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1 results

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

  • Part of
  • Bo Li, Guodong Pang
  • Journal:
    Journal of Applied Probability / Volume 61 / Issue 2 / June 2024
    Published online by Cambridge University Press:
    07 August 2023, pp. 490-514
    Print publication:
    June 2024
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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.