Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
A tactical planning model for a job shop
Operations Research
Probability, stochastic processes, and queueing theory: the mathematics of computer performance modeling
Stability and instability of fluid models for reentrant lines
Mathematics of Operations Research
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
The Stability of Two-Station Multitype Fluid Networks
Operations Research
Wafer fabrication: 300mm wafer fabrication line simulation model
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
Adjoint IMEX-based schemes for control problems governed by hyperbolic conservation laws
Computational Optimization and Applications
Modelling and Simulation in Engineering
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High-volume, multistage continuous production flow through a re-entrant factory is modeled through a conservation law for a continuous-density variable on a continuous-production line augmented by a state equation for the speed of the production along the production line. The resulting nonlinear, nonlocal hyperbolic conservation law allows fast and accurate simulations. Little's law is built into the model. It is argued that the state equation for a re-entrant factory should be nonlinear. Comparisons of simulations of the partial differential equation (PDE) model and discrete-event simulations are presented. A general analysis of the model shows that for any nonlinear state equation there exist two steady states of production below a critical start rate: A high-volume, high-throughput time state and a low-volume, low-throughput time state. The stability of the low-volume state is proved. Output is controlled by adjusting the start rate to a changed demand rate. Two linear factories and a re-entrant factory, each one modeled by a hyperbolic conservation law, are linked to provide proof of concept for efficient supply chain simulations. Instantaneous density and flux through the supply chain as well as work in progress (WIP) and output as a function of time are presented. Extensions to include multiple product flows and preference rules for products and dispatch rules for re-entrant choices are discussed.