A dynamically extending exclusion process

Sugden, Kate; Evans, Martin R.

doi:10.1088/1742-5468/2007/11/p11013

Cited by 46 publications

(77 citation statements)

References 26 publications

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“…In 46,47,48,49 the dynamically extending exclusion process (DEEP) has been introduced as a model for fungal growth. In the DEEP not all particles are removed from the system as they reach the end, but with some probability form a new lattice site.…”

Section: Applications and Related Modelsmentioning

confidence: 99%

Exclusive queueing processes and their application to traffic systems

Arita

Schadschneider

2014

Math. Models Methods Appl. Sci.

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The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by the M/M/1 queue that neglects the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered on a microscopic level. It is equivalent to a Totally Asymmetric Exclusion Process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability α and the service probability β. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used. In this article, we review the main properties of the EQP. We also mention extensions and applications of the EQP and some related models.

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Section: Applications and Related Modelsmentioning

confidence: 99%

Exclusive queueing processes and their application to traffic systems

Arita

Schadschneider

2014

Math. Models Methods Appl. Sci.

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“…28]. On the one hand, motivated by the transport of vesicles along microtubules that facilitate growth of fungal hyphae, or by growth of flagellar filaments, TASEP models have been considered in which a particle that reaches the end of the lattice may extend it by a single site [12,14,15,17,22]. On the other hand, in efforts to quantify experimental observations of motor-mediated microtubule depolymerization in vitro, dynamic latticegas models have proven useful for probing the regulation of microtubule length by motors that show unidirectional [16,18,29,30] or diffusive motion [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Self-organized system-size oscillation of a stochastic lattice-gas model

2018

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The totally asymmetric simple exclusion process (TASEP) is a paradigmatic stochastic model for nonequilibrium physics, and has been successfully applied to describe active transport of molecular motors along cytoskeletal filaments. Building on this simple model, we consider a two-lane lattice-gas model that couples directed transport (TASEP) to diffusive motion in a semiclosed geometry, and simultaneously accounts for spontaneous growth and particle-induced shrinkage of the system's size. This particular extension of the TASEP is motivated by the question of how active transport and diffusion might influence length regulation in confined systems. Surprisingly, we find that the size of our intrinsically stochastic system exhibits robust temporal patterns over a broad range of growth rates. More specifically, when particle diffusion is slow relative to the shrinkage dynamics, we observe quasiperiodic changes in length. We provide an intuitive explanation for the occurrence of these self-organized temporal patterns, which is based on the imbalance between the diffusion and shrinkage speed in the confined geometry. Finally, we formulate an effective theory for the oscillatory regime, which explains the origin of the oscillations and correctly predicts the dependence of key quantities, such as the oscillation frequency, on the growth rate.

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“…An earlier example is the dynamically extending exclusion process (DEEP) introduced in [ 7,8,9,10] as a model for fungal growth. In contrast to the EQP, the DEEP has no mechanism for reducing the system length and therefore the length of the system is always diverging.…”

Section: Introductionmentioning

confidence: 99%

Density profiles of the exclusive queuing process

Arita

Schadschneider

2012

J. Stat. Mech.

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The exclusive queueing process (EQP) incorporates the exclusion principle into classic queueing models. It can be interpreted as an exclusion process of variable system length. Here we extend previous studies of its phase diagram by identifying subphases which can be distinguished by the number of plateaus in the density profiles. Furthermore the influence of different update procedures (parallel, backward-ordered, continuous time) is determined.

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A dynamically extending exclusion process

Cited by 46 publications

References 26 publications

Exclusive queueing processes and their application to traffic systems

Exclusive queueing processes and their application to traffic systems

Self-organized system-size oscillation of a stochastic lattice-gas model

Density profiles of the exclusive queuing process

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