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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.
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the Equation-Free
Inverse problems are ubiquitous because they formalize the integration of data with mathematical models. In many scientific applications the forward model is expensive to evaluate, and adjoint computations are difficult to employ; in this setting der
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of indistinguishable
A re-entrant manufacturing system producing a large number of items and involving many steps can be approximately modeled by a hyperbolic partial differential equation (PDE) according to mass conservation law with respect to a continuous density of i
Scientists and engineers often create accurate, trustworthy, computational simulation schemes - but all too often these are too computationally expensive to execute over the time or spatial domain of interest. The equation-free approach is to marry s