Heavy-traffic limits for parallel single-server queues with randomly split Hawkes arrival processes

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We consider parallel single-server queues in heavy traffic with randomly split Hawkes arrival processes. The service times are assumed to be independent and identically distributed (i.i.d.) in each queue and are independent in different queues. In the critically loaded regime at each queue, it is shown that the diffusion-scaled queueing and workload processes converge to a multidimensional reflected Brownian motion in the non-negative orthant with orthonormal reflections. For the model with abandonment, we also show that the corresponding limit is a multidimensional reflected Ornstein-Uhlenbeck diffusion in the non-negative orthant.

Original languageEnglish (US)
Pages (from-to)490-514
Number of pages25
JournalJournal of Applied Probability
Issue number2
StatePublished - Jun 7 2024

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty

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