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AWQ criterion, Inspection, Invasive species, Maritime trade, Queuing theory, Q58, L51, D81,

The overflow stream from an M/PH/1 queue of finite capacity is used as the input to an unbounded queue with one or more exponential servers. It is shown that the combined system, consisting of the two queues, may be studied as a highly structured Markov process. In the stable case, this Markov process has a matrix-geometric invariant vector. Particular features of the infinitesimal generator of the process may be used to simplify the numerical computation of various steady-state features of the model. Several variants and numerical examples are discussed.

We thank the editor Tschangho John Kim, two anonymous referees, and session participants at the 2005 NARSC meeting in Las Vegas for their helpful comments on a previous version of this paper. In addition, Batabyal acknowledges financial support from the USDA's PREISM program by means of Cooperative Agreement 43-3AEM-4-80100 and from the Gosnell endowment at RIT. The usual disclaimer applies.

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