### Abstract

Mean sojourn time is one of the most important performance measures for queueing systems. It is difficult to obtain the real sojourn time of a customer directly, so it is also difficult to estimate the mean sojourn time. In this paper, we propose a new and relatively simple estimate of the mean sojourn time in a single server queue, using the number of arrivals and the number of departures. This method can be used for evaluating the quality and the performance of call processing in communication switching systems, for example. We evaluate the accuracy of this estimate for an M/M/1 queue, using some results obtained by Jenkins. This estimate is compared with two other standard estimates of the mean sojourn time obtained from the sequence of actual arrival and departure times.

Original language | English |
---|---|

Pages (from-to) | 7-15 |

Number of pages | 9 |

Journal | Computers and Mathematics with Applications |

Volume | 24 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1992 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

**Evaluating mean sojourn time estimates for the M/M/1 queue.** / Toyoizumi, Hiroshi.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 24, no. 1-2, pp. 7-15. https://doi.org/10.1016/0898-1221(92)90222-4

}

TY - JOUR

T1 - Evaluating mean sojourn time estimates for the M/M/1 queue

AU - Toyoizumi, Hiroshi

PY - 1992

Y1 - 1992

N2 - Mean sojourn time is one of the most important performance measures for queueing systems. It is difficult to obtain the real sojourn time of a customer directly, so it is also difficult to estimate the mean sojourn time. In this paper, we propose a new and relatively simple estimate of the mean sojourn time in a single server queue, using the number of arrivals and the number of departures. This method can be used for evaluating the quality and the performance of call processing in communication switching systems, for example. We evaluate the accuracy of this estimate for an M/M/1 queue, using some results obtained by Jenkins. This estimate is compared with two other standard estimates of the mean sojourn time obtained from the sequence of actual arrival and departure times.

AB - Mean sojourn time is one of the most important performance measures for queueing systems. It is difficult to obtain the real sojourn time of a customer directly, so it is also difficult to estimate the mean sojourn time. In this paper, we propose a new and relatively simple estimate of the mean sojourn time in a single server queue, using the number of arrivals and the number of departures. This method can be used for evaluating the quality and the performance of call processing in communication switching systems, for example. We evaluate the accuracy of this estimate for an M/M/1 queue, using some results obtained by Jenkins. This estimate is compared with two other standard estimates of the mean sojourn time obtained from the sequence of actual arrival and departure times.

UR - http://www.scopus.com/inward/record.url?scp=38249013109&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38249013109&partnerID=8YFLogxK

U2 - 10.1016/0898-1221(92)90222-4

DO - 10.1016/0898-1221(92)90222-4

M3 - Article

AN - SCOPUS:38249013109

VL - 24

SP - 7

EP - 15

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 1-2

ER -