On the core of cooperative queueing games

Özen, Ulaş; Reiman, Martin I.; Wang, Qiong

doi:10.1016/j.orl.2011.06.016

Cited by 27 publications

(25 citation statements)

References 7 publications

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“…Cost allocation problems for pooled queueing systems where waiting is not possible have been studied solely in the context of the M/G/s/s system. For M/G/s/s games where any coalition picks a number of common servers to minimize the sum of linear resource costs for servers and penalty costs for blocked customers,Özen, Reiman and Wang [13] and Karsten, Slikker and Van Houtum [9] have independently proven that the allocation of the collective costs proportional to players' arrival rates is stable. Karsten, Slikker and Van Houtum [11] extended this to non-identical resource cost parameters across players and additionally tackled M/G/s/s game variants with exogenously given numbers of servers.…”

Section: Introductionmentioning

confidence: 99%

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Domain Extensions of the Erlang Loss Function: Their Scalability and Its Applications to Cooperative Games

Karsten

Slikker

Houtum

2014

Prob. Eng. Inf. Sci.

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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.

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Section: Introductionmentioning

confidence: 99%

“…To prove these stability results, the scalability of L is instrumental -this proof approach differs from the one used byÖzen, Reiman and Wang [13].…”

Section: Introductionmentioning

confidence: 99%

Domain Extensions of the Erlang Loss Function: Their Scalability and Its Applications to Cooperative Games

Karsten

Slikker

Houtum

2014

Prob. Eng. Inf. Sci.

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“…The following theorem, due to for instance Özen et al , states that the proportional rule always yields core allocations.THEOREM The proportional rule

scriptP

satisfies the coalitional rationality property.…”

Section: Preliminariesmentioning

confidence: 99%

“…The proportional rule is easy to understand for practitioners due to its mathematical simplicity and is easy to compute. Moreover, due to elasticity of K , it always results in an allocation in the core of the associated cooperative game , which is a nice property that ensures that no subset of players has an incentive to split off and act separately.…”

Section: Introductionmentioning

confidence: 99%

Cost allocation rules for elastic single-attribute situations

Karsten

Slikker

Borm

2017

Naval Research Logistics

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Many cooperative games, especially ones stemming from resource pooling in queueing or inventory systems, are based on situations in which each player is associated with a single attribute (a real number representing, say, a demand) and in which the cost to optimally serve any sum of attributes is described by an elastic function (which means that the per-demand cost is non-increasing in the total demand served). For this class of situations, we introduce and analyze several cost allocation rules: the proportional rule, the serial cost sharing rule, the benefit-proportional rule, and various Shapley-esque rules. We study their appeal with regard to fairness criteria such as coalitional rationality, benefit ordering, and relaxations thereof. After showing the impossibility of combining coalitional rationality and benefit ordering, we show for each of the cost allocation rules which fairness criteria it satisfies.

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“…In [5] the core of cooperative queueing games is studied. The authors show that any single-attribute game embedded in an elastic function has a non-empty core.…”

Section: Introductionmentioning

confidence: 99%

Customer and Cost Sharing in a Jackson Network

Timmer

Scheinhardt

2018

Int. Game Theory Rev.

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In this paper we consider a Jackson network of independent service stations. To improve upon the total expected waiting time, the stations may redistribute the total arrival rate of customers over all queues. We investigate this situation by means of arrival rate games. These are cooperative TU cost games in which the stations are the players and the total cost of a coalition is linear in the total expected waiting time. We show that these games are totally balanced; cooperation is beneficial to all stations. Further, we provide a tailor-made cost allocation rule that belongs to the core of the game.

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On the core of cooperative queueing games

Cited by 27 publications

References 7 publications

Domain Extensions of the Erlang Loss Function: Their Scalability and Its Applications to Cooperative Games

Domain Extensions of the Erlang Loss Function: Their Scalability and Its Applications to Cooperative Games

Cost allocation rules for elastic single-attribute situations

Customer and Cost Sharing in a Jackson Network

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