### Abstract

_{t∈[0,L]}{Q0=0,At>ct} , i.e., queue Q

_{ t}is empty at 0 and for all t∊ [0, L] the amount of traffic A

_{t}arriving in [0,t) exceeds the server capacity. Also the event of exceeding some predefined threshold in a tandem queue, or a priority queue, can be written in terms of this kind of infinite intersections. This paper studies the probability of such infinite intersections in queueing systems fed by a large number n of i.i.d. traffic sources (the so-called ‘many-sources regime’). If the sources are of the exponential on-off type, and the queueing resources are scaled proportional to n, the probabilities under consideration decay exponentially; we explicitly characterize the corresponding decay rate. The techniques used stem from large deviations theory (particularly sample-path large deviations).

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

Pages (from-to) | 5-20 |

Journal | Queueing Systems |

Volume | 54 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2006 |

MoE publication type | A1 Journal article-refereed |

### Fingerprint

### Keywords

- sample-path large deviations
- on-off processes
- busy period
- tandem queue
- priority queue
- queueing theory

### Cite this

*Queueing Systems*,

*54*(1), 5-20. https://doi.org/10.1007/s11134-006-7781-7

}

*Queueing Systems*, vol. 54, no. 1, pp. 5-20. https://doi.org/10.1007/s11134-006-7781-7

**Queueing systems fed by many exponential on-off sources : An infinite-intersection approach.** / Mandjes, Michael; Mannersalo, Petteri (Corresponding Author).

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

TY - JOUR

T1 - Queueing systems fed by many exponential on-off sources

T2 - An infinite-intersection approach

AU - Mandjes, Michael

AU - Mannersalo, Petteri

PY - 2006

Y1 - 2006

N2 - In queueing theory, an important class of events can be written as ‘infinite intersections’. For instance, in a queue with constant service rate c, busy periods starting at 0 and exceeding L > 0 are determined by the intersection of the events ⋂t∈[0,L]{Q0=0,At>ct} , i.e., queue Q t is empty at 0 and for all t∊ [0, L] the amount of traffic A t arriving in [0,t) exceeds the server capacity. Also the event of exceeding some predefined threshold in a tandem queue, or a priority queue, can be written in terms of this kind of infinite intersections. This paper studies the probability of such infinite intersections in queueing systems fed by a large number n of i.i.d. traffic sources (the so-called ‘many-sources regime’). If the sources are of the exponential on-off type, and the queueing resources are scaled proportional to n, the probabilities under consideration decay exponentially; we explicitly characterize the corresponding decay rate. The techniques used stem from large deviations theory (particularly sample-path large deviations).

AB - In queueing theory, an important class of events can be written as ‘infinite intersections’. For instance, in a queue with constant service rate c, busy periods starting at 0 and exceeding L > 0 are determined by the intersection of the events ⋂t∈[0,L]{Q0=0,At>ct} , i.e., queue Q t is empty at 0 and for all t∊ [0, L] the amount of traffic A t arriving in [0,t) exceeds the server capacity. Also the event of exceeding some predefined threshold in a tandem queue, or a priority queue, can be written in terms of this kind of infinite intersections. This paper studies the probability of such infinite intersections in queueing systems fed by a large number n of i.i.d. traffic sources (the so-called ‘many-sources regime’). If the sources are of the exponential on-off type, and the queueing resources are scaled proportional to n, the probabilities under consideration decay exponentially; we explicitly characterize the corresponding decay rate. The techniques used stem from large deviations theory (particularly sample-path large deviations).

KW - sample-path large deviations

KW - on-off processes

KW - busy period

KW - tandem queue

KW - priority queue

KW - queueing theory

U2 - 10.1007/s11134-006-7781-7

DO - 10.1007/s11134-006-7781-7

M3 - Article

VL - 54

SP - 5

EP - 20

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

IS - 1

ER -