Balancing Queues by Mean Field Interaction

Dawson, Donald A.; Tang, Jiashan; Zhao, Yiqiang Q.

doi:10.1007/s11134-005-6971-z

Cited by 22 publications

(35 citation statements)

References 28 publications

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“…In recent years, the mean-field approach has also found an appeal in the area of communication networks. To name but a few of the many publications, the reader is referred to [9], [16], [8] and [7]. Perhaps closest to our model are [4], which uses a continuous time limit, and [5], which uses a combination of discrete and continuous time and assumes a perfectly exchangeable system (i.e.…”

Section: Introductionmentioning

confidence: 99%

A Generic Mean Field Convergence Result for Systems of Interacting Objects

Boudec

McDonald

Mundinger

2007

Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)

127

207

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Section: Introductionmentioning

confidence: 99%

A Generic Mean Field Convergence Result for Systems of Interacting Objects

Boudec

McDonald

Mundinger

2007

Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)

127

207

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“…This is probably one of the difficulties of these problems: little intuition can be extracted, a priori, from these polynomial equations. See Antunes et al [2], Dawson [10], Muzychka [27], and Rybko and Shlosman [30] for the analysis of other 'large' queueing models.…”

Section: Existence Number and Locations Of Equilibrium Pointsmentioning

confidence: 99%

The equilibrium states of large networks of Erlang queues

Martirosyan

Pierpoint

2020

Adv. Appl. Probab.

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The equilibrium properties of allocation algorithms for networks with a large number of nodes with finite capacity are investigated. Every node receives a flow of requests. When a request arrives at a saturated node, i.e. a node whose capacity is fully utilized, an allocation algorithm may attempt to reallocate the request to a non-saturated node. For the algorithms considered, the reallocation comes at a price: either extra capacity is required in the system, or the processing time of a reallocated request is increased. The paper analyzes the properties of the equilibrium points of the associated asymptotic dynamical system when the number of nodes gets large. At this occasion the classical model of Gibbens, Hunt, and Kelly (1990) in this domain is revisited. The absence of known Lyapunov functions for the corresponding dynamical system significantly complicates the analysis. Several techniques are used. Analytic and scaling methods are used to identify the equilibrium points. We identify the subset of parameters for which the limiting stochastic model of these networks has multiple equilibrium points. Probabilistic approaches are used to prove the stability of some of them. A criterion of exponential stability with the spectral gap of the associated linear operator of equilibrium points is also obtained.

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“…A particle is seen as under a collective force generated by the other particles in a continuous time and space setting. In the area of communication networks, mean-field convergence results have been applied in various forms to a variety of case studies, including TCP connections [17], [18], [19], [20], HTTP flows [21], bandwidth sharing [22], transportation networks [23], swarm robotic systems [24], reputation determination [15], queueing networks [25], [26], [27] and Internet congestion control [28]. We are not familiar with prior work dealing with meanfield theory for the evaluation of gossip protocols.…”

Section: Related Workmentioning

confidence: 99%

Mean-Field Analysis for the Evaluation of Gossip Protocols

Bakhshi

Cloth

Fokkink

et al. 2009

2009 Sixth International Conference on the Quantitative Evaluation of Systems

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Abstract-Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, that tend to be expensive in computation time and memory consumption.We employ mean-field approximation for an analytical evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic models. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to infinity, however, mean-field analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

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Balancing Queues by Mean Field Interaction

Abstract: Consider a queueing network with N nodes in which queue lengths are balanced through meanfield interaction. When N is large, we study the performance of such a network in terms of limiting results as N goes to infinity.

Cited by 22 publications

References 28 publications

A Generic Mean Field Convergence Result for Systems of Interacting Objects

A Generic Mean Field Convergence Result for Systems of Interacting Objects

The equilibrium states of large networks of Erlang queues

Mean-Field Analysis for the Evaluation of Gossip Protocols

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