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Heavy-traffic limits for parallel single-server queues with randomly split Hawkes arrival processes
Published online by Cambridge University Press: 07 August 2023
Abstract
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.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust
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