Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extreme-value theory for large fork-join queues, with an application to
  high-tech supply chains   We study extreme values in certain fork-join queueing networks: consider $N$
identical queues with a common arrival process and independent service
processes. All arrival and service processes are deterministic with random
perturbations following Brownian motions. We prove that as $N\rightarrow
\infty$, the scaled maximum of $N$ steady-state queue lengths converges in
distribution to a normally distributed random variable. We explore
repercussions of this result for original equipment manufacturers (OEMs) that
assemble a large number of components, each produced using specialized
equipment, into complex systems. Component production capacity is subject to
fluctuations, causing high risk of shortages of at least one component, which
results in costly system production delays. OEMs hedge this risk by investing
in a combination of excess production capacity and component inventories. We
formulate a stylized model of the OEM that enables us to study the resulting
trade-off between shortage risk, inventory costs, and capacity costs. Our
asymptotic extreme value results translate into asymptotically exact methods
for cost-optimal inventory and capacity decisions, some of which are in closed
form. We validate our asymptotic results with a set of detailed numerical
experiments. These experiments indicate that our results are asymptotically
exact, while for transient times they depend on model parameters.

14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th