Exclusive queueing processes and their application to traffic systems

Arita, Chikashi; Schadschneider, Andreas

doi:10.1142/s0218202515400011

Cited by 21 publications

(15 citation statements)

References 45 publications

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“…The stochastic lattice model, which was started with the cellular automata (CA) by Neumann and Ulam [1], has been acknowledged in studies on traffic flow problems. Above all, the totally asymmetric simple exclusion process (TASEP) has successfully described various kinds of traffic flow systems ranging from molecular mechanics [2,3] to vehicular traffic systems [4][5][6][7][8], all because of a simple mechanism: each particle hops to the neighboring cite in a one-way direction only when the site is empty.…”

Section: Introductionmentioning

confidence: 99%

Throughput reduction on an air-ground transport system by the simultaneous effect of multiple traveling routes equipped with parking sites

2020

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This paper examines the traffic flows on a two-dimensional stochastic lattice model that comprises a junction of two traveling routes: the domestic route and the international route each of which has parking sites. In our model, the system distributes the arrived particles to either of the two routes and selects one of the parking sites in the route for each particle, which stops at the parking site once during its travel. Because each particle has antennas in the back and front directions to detect other approaching particles, the effect of the volume exclusion of each particle extends in the moving direction. The system displays interesting behavior; remarkably, the dependence of the throughput on the distribution ratio of particles to the domestic route reduces after reaching the maximum parking capacity of the domestic route. Our simulations and analysis with the queueing model describe this phenomenon and suggest the following fact: as the distribution ratio of particles to the international route decreases, the throughput of the international route reduces, and simultaneously, that of the domestic route saturates. The simultaneous effect of the decrease and saturation causes a reduction in the throughput of the entire system.

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Section: Introductionmentioning

confidence: 99%

Throughput reduction on an air-ground transport system by the simultaneous effect of multiple traveling routes equipped with parking sites

2020

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“…3 (b), L t decreases until t ∼ 2 · 10 4 and then increases. In the rest of this work, we shall try to understand this unexpected phenomenon with the specific set of parameter values (5). We emphasize that this unexpected behavior is observed generically in a larger parameter regime [31,32].…”

Section: Dependence On Initial Conditionsmentioning

confidence: 99%

Effective ergodicity breaking in an exclusion process with varying system length

Schultens

Schadschneider

Arita

2015

Physica A: Statistical Mechanics and its Applications

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Stochastic processes of interacting particles in systems with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the exclusive queueing process that can be viewed as a one-dimensional exclusion process with varying length, by introducing Langmuir kinetics. This process can be interpreted as an effective model for a queue that interacts with other queues by allowing incoming and leaving of customers in the bulk. We find surprising indications for breaking of ergodicity in a certain parameter regime, where the asymptotic growth behavior depends on the initial length. We show that a random walk with site-dependent hopping probabilities exhibits qualitatively the same behavior.

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“…Because ρ lies in the range 0 ≤ ρ ≤ 1, this solution is inappropriate, and because the system must evolve into only one steady state, we obtain Eq. (10).…”

Section: Discussionmentioning

confidence: 99%

“…A special version of ASEP, in which particles on a lattice can hop unidirectionally, is referred to as a totally asymmetric simple exclusion process (TASEP). Researchers have applied TASEPs to traffic flows of self-driven particles, as in biological transport [4][5][6][7], vehicular traffic [8,9], and pedestrian flow [10][11][12]. Recently, one-lane TASEPs with varying hopping probabilities [13,14] and multi-lane TASEPs with interactions between lanes [15][16][17][18][19][20][21] have begun to be investigated.…”

Section: Introductionmentioning

confidence: 99%

Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics

Yamamoto,

Ichiki,

Yanagisawa

et al. 2021

Preprint

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Multi-lane totally asymmetric simple exclusion processes with interactions between the lanes have recently been investigated actively. This paper proposes a two-lane model with extended Langmuir kinetics on a periodic lattice. Both bidirectional and unidirectional flows are investigated. In our model, the hopping, attachment, and detachment rates vary depending on the state of the corresponding site in the other lane. We obtain a theoretical expression for the global density of the system in the steady state from three kinds of mean-field analyses (1-, 2-, and 4-cluster cases). We verify that the 4-cluster mean-field analysis approximates well the results of computer simulations for the two directional flows and reproduces the differences between them. We expect these findings to contribute to a deeper understanding of the dynamic features of actual traffic systems.

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Exclusive queueing processes and their application to traffic systems

Cited by 21 publications

References 45 publications

Throughput reduction on an air-ground transport system by the simultaneous effect of multiple traveling routes equipped with parking sites

Throughput reduction on an air-ground transport system by the simultaneous effect of multiple traveling routes equipped with parking sites

Effective ergodicity breaking in an exclusion process with varying system length

Two-lane totally asymmetric simple exclusion process with extended Langmuir kinetics

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