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

Karsten, Fjp Frank; Slikker, Marco; Houtum, Geert‐Jan van

doi:10.1017/s0269964814000102

Cited by 13 publications

(5 citation statements)

References 13 publications

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“…Hence, by Theorem 3, the proportional allocation

P (φ)

is a coalitionally rational allocation for the associated single‐attribute game

(N, c^{φ})

. This result was also derived by Karsten et al using an alternative proof. ◊EXAMPLE (EOQ games): Consider a set N of players (e.g., retailers) who have to meet deterministic demand for items (e.g., office supplies) occurring at a constant rate.…”

Section: Preliminariessupporting

confidence: 66%

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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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“…Hence, by Theorem 3, the proportional allocation

P (φ)

is a coalitionally rational allocation for the associated single‐attribute game

(N, c^{φ})

Section: Preliminariessupporting

confidence: 66%

“…As pointed out by Özen et al , many of them fit the framework of an elastic single‐attribute situation. We mention EOQ inventory situations ,

(S - 1, S)

inventory situations ,

M / M / s

queueing situations , and

M / G / s / s

queueing situations . They are described in more detail in Section 2.3.…”

Section: Introductionmentioning

confidence: 99%

Cost allocation rules for elastic single-attribute situations

Karsten

Slikker

Borm

2017

Naval Research Logistics

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“…Some papers have considered resource pooling in the context of cooperative games, see e.g., Anily and Haviv (2010), Chakravarthy (2016), Karsten (2013), Karsten et al. (2009, 2011), Timmer and Scheinhardt (2013) and Yu et al. (2015).…”

Section: Review On Cooperative Gamesmentioning

confidence: 99%

Line Balancing in Parallel M/M/1 Lines and Loss Systems as Cooperative Games

Anily

Haviv

2017

Production and Operations Management

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We consider production and service systems that consist of parallel lines of two types: (i) M/M/1 lines and (ii) lines that have no buffers (loss systems). Each line is assumed to be controlled by a dedicated supervisor. The management measures the effectiveness of the supervisors by the long run expected cost of their line. Unbalanced lines cause congestion and bottlenecks, large variation in output, unnecessary wastes and, ultimately, high operating costs. Thus, the supervisors are expected to join forces and reduce the cost of the whole system by applying line‐balancing techniques, possibly combined with either strategic outsourcing or capacity reduction practices. By solving appropriate mathematical programming formulations, the policy that minimizes the long run expected cost of each of the parallel‐lines system, is identified. The next question to be asked is how to allocate the new total cost of each system among the lines' supervisors so that the cooperation's stability is preserved. For that sake, we associate a cooperative game to each system and we investigate its core. We show that the cooperative games are reducible to market games and therefore they are totally balanced, that is, their core and the core of their subgames are non‐empty. For each game a core cost allocation based on competitive equilibrium prices is identified.

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“…Another line of literature treats each coalition as a multi-server loss system- Karsten et al (2012) considers the case where the number of servers with each player is fixed apriori, and Özen et al (2011), Karsten et al (2014) consider the case where a coalition optimizes the number of servers it operates. Finally, Karsten et al (2015) analyses the setting where each coalition is an M/M/s queue (Erlang C); they consider both the above mentioned models for the service capacity of a coalition.…”

Section: Related Literaturementioning

confidence: 99%

“…Naturally, the resulting aggregate payoff must be divided between the providers in a stable manner, i.e., in such a way that no subset of providers has an incentive to 'break away' from the grand coalition. Such stable payoff allocations have been demonstrated in a wide range of settings, including single/multiple server environments, and loss/queue-based environments (see Karsten et al (2015Karsten et al ( , 2014 and the references therein). a significant extension; it includes an impossibility result under classical notions of stability (Section 3), an analysis of stable configurations under an extension of the Shapley value for partition form games (Section 4), a complete characterisation of stable configurations in heavy and light traffic regimes (Section 5), and a comprehensive numerical case study (Section 6).…”

Section: Introductionmentioning

confidence: 98%

Coalition Formation in Constant Sum Queueing Games

Singhal¹,

Kavitha²,

Nair

2021

2021 60th IEEE Conference on Decision and Control (CDC)

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

Cited by 13 publications

References 13 publications

Cost allocation rules for elastic single-attribute situations

Cost allocation rules for elastic single-attribute situations

Line Balancing in Parallel M/M/1 Lines and Loss Systems as Cooperative Games

Coalition Formation in Constant Sum Queueing Games

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