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Motivated by re-entrant manufacturing processes in semiconductor wafer processing we model the queue changes associated with each step in the manufacturing process by a set of constant differential equations. A Poincare map reduces this to sets of piecewise linear maps. It is proved for a specific example of a 2--4 step--2 machine problem, that these maps do not show chaotic behavior but instead lead to periodic orbits of arbitrary period depending on the processing rates. A partly dissipative, partly conservative phase space is indentified and typical bifurcations are analyzed. This is contrasted with a switched arrival queuing system which shows chaotic behavior and where control of chaos ideas lead to the stabilization of unstable periodic orbits.
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