Fluid Limits for Bandwidth-Sharing Networks in Overload

Borst, Sem; Egorova, Regina; Zwart, Bert

doi:10.1287/moor.2013.0618

Cited by 8 publications

(21 citation statements)

References 23 publications

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“…Results of a similar nature may also be found in Lemma A.3 of Kelly and Williams (2004) and Proposition 4.1 of Borst et al (2014). These authors, respectively, established continuity and Lipschitz continuity of · defined above for special cases, with no rate constraints.…”

Section: The Bandwidth Allocation Mechanism and Its Propertiessupporting

confidence: 59%

“…Fundamental papers on fluid limit approximations for bandwidth-sharing networks are Kelly and Williams (2004) and Gromoll and Williams (2009). Properties of overloaded bandwidth-sharing networks have subsequently been derived by Borst et al (2014) and Egorova et al (2007). A diffusion approximation for bandwidth-sharing networks was derived in Kang et al (2009).…”

Section: Introductionmentioning

confidence: 99%

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Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

Reed

Zwart

2014

Operations Research

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Bandwidth-sharing networks provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers in computer and communication systems, and can be used to develop traffic pricing/charging mechanisms. At the same time, such models are exciting from an operations research perspective because their analysis requires techniques from stochastic modeling and optimization.In this paper, we develop a framework to approximate bandwidth-sharing networks under the assumption that the number of users as well as the capacities of the system are large, and the assumption that the traffic that each user is allowed to submit is bounded above by some rate, which is standard in practice. We also assume that customers on each route in the network abandon according to exponential patience times. Under Markovian assumptions, we develop fluid and diffusion approximations, which are quite tractable: for most parameter combinations, the invariant distribution is multivariate normal, with mean and diffusion coefficients that can be computed in polynomial time as a function of the size of the network.

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Section: The Bandwidth Allocation Mechanism and Its Propertiessupporting

confidence: 59%

Section: Introductionmentioning

confidence: 99%

Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

Reed

Zwart

2014

Operations Research

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“…By adapting techniques from [12], it can be shown that this assumption holds in the linearized Distflow model. Proposition 1.…”

Section: Fluid Approximationmentioning

confidence: 99%

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

Aveklouris

Vlasiou

Zwart

2019

IEEE Trans. Control Netw. Syst.

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We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.

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“…In order to prove uniqueness of a (0, a)-solution, we derive a proper estimate for it via solutions with other parameters. The whole idea of this proof is adopted from [4].…”

Section: Proposition 1 (Gronwall Inequality) Suppose That Functions Umentioning

confidence: 99%

Fluid limits for an ALOHA-type model with impatient customers

2012

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Random multiple-access protocols of type ALOHA are used to regulate networks with a star configuration where client nodes talk to the hub node at the same frequency (finding a wide range of applications among telecommunication systems, including mobile telephone networks and WiFi networks). Such protocols control who talks at what time sharing the common idea "try to send your data and, if your message collides with another transmission, try resending later".In the present paper, we consider a time-slotted ALOHA model where users are allowed to renege before transmission completion. We focus on the scenario that leads to overload in the absence of impatience. Under mild assumptions, we show that the fluid (or law-of-large-numbers) limit of the system workload coincides a.s. with the unique solution to a certain integral equation. We also demonstrate that the fluid limits for distinct initial conditions converge to the same value as time tends to infinity. Keywords

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Fluid Limits for Bandwidth-Sharing Networks in Overload

Cited by 8 publications

References 23 publications

Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

Limit Theorems for Markovian Bandwidth-Sharing Networks with Rate Constraints

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

Fluid limits for an ALOHA-type model with impatient customers

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