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Role of network junctions for the totally asymmetric simple exclusion process
Adélaïde Raguin1, Andrea Parmeggiani, Norbert Kern
1Université Montpellier 2, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France and CNRS, Laboratoire Charles Coulomb UMR 5221, F-34095, Montpellier, France and Université Montpellier 1, Laboratoire DIMNP UMR 5235, F-34095, Montpellier, France and Université Montpellier 2, Laboratoire DIMNP UMR 5235, F-34095, Montpellier, France and CNRS, Laboratoire DIMNP UMR 5235, F-34095, Montpellier, France.
Abstract:
We study the effect of local regulation mechanisms on stochastic network traffic, based on simple examples. Using the totally asymmetric simple exclusion process on a multiloop structure in which several segments share a single junction, we illustrate several mechanisms: (i) additional segments improve transport but the effect saturates due to blockage, (ii) bias reduces the overall transport and leads to several regimes, (iii) "pumping" particles out of the junctions, via a locally increased hopping rate, allows us to compensate the bottlenecks but becomes futile beyond a characteristic rate which we determine. We provide a generic discussion of combinations of these effects, including phase diagrams in terms of the control parameters.
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