Delays and mixing times in random-access networks

Bouman, Niek J.; Borst, Sem; Leeuwaarden, Johan van

doi:10.1145/2465529.2465759

Cited by 3 publications

(3 citation statements)

References 38 publications

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“…In the specific case of an L × L grid, the fluid-limit results in [24] suggest that maximum stability would actually be maintained as long as the function p(q) decays no faster than q −2/L 2 . The lower bounds in [23] then indicate that the delays grow as (1 − ρ) −L 2 /2 , which is still faster than the bounds we obtained for fixed back-off probabilities. In order for the lower bounds for queue-based back-off probabilities in [23] to match the lower bounds in the present paper for fixed back-off probabilities, the function p(q) should decay as q −1/L , but it is not clear whether maximum stability would remain guaranteed in that case.…”

Section: Discussionmentioning

confidence: 51%

“…Remarkably, for suitable choices of the function p(·) such algorithms are guaranteed to provide maximum stability in arbitrary topologies, without any explicit knowledge of the arrival rates. However, lower bounds in [23] demonstrate that for such choices of p(·) the delays are of the order exp 1 2(1−ρ) , growing even faster with the load than the (1 − ρ) −L scaling we obtained for the L × L toric grid.…”

Section: Discussionmentioning

confidence: 69%

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Delay performance in random-access grid networks

Zocca

Borst

Leeuwaarden

et al. 2013

Performance Evaluation

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We examine the impact of torpid mixing and meta-stability issues on the delay performance in wireless random-access networks. Focusing on regular meshes as prototypical scenarios, we show that the mean delays in an L × L toric grid with normalized load ρ are of the order ( 1 1−ρ ) L . This superlinear delay scaling is to be contrasted with the usual linear growth of the order 1 1−ρ in conventional queueing networks. The intuitive explanation for the poor delay characteristics is that (i) high load requires a high activity factor, (ii) a high activity factor implies extremely slow transitions between dominant activity states, and (iii) slow transitions cause starvation and hence excessively long queues and delays.Our proof method combines both renewal and conductance arguments. A critical ingredient in quantifying the long transition times is the derivation of the communication height of the uniformized Markov chain associated with the activity process. We also discuss connections with Glauber dynamics, conductance and mixing times. Our proof framework can be applied to other topologies as well, and is also relevant for the hard-core model in statistical physics and the sampling from independent sets using single-site update Markov chains.

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Section: Discussionmentioning

confidence: 51%

Section: Discussionmentioning

confidence: 69%

Delay performance in random-access grid networks

Zocca

Borst

Leeuwaarden

et al. 2013

Performance Evaluation

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show abstract

“…The definition (6) of κ(x)/τ (x) consists of the first positive and second negative terms. If the weights of schedules are close to the maximum weight, the negative draft of L occurs, which contributes the first positive term of (6). The second negative term of (6) bounds the possible positive draft of L for other cases.…”

Section: Proof Outline Of Theoremmentioning

confidence: 99%

Scheduling Using Interactive Optimization Oracles for Constrained Queueing Networks

Suk¹,

Shin²

2017

Mathematics of OR

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Ever since Tassiulas and Ephremides (1992) proposed the maximum weight scheduling algorithm of throughput-optimality for constrained queueing networks that arise in the context of communication networks, extensive efforts have been devoted to resolving its most important drawback: high complexity. This paper proposes a generic framework for designing throughputoptimal and low-complexity scheduling algorithms for constrained queueing networks. Under our framework, a scheduling algorithm updates current schedules by interacting with a given oracle system that generates an approximate solution to a related optimization task. One can utilize our framework to design a variety of scheduling algorithms by choosing an oracle system such as random search, Markov chain, belief propagation, and primal-dual methods. The complexity of the resulting scheduling algorithm is determined by the number of operations required for an oracle to process a single query, which is typically small. We provide sufficient conditions for throughput-optimality of the scheduling algorithm in general constrained queueing network models. The linear-time algorithm of Tassiulas (1998) and the random access algorithm of Shah and Shin (2012) correspond to special cases of our framework using random search and Markov chain oracles, respectively. Our generic framework, however, provides a unified proof with milder assumptions.

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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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Delays and mixing times in random-access networks

Cited by 3 publications

References 38 publications

Delay performance in random-access grid networks

Delay performance in random-access grid networks

Scheduling Using Interactive Optimization Oracles for Constrained Queueing Networks

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

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