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DOMAIN EXTENSIONS OF THE ERLANG LOSS FUNCTION: THEIR SCALABILITY AND ITS APPLICATIONS TO COOPERATIVE GAMES

Published online by Cambridge University Press:  05 September 2014

Frank Karsten ,
Marco Slikker  and
Geert-Jan van Houtum
Frank Karsten
Affiliation:
School of Industrial Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, EindhovenThe Netherlands E-mails: [email protected]; [email protected]; [email protected]
Marco Slikker
Affiliation:
School of Industrial Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, EindhovenThe Netherlands E-mails: [email protected]; [email protected]; [email protected]
Geert-Jan van Houtum
Affiliation:
School of Industrial Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, EindhovenThe Netherlands E-mails: [email protected]; [email protected]; [email protected]
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Abstract

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We prove that several extensions of the classic Erlang loss function to non-integral numbers of servers are scalable: the blocking probability as described by the extension decreases when the offered load and the number of servers s are increased with the same relative amount, even when scaling up from integral s to non-integral s. We use this to prove that when several Erlang loss systems pool their resources for efficiency, various corresponding cooperative games have a non-empty core.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 4 , October 2014 , pp. 473 - 488
Copyright
Copyright © Cambridge University Press 2014 

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