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Stochastic Volterra integral equations with ranks as scaling limits of parallel infinite-server queues under weighted shortest queue policy
- Part of
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- Journal:
- Journal of Applied Probability , First View
- Published online by Cambridge University Press:
- 02 December 2025, pp. 1-17
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We study a queueing system with a fixed number of parallel service stations of infinite servers, each having a dedicated arrival process, and one flexible arrival stream that is routed to one of the service stations according to a ‘weighted’ shortest queue policy. We consider the model with general arrival processes and general service time distributions. Assuming that the dedicated arrival rates are of order n and the flexible arrival rate is of order
$\sqrt{n}$, we show that the diffusion-scaled queueing processes converge to a stochastic Volterra integral equation with ‘ranks’ driven by a continuous Gaussian process. It reduces to the limiting diffusion with a discontinuous drift in the Markovian setting.
