6 research outputs found
Random walk theory of jamming in a cellular automaton model for traffic flow
The jamming behavior of a single lane traffic model based on a cellular
automaton approach is studied. Our investigations concentrate on the so-called
VDR model which is a simple generalization of the well-known
Nagel-Schreckenberg model. In the VDR model one finds a separation between a
free flow phase and jammed vehicles. This phase separation allows to use random
walk like arguments to predict the resolving probabilities and lifetimes of jam
clusters or disturbances. These predictions are in good agreement with the
results of computer simulations and even become exact for a special case of the
model. Our findings allow a deeper insight into the dynamics of wide jams
occuring in the model.Comment: 16 pages, 7 figure
Traffic Jams: Cluster Formation in Low-Dimensional Cellular Automata Models for Highway and City Traffic
Cellular automata (CA) models are quite popular in the field of traffic flow. They allow an effective implementation of real-time traffic computer-simulations. Therefore, various approaches based on CA models have been suggested in recent years. The first part of this thesis focuses on the so-called VDR (velocity-dependent randomization) model which is a modified version of the well known Nagel-Schreckenberg (NaSch) CA model. This choice is motivated by the fact that wide phase separated jams occur in the model. On the basis of random walk theory an analytical approach to the dynamics of these separated jam clusters is given. The predictions are in good agreement with the results of computer simulations and provide a deeper insight into the dynamics of wide jams which seem to be generic for CA approaches and are therefore of special interest. Furthermore, the impact of a localized defect in a periodic system is analyzed in the VDR model. It turns out that depending on the magnitude of the defect stop-and-go traffic can occur which can not be found in the VDR model without lattice defects. Finally, the VDR model is studied with open boundaries. The phase diagrams, obtained by Monte-Carlo simulations, reveal two jam phases with a stripped microscopic structure and for finite systems the existence of a new high-flow phase is shown. The second part of this thesis concentrates on CA models for city traffic with the focus on the Chowdhury-Schadschneider (ChSch) model. In the context of jam clusters the model reveals interesting features since two factors exert influence on the jamming behavior. On the one hand, jams are induced at crossings due to the traffic lights, i.e., cars are forced to stop at a ``red light', and, on the other hand, the dynamics of such induced jams is governed by the NaSch model rules. One part of the investigations covers global (fixed) traffic light strategies. These are found to lead to strong oscillations in the global flow except for the case of randomly switching lights. Furthermore, the impact of adaptive (local) traffic light control is analyzed. It is found that the autonomous strategies can nearly match the global optimum of the ChSch model. In order to provide a more realistic vehicle distribution, the ChSch model is enhanced by a stochastic turning of vehicles and by inhomogeneous densities. Here, the autonomous strategies can outperform the global ones in some cases
A Microscopic Model for Packet Transport in the Internet
A microscopic description of packet transport in the Internet by using a
simple cellular automaton model is presented. A generalised exclusion process
is introduced which allows to study travel times of the particles ('data
packets') along a fixed path in the network. Computer simulations reveal the
appearance of a free flow and a jammed phase separated by a (critical)
transition regime. The power spectra are compared to empirical data for the RTT
(Round Trip Time) obtained from measurements in the Internet. We find that the
model is able to reproduce the characteristic statistical behaviour in
agreement with the empirical data for both phases (free flow and congested).
The phases are therefore jamming properties and not related to the structure of
the network. Moreover the model shows, as observed in reality, critical
behaviour (1/f-noise) for paths with critical load.Comment: 9 pages, 7 figure
Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic
We study the impact of global traffic light control strategies in a recently
proposed cellular automaton model for vehicular traffic in city networks. The
model combines basic ideas of the Biham-Middleton-Levine model for city traffic
and the Nagel-Schreckenberg model for highway traffic. The city network has a
simple square lattice geometry. All streets and intersections are treated
equally, i.e., there are no dominant streets. Starting from a simple
synchronized strategy we show that the capacity of the network strongly depends
on the cycle times of the traffic lights. Moreover we point out that the
optimal time periods are determined by the geometric characteristics of the
network, i.e., the distance between the intersections. In the case of
synchronized traffic lights the derivation of the optimal cycle times in the
network can be reduced to a simpler problem, the flow optimization of a single
street with one traffic light operating as a bottleneck. In order to obtain an
enhanced throughput in the model improved global strategies are tested, e.g.,
green wave and random switching strategies, which lead to surprising results.Comment: 13 pages, 10 figure
Mechanical restriction versus human overreaction triggering congested traffic states
A new cellular automaton (CA) traffic model is presented. The focus is on
mechanical restrictions of vehicles realized by limited acceleration and
deceleration capabilities. These features are incorporated into the model in
order to construct the condition of collision-free movement. The strict
collision-free criterion imposed by the mechanical restrictions is softened in
certain traffic situations, reflecting human overreaction. It is shown that the
present model reliably reproduces most empirical findings including
synchronized flow, the so-called {\it pinch effect}, and the time-headway
distribution of free flow. The findings suggest that many free flow phenomena
can be attributed to the platoon formation of vehicles ({\it platoon effect})Comment: 5 pages, 3 figures, to appear in PR
Optimal traffic states in a cellular automaton for city traffic
The impact of global traffic light control strategies for city networks is analyzed in a recently proposed cellular automaton model. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nage-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets