Rational joining behavior in a queueing system with abandonments

Abstract We consider individually and socially-optimal joining behavior in a first-come first-served M/M/1 queueing system where a customer's need for service may expire after an exponentially distributed length of time. We show that the individual behavior is independent of the rate of abandonment. We use the fact that the individual behavior in a last-come first-served M/M/1 queue is socially-optimal to compute the socially-optimal threshold.

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