Abstract
Using a fluid model approach, we obtain a sufficient condition for re-entrant lines with infinite supply of work to be unstable, which generalizes the results for re-entrant line of Dai (Ann. Appl. Probab. 6: 751–757, 1996). We apply the result to two special re-entrant lines with infinite supply of work as follows. In addition, we get necessary conditions for the corresponding fluid model to be weakly stable.
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