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A \(GI/Geo/1\) queue with negative and positive customers. (English) Zbl 1193.60107

Summary: The arrival of a negative customer to a queueing system causes one positive customer to be removed if any is present. Continuous-time queues with negative and positive customers have been thoroughly investigated over the last two decades. On the other hand, a discrete-time \(Geo/Geo/1\) queue with negative and positive customers appeared only recently in the literature. We extend this \(Geo/Geo/1\) queue to a corresponding \(GI/Geo/1\) queue. We present both the stationary queue length distribution and the sojourn time distribution.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
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References:

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