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3 results

  • Batch sojourn and delivery times in polling systems on a circle

  • Part of
  • Tim Engels, Ivo Adan, Onno Boxma, Jacques Resing
  • Journal:
    Probability in the Engineering and Informational Sciences , First View
    Published online by Cambridge University Press:
    27 December 2024, pp. 1-26
    • Article
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  • 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.