Slow Transitions and Starvation in Dense Random-Access Networks

Zocca, Alessandro; Borst, Sem; Leeuwaarden, Johan S. H. van

doi:10.1080/15326349.2015.1018441

Cited by 3 publications

(3 citation statements)

References 33 publications

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“…We briefly outline here the proof strategy of Theorem , to which is devoted the rest of this section. As illustrated by the state space diagram in Figure , there is not a unique bottleneck separating the stable configurations (this was the case for complete partite graphs ) and there are in fact exponentially many possible ways for the Markov chain

{false{X_{t}^{β} false}}_{t \in double-struckN}

to make such transitions. This makes the task of identifying the energy barrier between stable configurations much harder.…”

Section: Energy Landscape Analysismentioning

confidence: 99%

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Tunneling of the hard‐core model on finite triangular lattices

Zocca

2018

Random Struct Algorithms

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We consider the hard‐core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice sizes, this interacting particle system has 3 maximum‐occupancy configurations and we investigate its high‐fugacity behavior by studying tunneling times, that is, the first hitting times between these maximum‐occupancy configurations, and the mixing time. The proof method relies on the analysis of the corresponding state space using geometrical and combinatorial properties of the hard‐core configurations on finite triangular lattices, in combination with known results for first hitting times of Metropolis Markov chains in the equivalent zero‐temperature limit. In particular, we show how the order of magnitude of the expected tunneling times depends on the triangular lattice sizes in the low‐temperature regime and prove the asymptotic exponentiality of the rescaled tunneling time leveraging the intrinsic symmetry of the state space.

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{false{X_{t}^{β} false}}_{t \in double-struckN}

to make such transitions. This makes the task of identifying the energy barrier between stable configurations much harder.…”

Section: Energy Landscape Analysismentioning

confidence: 99%

“…Tunneling phenomena of the hard-core model have already been studied on complete partite graphs [26,27] and on square grid graphs [20]. In this work we focus on the case where Λ is a finite triangular lattice.…”

Section: Introductionmentioning

confidence: 99%

Tunneling of the hard‐core model on finite triangular lattices

Zocca

2018

Random Struct Algorithms

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“…In order to bound the mixing time of the activity process {X C (t)} t≥0 , we will make use of the continuous-time counterpart of that theorem, which is summarized in the following lemma, see [19,Lemma 7.1] for a proof. Lemma 6.2.…”

Section: Asymptotic Lower Bound For the Mixing Timementioning

confidence: 99%

Temporal starvation in multi-channel CSMA networks: an analytical framework

Zocca

2019

Queueing Syst

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In this paper we consider a stochastic model for a frequency-agile CSMA protocol for wireless networks where multiple orthogonal frequency channels are available. Even when the possible interference on the different channels is described by different conflict graphs, we show that the network dynamics can be equivalently described as that of a single-channel CSMA algorithm on an appropriate virtual network. Our focus is on the asymptotic regime in which the network nodes try to activate aggressively in order to achieve maximum throughput. Of particular interest is the scenario where the number of available channels is not sufficient for all nodes of the network to be simultaneously active and the well-studied temporal starvation issues of the singlechannel CSMA dynamics persist. For most networks we expect that a larger number of available channels should alleviate these temporal starvation issues. However, we prove that the aggregate throughput is a non-increasing function of the number of available channels. To investigate this trade-off that emerges between aggregate throughput and temporal starvation phenomena, we propose an analytical framework to study the transient dynamics of multi-channel CSMA networks by means of first hitting times. Our analysis further reveals that the mixing time of the activity process does not always correctly characterize the temporal starvation in the multi-channel scenario and often leads to pessimistic performance estimates.

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Optimization of the quality management path of physical education teaching in colleges and universities integrating modern network technology

Zhi-hua

Xie

2023

Applied Mathematics and Nonlinear Sciences

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Since the 21st century, with the rapid development of network information technology, network technology has begun to be widely used in education. Seizing the opportunity of developing new generation information network technology, establishing a broad coverage education informatization system, strengthening the construction and application of network teaching resource system, and accelerating the development and sharing of high-quality educational resources are the current development goals of education informatization. The open sharing platform of physical education curriculum resources based on MOOC network is an important way to “promote the construction, popularization, and sharing of high-quality physical education resources”. The open-sharing platform of teaching course resources based on MOOC network construction and application has increased access to course resources by 10%. It can promote the exchange and sharing of high-quality teaching resources among universities, realize inter-college cooperation and optimal integration of resources, enrich physical education course resources, and promote the overall improvement of the teaching environment. Furthermore, such improvement in physical education teaching mode improves students’ interest, promotes overall physical education development, guarantees the quality of course teaching, and finally enhances the overall teaching level of the school.

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Slow Transitions and Starvation in Dense Random-Access Networks

Cited by 3 publications

References 33 publications

Tunneling of the hard‐core model on finite triangular lattices

Tunneling of the hard‐core model on finite triangular lattices

Temporal starvation in multi-channel CSMA networks: an analytical framework

Optimization of the quality management path of physical education teaching in colleges and universities integrating modern network technology

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