Section 5 contains a discussion of the results and compares them to values in reality. A preliminary account of the model is given in [8]. The model. Our computational model is defined on a one-dimensional array of L sites and with open or periodic boundary conditions. Each site may either be occupied by one vehicle, or it may be empty.
Each vehicle has an integer velocity with values between zero and vmax. Through the steps very general properties of single lane one to four traffic are modelled on the basis of integer probabilistic cellular valued automaton rules [9, 10].
Already this simple model shows nontrivial and realistic behavior. Step 3 is essential in simulating realistic traffic flow since otherwise the dynamics is completely deterministic. It takes into account natural velocity fluctuations due to human behavior or due to varying external conditions.
Without this randomness, every initial configuration of vehicles and corresponding velocities reaches very quickly a stationary pattern which is shifted backwards I. The model has been implemented in FORTRAN, using a logical array for the positions of the cars and an integer array for the velocities. As the expected gain of multispin coding would therefore give only a factor of about six, we postponed the work on a bitwise implementation. A significant part of the Monte-Carlo simulation runs have been carried out on an iPSC Hypercube using up to 16 nodes, with only slight modifications of the prc- gram.
The model's speed on one processor of the Hypercube was about the same as on the workstation. Waific on a circle closed system. In this section we present results from systems periodic boundary with conditions thus sim- ulating traffic in a closed loop "as in car only races" on a single lane. Simulated traffic at a low density of o. Each new line shows the traffic lane after one further complete velocity-update and just before the car motion.
Empty sites are represented by a dot, sites which are occupied by a car are represented by the integer number of its velocity. At low densities, we see undisturbed motion. With these was definitions, easy perform it to many simulations with different densities p, thus after relaxation to equilibrium getting data for the commonly used fundamental diagrams which plot vehicle flow vs. In figures I and 2 we sho,v typical situations at low and high densities.
Whereas we find laminar traffic at low densities, there are congestion clusters small jams at higher densities, which are formed randomly due to velocity-fluctuations of the cars. If one follows in Fig. Same picture as figure I, but at a higher density of o.
I cars per site. Note the backward motion of the traffic jam. There it stays stuck in the queue for a certain time with some slow advances, and can accelerate to full speed after having left the cluster at its end. So the cluster represents a typical start-stop-wave as found in freeway traffic cf. We present the fundamental diagram of our model in figure 4.
It can clearly be seen that a change-over takes place near p 0. Simulations without randomization do not show a dependence on the system size. However, it is not clear from these pictures where to locate an exact transition point. The question in the update procedure then is simply if the next site is free step two and if the speed is randomly set to zero step three.
Space-time-lines trajectories for cars from Aerial Photography after [16]. Each fine represents the movement of one vehicle in the space-time-domain. Traffic flow q in cars per time step vs. Traffic flow q in cars per hour us. Occupancy is the percentage of the road which is covered by vehicles after [17]. For speeds larger than I an additional parameter for the current speed is needed which gives serious difficulties for analytical treatments.
However, even in this case a kind of mean-field approximation is possible and the results will be reported elsewhere [12]. For direct calculations the easiest dynamics is on the basis of a master way to formulate the equation with continuous time and random sequential update.
This makes of course a difference to the parallel updating which can simply be seen by simulating the two different updates but the results should be qualitatively similar and the randomization parameter p plays a particular simple role for random sequential update. Waific in a bottleneck situation Open system. For this section, we apply different boundary conditions, leaving the rest of the model un- changed:.
When the leftmost site site I is empty, we occupy it with a car of velocity 0. As our traffic is going from left to right, one may imagine a bottleneck situation where a saturated twc-lane-street feeds a street of only one lane which we simulate.
At the right side I. This simulates the beginning of an expanded four-lane freeway. Again the situation here simplifies considerably for vmax I. The case tx fl I in the notation of Refs. In this section, we make some rough arguments concerning the length scale and time scale of the simulation model. View via Publisher. Save to Library Save. Create Alert Alert. Share This Paper. Background Citations. Methods Citations. Results Citations.
Citation Type. Has PDF. Publication Type. More Filters. View 1 excerpt, cites methods. Cellular automata for one-lane traffic flow modeling. A probabilistic cellular automata model for highway traffic simulation. The modelling and prediction of traffic flow is one of the future challenges for science. We present a simulation tool for an urban road network based on real-time traffic data and a cellular … Expand. Simulating multilane traffic flows based on cellular automata theory.
Stochastic noise :. The behaviour of cellular automata CA models is … Expand.
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