### Abstract

Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service durations, in both queues, are drawn independently from the same distribution. A setup time is incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holdings costs, assumed linear in queue length and having the same rate at the two queues, the service at each queue should be exhaustive. A 'threshold policy' is defined as a policy under which the server switches (from an empty queue) only when the other reaches a critical size. It is shown to be a likely candidate for the optimal policy, both for the discounted version and for the long-time average criterion. The steady-state performance of this policy (under somewhat more general distributional assumptions) and the optimal thresholds are determined for a number of cases.

Original language | English (US) |
---|---|

Pages (from-to) | 399-420 |

Number of pages | 22 |

Journal | SIAM Journal on Computing |

Volume | 16 |

Issue number | 2 |

State | Published - Apr 1987 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*16*(2), 399-420.

**ON THE OPTIMAL CONTROL OF TWO QUEUES WITH SERVER SETUP TIMES AND ITS ANALYSIS.** / Hofri, Micha; Ross, Keith.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 16, no. 2, pp. 399-420.

}

TY - JOUR

T1 - ON THE OPTIMAL CONTROL OF TWO QUEUES WITH SERVER SETUP TIMES AND ITS ANALYSIS.

AU - Hofri, Micha

AU - Ross, Keith

PY - 1987/4

Y1 - 1987/4

N2 - Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service durations, in both queues, are drawn independently from the same distribution. A setup time is incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holdings costs, assumed linear in queue length and having the same rate at the two queues, the service at each queue should be exhaustive. A 'threshold policy' is defined as a policy under which the server switches (from an empty queue) only when the other reaches a critical size. It is shown to be a likely candidate for the optimal policy, both for the discounted version and for the long-time average criterion. The steady-state performance of this policy (under somewhat more general distributional assumptions) and the optimal thresholds are determined for a number of cases.

AB - Two queues are fed by independent, time-homogeneous Poisson arrival processes. One server is available to handle both. All service durations, in both queues, are drawn independently from the same distribution. A setup time is incurred whenever the server moves (switches) from one queue to the other. We prove that in order to minimize the sum of discounted setup charges and holdings costs, assumed linear in queue length and having the same rate at the two queues, the service at each queue should be exhaustive. A 'threshold policy' is defined as a policy under which the server switches (from an empty queue) only when the other reaches a critical size. It is shown to be a likely candidate for the optimal policy, both for the discounted version and for the long-time average criterion. The steady-state performance of this policy (under somewhat more general distributional assumptions) and the optimal thresholds are determined for a number of cases.

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M3 - Article

AN - SCOPUS:0023329388

VL - 16

SP - 399

EP - 420

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 2

ER -