Batch sojourn and delivery times in polling systems on a circle

Tim Engels; Ivo Adan; Onno Boxma; Jacques Resing

doi:10.1017/S0269964824000238

Batch sojourn and delivery times in polling systems on a circle

Tim Engels (Corresponding author), Ivo Adan, Onno Boxma, Jacques Resing

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

Abstract

In this paper, we analyze a polling system on a circle. Random batches of customers arrive at a circle, where each customer, independently, obtains a location that is uniformly distributed on the circle. A single server cyclically traverses the circle to serve all customers. Using mean value analysis, we derive the expected number of waiting customers within a given distance of the server. We exploit this to obtain closed-form expressions for both the mean batch sojourn time and the mean time to delivery.

Original language	English
Pages (from-to)	217-242
Number of pages	26
Journal	Probability in the Engineering and Informational Sciences
Volume	39
Issue number	2
DOIs	https://doi.org/10.1017/S0269964824000238
Publication status	Published - Apr 2025

Bibliographical note

Publisher Copyright:
© The Author(s), 2024. Published by Cambridge University Press.

Funding

The research of Tim Engels and Onno Boxma was partly funded by the NWO Gravitation project NETWORKS, grant number 024.002.003.

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	024.002.003

Keywords

Milk-run systems
Polling systems
Queueing theory
Warehousing

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Cite this

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AU - Resing, Jacques

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Batch sojourn and delivery times in polling systems on a circle

Abstract

Bibliographical note

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Keywords

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