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SUMMARY:Brownian Fork-Join Queues - Maria Vlasiou (Universiteit Twente)
DTSTART:20240805T103000Z
DTEND:20240805T113000Z
UID:TALK215656@talks.cam.ac.uk
DESCRIPTION:In this presentation\, we discuss large deviations results for
  the maximum queue length of a Brownian fork-join system\, as the number N
  of single-server stations goes to infinity. We show that there are three 
 regimes of large deviations: one in which the dependence structure between
  queue lengths is recognised in the limit\; one that exhibits asymptotic i
 ndependence between the queue lengths\; and a nontrivial transition in the
  boundary of the two. If time permits\, we explore repercussions of this r
 esult for original equipment manufacturers (OEMs) that assemble a large nu
 mber of components\, each produced using specialised equipment\, into comp
 lex systems. Specifically\, we formulate a stylised model of the OEM that 
 enables us to study the resulting trade-off between shortage risk\, invent
 ory costs\, and capacity costs. Our asymptotic extreme-value results trans
 late into asymptotically exact methods for cost-optimal inventory and capa
 city decisions\, some of which are in closed form.
LOCATION:External
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