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General single server queues are considered with (i) arrivals in single units and batched departures, (ii) batched arrivals and departures in single units. Queue sizes at the following instants are compared: (1) just before arrivals; (2) just after departures; (3) through time. It is shown how formulas for batched queues are related to those for certain associated unit queues.
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F. G. Foster (1964) studied this question.
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