFR) and (c) The conditional distribution of the remaining service time given the number of customers in the system, is stochastically decreasing (increasing) with the number of customers in the system.

Name | Report Eurandom |
---|

Volume | 2009018 |
---|

ISSN (Print) | 1389-2355 |
---|