Lowest priority waiting time distribution in an accumulating priority Lévy queue

Offer Kella; Liron Ravner

doi:10.1016/j.orl.2016.11.007

Lowest priority waiting time distribution in an accumulating priority Lévy queue

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

Abstract

We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.

Original language	English
Pages (from-to)	40-45
Number of pages	6
Journal	Operations Research Letters
Volume	45
Issue number	1
DOIs	https://doi.org/10.1016/j.orl.2016.11.007
State	Published - 1 Jan 2017
Externally published	Yes

Bibliographical note

Funding Information:
We wish to thank an anonymous referee whose helpful comments helped improve this paper. This work was supported in part by grant 1462/13 from the Israel Science Foundation and the Vigevani Chair in Statistics.

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Accumulating priority
First passage time
Lévy driven queues
Lévy processes
Priority queues

ASJC Scopus subject areas

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2016.11.007

Cite this

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abstract = "We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive L{\'e}vy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.",

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AU - Ravner, Liron

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N2 - We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.

AB - We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.

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Lowest priority waiting time distribution in an accumulating priority Lévy queue

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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