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

Offer Kella, Liron Ravner^*

^*Corresponding author for this work

Department of Statistics

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

4 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

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

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10.1016/j.orl.2016.11.007

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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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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.

KW - Accumulating priority

KW - First passage time

KW - Lévy driven queues

KW - Lévy processes

KW - Priority queues

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JF - Operations Research Letters

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ER -

Lowest priority waiting time distribution in an accumulating priority Lévy queue

Abstract

Bibliographical note

Keywords

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