The M/M/1+M queue with a utility-maximizing server |
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Authors: | Dongyuan Zhan Amy R. Ward |
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Affiliation: | 1. School of Management, University College London, London E14 5AB, United Kingdom;2. Booth School of Business, University of Chicago, Chicago, IL 60637, United States |
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Abstract: | We consider an M/M/1+M queue with a human server, who is influenced by incentives. Specifically, the server chooses his service rate by maximizing his utility function. Our objective is to guarantee the existence of a unique maximum. The complication is that most sensible utility functions depend on the server utilization, a non-simple expression. We derive a property of the utilization that guarantees quasiconcavity of any utility function that multiplies the server’s concave (including linear) “value” of his service rate by the server utilization. |
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Keywords: | M/M/1+M Utilization Server utility Endogenous service rate |
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