### Abstract

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

Pages (from-to) | 257-292 |

Number of pages | 36 |

Journal | Queueing systems |

Volume | 92 |

Issue number | 3-4 |

Early online date | 17 May 2019 |

DOIs | |

Publication status | Published - 1 Aug 2019 |

### Fingerprint

### Keywords

- UT-Hybrid-D
- Fixed-cycle traffic-light model
- Roots
- Contour integrals
- Bulk-service queue

### Cite this

*Queueing systems*,

*92*(3-4), 257-292. https://doi.org/10.1007/s11134-019-09614-1

}

*Queueing systems*, vol. 92, no. 3-4, pp. 257-292. https://doi.org/10.1007/s11134-019-09614-1

**An exact root-free method for the expected queue length for a class of discrete-time queueing systems.** / Oblakova, Anna ; Al Hanbali, Ahmad ; Boucherie, Richard; van Ommeren, Jan C.W.; Zijm, Henk.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - An exact root-free method for the expected queue length for a class of discrete-time queueing systems

AU - Oblakova, Anna

AU - Al Hanbali, Ahmad

AU - Boucherie, Richard

AU - van Ommeren, Jan C.W.

AU - Zijm, Henk

N1 - Springer deal

PY - 2019/8/1

Y1 - 2019/8/1

N2 - For a class of discrete-time queueing systems, we present a new exact method of computing both the expectation and the distribution of the queue length. This class of systems includes the bulk-service queue and the fixed-cycle traffic-light (FCTL) queue, which is a basic model in traffic-control research and can be seen as a non-exhaustive time-limited polling system. Our method avoids finding the roots of the characteristic equation, which enhances both the reliability and the speed of the computations compared to the classical root-finding approach. We represent the queue-length expectation in an exact closed-form expression using a contour integral. We also introduce several realistic modifications of the FCTL model. For the FCTL model for a turning flow, we prove a decomposition result. This allows us to derive a bound on the difference between the bulk-service and FCTL expected queue lengths, which turns out to be small in most of the realistic cases.

AB - For a class of discrete-time queueing systems, we present a new exact method of computing both the expectation and the distribution of the queue length. This class of systems includes the bulk-service queue and the fixed-cycle traffic-light (FCTL) queue, which is a basic model in traffic-control research and can be seen as a non-exhaustive time-limited polling system. Our method avoids finding the roots of the characteristic equation, which enhances both the reliability and the speed of the computations compared to the classical root-finding approach. We represent the queue-length expectation in an exact closed-form expression using a contour integral. We also introduce several realistic modifications of the FCTL model. For the FCTL model for a turning flow, we prove a decomposition result. This allows us to derive a bound on the difference between the bulk-service and FCTL expected queue lengths, which turns out to be small in most of the realistic cases.

KW - UT-Hybrid-D

KW - Fixed-cycle traffic-light model

KW - Roots

KW - Contour integrals

KW - Bulk-service queue

U2 - 10.1007/s11134-019-09614-1

DO - 10.1007/s11134-019-09614-1

M3 - Article

VL - 92

SP - 257

EP - 292

JO - Queueing systems

JF - Queueing systems

SN - 0257-0130

IS - 3-4

ER -