Abstract

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 independence between the queue lengths; and a nontrivial transition in the boundary of the two. If time permits, we explore repercussions of this result for original equipment manufacturers (OEMs) that assemble a large number of components, each produced using specialised equipment, into complex systems. Specifically, we formulate a stylised 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.