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- Tobias Kretz, Marko Woelki, Michael Schreckenberg
- ArXiv
- 2006

“Oscillations” occur in quite different kinds of many-particle-systems when two groups of particles with different directions of motion meet or intersect at a certain spot. In this work a model of pedestrian motion is presented that is able to reproduce oscillations with different characteristics. The Wald-Wolfowitz test and Gillis’ correlated random walk… (More)

The asymmetric simple exclusion process (ASEP) with periodic boundary conditions is investigated for shuffled dynamics. In this type of update, in each discrete timestep the particles are updated in a random sequence. Such an update is important for several applications, e.g. for certain models of pedestrian flow in two dimensions. For the ASEP with… (More)

- Marko Woelki
- 2009

Abstract. In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type of state is also obtained for an ASEP on a ring in which particles can move one or two sites. The dynamics… (More)

An asymmetric exclusion process with N particles on L sites is considered where particles can move one or two sites per infinitesimal time-step. An exact analysis for N = 2 and a mean-field theory in comparison with simulations show even/odd oscillations in the headway distribution of particles. Oscillations become maximal if particles try to move as far as… (More)

- Marko Woelki
- ACRI
- 2010

A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular automata for traffic flow with non-local jumps for the kinetic constraint to drive as fast as possible. The exactly solvable… (More)

- Marko Woelki
- Physical review. E, Statistical, nonlinear, and…
- 2013

A bottleneck situation in one-lane traffic flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal realization of this mechanism to which we refer to as density-feedback control (DFC): If the actual density in the… (More)

- Marko Woelki
- 2013

In this paper the totally asymmetric exclusion process (TASEP) with parallel update on an open lattice of size L is considered in the maximum-current region. A formal expression for the generating function for the weight of configurations with N particles is given. Further an interpretation in terms of (u, l, d)-colored weighted Motzkin paths is presented.… (More)

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