Dennis Schol

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math.PR2023

Extreme values for the waiting time in large fork-join queues

Dennis Schol, Maria Vlasiou, Bert Zwart

We prove that the scaled maximum steady-state waiting time and the scaled maximum steady-state queue length among $N$ $G I / G I /1$ -queues in the $N$ -server fork-join queue, converge t…

math.PR2022

Tail Asymptotics for the Delay in a Brownian Fork-Join Queue

Dennis Schol, Maria Vlasiou, Bert Zwart

In this paper, we study the tail behavior of $max_{i \leq N} sup_{s > 0} (W_{i} (s) + W_{A} (s) - β s)$ as $N \to \infty$ , with $(W_{i}, i \leq N)$ i.i.d. Brownian motions and $W_{A}$ an inde…