### Abstract

Using sample path analysis we show that under the same load the mean delay in queue in the M/G/2 system is smaller than that in the corresponding M/G/1 system, when the service time has either the DMRL or NBU property and the service discipline is FCFS. The proof technique uses a new device that equalizes the work in a two server system with that in a single sterver system. Other interesting quantities such as the average difference in work between the two servers in the GI/G/2 system and an exact alternate derivation of the mean delay in the M/M/2 system from sample path analysis are presented. For the same load, we also show that the mean delay in the M/G/C system with general service time distribution is smaller than that in the M/G/1 system when the traffic intensity is less than 1/c.

Original language | English (US) |
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Pages (from-to) | 256-266 |

Number of pages | 11 |

Journal | Journal of Applied Probability |

Volume | 33 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1996 |

Externally published | Yes |

### Keywords

- Bounds for mean delay
- Multi-server queue
- Sample path analysis

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty