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The M/M/1+M queue with a utility-maximizing server

Zhan, D; Ward, AR; (2018) The M/M/1+M queue with a utility-maximizing server. Operations Research Letters , 46 (5) pp. 518-522. 10.1016/j.orl.2018.08.004. Green open access

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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.

Type: Article
Title: The M/M/1+M queue with a utility-maximizing server
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.orl.2018.08.004
Publisher version: https://doi.org/10.1016/j.orl.2018.08.004
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: M/M/1+M, Utilization, Server utility, Endogenous service rate
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > UCL School of Management
URI: https://discovery.ucl.ac.uk/id/eprint/10061796
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