Analysis of resource pooling games via a new extension of the Erlang loss function

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Abstract

We study a situation where several independent service providers collaborate by pooling their resources into a joint service system. These service providers may represent such diverse organizations as hospitals that pool intensive care beds and ambulances, airline companies that share spare parts, or car rental agencies that pool rental cars. We model the service systems as Erlang loss systems that face a fixed cost rate per server and penalty costs for lost customers. We examine the allocation of costs of the pooled system amongst the participants by formulating a cooperative cost game in which each coalition optimizes the number of servers. We identify a cost allocation that is in the core of this game, giving no subset of players an incentive to split off and form a separate pooling group. Moreover, we axiomatically characterize this allocation rule and show that it can be reached through a population monotonic allocation scheme. To obtain these results, we introduce a new extension of the classic Erlang loss function to non-integral numbers of servers and establish several of its structural properties.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages36
ISBN (Print)978-90-386-2485-3
Publication statusPublished - 2011

Publication series

NameBETA publicatie : working papers
Volume344
ISSN (Print)1386-9213

Fingerprint

Resource pooling
Costs
Loss function
Car
Service provider
Service system
Spare parts
Fixed costs
Incentives
Allocation rules
Population monotonic allocation schemes
Cost allocation
Structural properties
Penalty
Pooling
Airlines

Cite this

Karsten, F. J. P., Slikker, M., & Houtum, van, G. J. J. A. N. (2011). Analysis of resource pooling games via a new extension of the Erlang loss function. (BETA publicatie : working papers; Vol. 344). Eindhoven: Technische Universiteit Eindhoven.
Karsten, F.J.P. ; Slikker, M. ; Houtum, van, G.J.J.A.N. / Analysis of resource pooling games via a new extension of the Erlang loss function. Eindhoven : Technische Universiteit Eindhoven, 2011. 36 p. (BETA publicatie : working papers).
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Karsten, FJP, Slikker, M & Houtum, van, GJJAN 2011, Analysis of resource pooling games via a new extension of the Erlang loss function. BETA publicatie : working papers, vol. 344, Technische Universiteit Eindhoven, Eindhoven.

Analysis of resource pooling games via a new extension of the Erlang loss function. / Karsten, F.J.P.; Slikker, M.; Houtum, van, G.J.J.A.N.

Eindhoven : Technische Universiteit Eindhoven, 2011. 36 p. (BETA publicatie : working papers; Vol. 344).

Research output: Book/ReportReportAcademic

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AB - We study a situation where several independent service providers collaborate by pooling their resources into a joint service system. These service providers may represent such diverse organizations as hospitals that pool intensive care beds and ambulances, airline companies that share spare parts, or car rental agencies that pool rental cars. We model the service systems as Erlang loss systems that face a fixed cost rate per server and penalty costs for lost customers. We examine the allocation of costs of the pooled system amongst the participants by formulating a cooperative cost game in which each coalition optimizes the number of servers. We identify a cost allocation that is in the core of this game, giving no subset of players an incentive to split off and form a separate pooling group. Moreover, we axiomatically characterize this allocation rule and show that it can be reached through a population monotonic allocation scheme. To obtain these results, we introduce a new extension of the classic Erlang loss function to non-integral numbers of servers and establish several of its structural properties.

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Karsten FJP, Slikker M, Houtum, van GJJAN. Analysis of resource pooling games via a new extension of the Erlang loss function. Eindhoven: Technische Universiteit Eindhoven, 2011. 36 p. (BETA publicatie : working papers).