The parallel TASEP, fixed particle number and weighted Motzkin paths

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. Using previous results (Woelki and Schreckenberg 2009 {\it J. Stat. Mech} P05014, Woelki 2010 {\it Cellular Automata}, pp 637-645) the generating function is compared with the one for a possible 2nd-class particle dynamics for the parallel TASEP. It is shown that both become physically equivalent in the thermodynamic limit.Comment: 11 pages, 3 figure

Density-feedback control in traffic and transport far from equilibrium

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 bottleneck is above a certain threshold, the reservoir density of possibly entering cars is reduced to a different constant value. By numerical solution of the discretized viscid Burgers equation a rich stationary phase diagram is found. In order to maximize the flow, which is the goal of typical traffic-management strategies, we find the optimal choice of the threshold. Analytical results are verified by computer simulations of the microscopic TASEP with DFC.Comment: 7 pages, 5 figure

Queuing model of a traffic bottleneck with bimodal arrival rate

This paper revisits the problem of tuning the density in a traffic bottleneck by reduction of the arrival rate when the queue length exceeds a certain threshold, studied recently for variants of totally asymmetric simple exclusion process (TASEP) and Burgers equation. In the present approach, a simple finite queuing system is considered and its contrasting “phase diagram” is derived. One can observe one jammed region, one low-density region and one region where the queue length is equilibrated around the threshold. Despite the simplicity of the model the physics is in accordance with the previous approach: The density is tuned at the threshold if the exit rate lies in between the two arrival rates

Risk-minimal routes for emergency cars

The computation of an optimal route for given start and destination in a static transportation network is used in many applications of private route planning. In this work we focus on route planning for emergency cars, such as for example police, fire brigade and ambulance. In case of private route planning typical quantities to be minimized are travel time or route length. However, the idea of this paper is to minimize the risk of a travel time exceeding a certain limit. This is inspired by the fact that the emergency cars have to reach the destination within a legal time. We consider mainly two approaches. The first approach takes into account relevant information to determine the weight, i.e. the desirability of certain edges of a graph during the minimization procedure. One possible risk factor to be aware of would be a suddenly jammed single-lane road on which the emergency car has no chance to make use of the benefits of the siren for instance. The same holds for full-closure situations and railroad crossings. We present a catalogue of risk factors along with an appropriate algorithm for practical route planning in emergency situations. The second one takes into account a weekly updated set of probe-vehicle data for each minute of the week along with data of current travel times. Comparing those travel-time data allows calculation of the associated risk for traveling certain edges of a route in a road network. We expect our algorithm to be a major advancement especially for destinations that lie outside the typical region travelled weekdays. In this case the automatic route planning naturally goes along with an additional gain of time

Transfer matrices for the totally asymmetric exclusion process

We consider the totally asymmetric simple exclusion process (TASEP) on a finite lattice with open boundaries. We show, using the recursive structure of the Markov matrix that encodes the dynamics, that there exist two transfer matrices $T_{L-1,L}$ and $\tilde{T}_{L-1,L}$ that intertwine the Markov matrices of consecutive system sizes: $\tilde{T}_{L-1,L}M_{L-1}=M_{L}T_{L-1,L}$. This semi-conjugation property of the dynamics provides an algebraic counterpart for the matrix-product representation of the steady state of the process.Comment: 7 page

Decoherence-induced conductivity in the discrete 1D Anderson model: A novel approach to even-order generalized Lyapunov exponents

A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent $\xi^{-1}$. We determine the exact value of $\xi^{-1}$ of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all higher even-order generalized Lyapunov exponents can be calculated, as exemplified for fourth order. An approximation for the localization length (inverse standard Lyapunov exponent) is presented, by assuming a log-normal limiting distribution for the dimensionless conductance $T$. This approximation works well in the limit of weak disorder, with the exception of the band edges and the band center.Comment: 12 pages, 5 figure

Routing für Einsatzfahrzeuge

Ergebnisse aus VABENE und VABENE++ zu den Themen Risikorouting, Blaulichtrouting, Alternativrouten, Isochronen