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arXiv · 2308.12793

Batch sojourn time in polling systems on a circle

Tim Engels·Ivo Adan·Onno Boxma·Jacques Resing
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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 uniform location. A single server cyclically travels over 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 and a closed form expression for the mean batch sojourn time.

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Tim Engels, Ivo Adan, Onno Boxma, Jacques Resing. 2023-08-24. Batch sojourn time in polling systems on a circle. https://doi.org/10.1017/s0269964824000238

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