### Abstract

We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.

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

Pages (from-to) | 1-32 |

Number of pages | 32 |

Journal | Queueing Systems |

DOIs | |

Publication status | Accepted/In press - 2017 Sep 9 |

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### Keywords

- Glue periods
- Polling system
- Retrials

### ASJC Scopus subject areas

- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics

### Cite this

*Queueing Systems*, 1-32. https://doi.org/10.1007/s11134-017-9545-y

**Performance analysis of polling systems with retrials and glue periods.** / Abidini, Murtuza Ali; Boxma, Onno; Kim, Bara; Kim, Jeongsim; Resing, Jacques.

Research output: Contribution to journal › Article

*Queueing Systems*, pp. 1-32. https://doi.org/10.1007/s11134-017-9545-y

}

TY - JOUR

T1 - Performance analysis of polling systems with retrials and glue periods

AU - Abidini, Murtuza Ali

AU - Boxma, Onno

AU - Kim, Bara

AU - Kim, Jeongsim

AU - Resing, Jacques

PY - 2017/9/9

Y1 - 2017/9/9

N2 - We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.

AB - We consider gated polling systems with two special features: (i) retrials and (ii) glue or reservation periods. When a type-i customer arrives, or retries, during a glue period of the station i, it will be served in the following service period of that station. Customers arriving at station i in any other period join the orbit of that station and will retry after an exponentially distributed time. Such polling systems can be used to study the performance of certain switches in optical communication systems. When the glue periods are exponentially distributed, we obtain equations for the joint generating functions of the number of customers in each station. We also present an algorithm to obtain the moments of the number of customers in each station. When the glue periods are generally distributed, we consider the distribution of the total workload in the system, using it to derive a pseudo-conservation law which in turn is used to obtain accurate approximations of the individual mean waiting times. We also investigate the problem of choosing the lengths of the glue periods, under a constraint on the total glue period per cycle, so as to minimize a weighted sum of the mean waiting times.

KW - Glue periods

KW - Polling system

KW - Retrials

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U2 - 10.1007/s11134-017-9545-y

DO - 10.1007/s11134-017-9545-y

M3 - Article

SP - 1

EP - 32

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

ER -