The computer-assisted modeling of re-entrant production lines, and, in
particular, simulation scalability, is attracting a lot of attention due to the
importance of such lines in semiconductor manufacturing. Re-entrant flows lead
to competition for processing capacity among the items produced, which
significantly impacts their throughput time (TPT). Such production models
naturally exhibit two time scales: a short one, characteristic of single items
processed through individual machines, and a longer one, characteristic of the
response time of the entire factory. Coarse-grained partial differential
equations for the spatio-temporal evolution of a "phase density" were obtained
through a kinetic theory approach in Armbruster et al. [2]. We take advantage
of the time scale separation to directly solve such coarse-grained equations,
even when we cannot derive them explicitly, through an equation-free
computational approach. Short bursts of appropriately initialized stochastic
fine-scale simulation are used to perform coarse projective integration on the
phase density. The key step in this process is lifting: the construction of
fine-scale, discrete realizations consistent with a given coarse-grained phase
density field. We achieve this through computational evaluation of conditional
distributions of a "phase velocity" at the limit of large item influxes.Comment: 14 pages, 17 figure