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We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFOGI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.
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Gelenbe et al. (1991) studied this question.
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