## Abstract

We consider the transient analysis of the M/G/1/0 queue, for which Pn(t) denotes the probability that there are no customers in the system at time t, given that there are n (n = 0,1) customers in the system at time 0. The analysis, which is based upon coupling theory, leads to simple bounds on P_{n}(t) for the M/G/1/0 and M/PH/1/0 queues and improved bounds for the special case M/Er/1/0. Numerical results are presented for various values of the mean arrival rate A to demonstrate the increasing accuracy of approximations based upon the above bounds in light traffic, i.e., as λ→0. An important area of application for the M/G/1/0 queue is as a reliability model for a single repairable component. Since most practical reliability problems have A values that are small relative to the mean service rate, the approximations are potentially useful in that context. A duality relation between the M/G/1/0 and GI/M/1/0 queues is also described.

Original language | English |
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Pages (from-to) | 347-359 |

Number of pages | 13 |

Journal | Journal of Applied Mathematics and Stochastic Analysis |

Volume | 8 |

Issue number | 4 |

DOIs | |

State | Published - 1995 |

Externally published | Yes |

## Keywords

- Approximations
- Bounds
- Coupling Theory
- Duality
- GI/M/1/0
- Light Traffic
- M/E/1/0
- M/G/1/0
- M/PH/1/0
- Queues
- Reliability
- Transient Analysis