K. Nagel and S. Rasmussen. Traffic at the edge of chaos. In R. A. Brooks and P. Maes, editors, Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, pages 222--235. MIT Press, Cambridge, MA, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....average values of flow metrics but also their higher moments (e.g. variance) Finally, CA models are amenable to representing both single and multi lane traffic, which is particularly crucial for the modeling of highways. In this paper, we build on the pioneering work of Nagel and his colleagues [7, 8, 10, 11, 15] who were among the first to recognize the usefulness of cellular automata to traffic flow modeling. Their models have been extended by several others in the last few years [2, 5, 6 , 13, 14] However, most of the existing models have focused on describing the relationship between the first ....

....in variability (i.e. a smaller p) results in only limited reduction in speed variance. This means that the presence of any amount variability is sufficient to result in high speed variance. Our findings are consistent with those obtained by Nagel et al..who conducted somewhat similar experiments [10]. 3.3 Stochastic Cellular Automata for Two Lane Traffic Flow Most roadways do not consist of a single lane only. In fact, most highways provide two or more lanes. Despite this prevalence, existing literature offers few analytical models for multi lane traffic. This can, in part, be explained by ....

Nagel, K. and S. Rasmussen, "Traffic at the Edge of Chaos," Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, MIT Press, pp. 222-235, 1994.

....planners with a tool to assess the impact of changes to urban road networks. The model presented here is far more modest in its aims. It cannot offer quantitative predictions but merely qualitative suggestions concerning the likely effects of new technologies on traffic system performance. In [44] the authors cite a simulation model to argue that traffic systems are unstable when operating at maximum flow, and therefore Advanced Traffic Management Systems (ATMS) should not be used to push road networks toward maximal flow. As in [27] the argument here is that ATIS technologies may enable ....

....we should prefer ATIS systems which facilitate them. Other obvious directions for future work involve other microsimulation techniques. Now that car following and link performance functions have been explored it might be worthwhile to implement a particle hopping (i.e. cellular automata) model [44, 43, 54]. Another dimension along which the model might be varied is agent strategy. A variety of adaptive rules other than those used here, for instance that of equation 1, might be DRAFT Terence Kelly ATIS at Rush Hour May 18, 1997 15 used. Or the mean rule and OLS rule could be modified to examine ....

Kai Nagel and Steen Rasmussen. Traffic at the edge of chaos. In Rodney A. Brooks and Pattie Maes, editors, Artificial Life IV, pages 222--235. MIT Press, 1994. This is the paper that got me interested in traffic modeling. Some time after seeing Nagel's presentation at the Alife IV conference I wrote [27]. ISBN 0-262-52190-3.

....power available to individual motorists must be evaluated with caution. 2 Methods 2. 1 The Model 1 District 5 4 3 2 Suburb Highway Business Figure 1: The Rush Hour World In Figure 1 we see a depiction of my rush hour world, a model inspired by but not similar to that described in [8]. We have a two lane road divided into three sections: a suburb containing evenly spaced sources of cars or houses, a highway which contains neither sources nor sinks of cars, and a business district containing offices or destinations. At the beginning of a simulation run, each car is ....

....Each day every commuter decides upon a time to leave home. A driver s strategy is the mapping from its past experience to this decision. The driver population is homogeneous with respect to strategy, i.e. during any given run of the simulation every car uses the same strategy every day. See [8] and the references therein for more general discussions of similar models. Cars enter and leave the highway at zero speed. At each tick of the clock Deltat, each car calculates a new speed and advances at the new speed along the 2 road. The new speed is subject to the following constraints: it ....

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Kai Nagel and Steen Rasmussen. Traffic at the edge of chaos. In Rodney A. Brooks and Pattie Maes, editors, Artificial Life IV, pages 222--235. MIT Press, 1994.

....it must be considered that near the transition from free to congested flow large fluctuations occur, which also effect errors in the relevant measurands. Therefore it is possible, that in particular the route guidance system drives the system into a state, in which it is more difficult to control [15]. For urban areas this seems to be neglectable, since large fluctuations are suppressed by the traffic lights. The different parameters for the density based route guidance were varied for the same scenario like in the previous section. The average travel time is plotted in Fig. 3 as function of ....

K. Nagel and S. Rasmussen, Traffic at the edge of chaos, in Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, edited by R. A. Brooks and P. Maes, MIT Press, Cambridge, MA, 1994

.... well suited are: ffl Economic models, with economic agents interacting with each other through a market[20, 9] ffl Social insects building nests[1] foraging for food[18] or performing other actions [19, 8] ffl Molecules interacting in an artificial chemistry[5, 6, 7] ffl Traffic simulation[18, 15]. ffl Ecological simulations[10, 4, 14, 17, 16] ffl Simulation games such as SimLife, SimCity, etc. 13] ffl Artificial intelligence applications[3] ffl General studies of complex systems, artificial life, cellular automata, emergent phenomena, etc. Simple versions of several of the above ....

K. Nagel and S. Rasmussen. Traffic at the edge of chaos. In R. Brooks and P. Maes, editors, Artificial Life IV. MIT Press, 1994.

....or late, very small differences in the individual average departure time will result in large differences in the individual average arrival time, and because of stochasticity there will be strong fluctuations in the arrival time from day to day even if the departure time remains constant. Ref. [32] reports from a scenario where road pricing is used to push traffic closer towards the system optimum. Also in this case, the improved system performance is accompanied by increased variability. Both results were obtained with day to day replanning. 14 660 680 700 720 740 760 780 0 20 40 ....

K. Nagel and S. Rasmussen. Traffic at the edge of chaos. In R. A. Brooks and P. Maes, editors, Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, pages 222--235. MIT Press, Cambridge, MA, 1994.

....congestion, a motorist s optimal strategy may be able to safely ignore real time congestion information. The value of real time information seems to be highest when the system operates near capacity; the observation that the system is probably least predictable in that regime has been made before [30]. Another implication may be that, regarding the initial plan set of the iteration process, it may make sense to have a certain amount of drivers chose geometrically shortest paths during peak period in order to speed up the relaxation process. 16 14 Computational considerations For computing ....

K. Nagel and S. Rasmussen. Traffic at the edge of chaos. In R. A. Brooks and P. Maes, editors, Artificial Life IV: Proceedings of the Fourth International Workshop on the Synthesis and Simulation of Living Systems, pages 222--235. MIT Press, Cambridge, MA, 1994.

....Dichte Abbildung 3: Relative Fluktuaionen ( mittlerer relativer Vorhersagefehler) der Fahrzeit uber einen Abschnitt der L ange l = 100 bei einer Systemgr o e von L = 1000. Bei der Dichte ae 0:1, also in der N ahe der optimalen Dichte ae opt , steigt dieser Wert pl otzlich drastisch an. Aus: [21]) Ein Problem ist, da Messungen in der Realit at ausgerechnet an dieser Stelle sehr hohe Fluktuationen zeigen, so da zur Bestimmung eines maximal m oglichen mittleren Durchflusses das bisherige Datenmaterial nicht ausreichend ist. Bei Simulationen ist es nat urlich einfach, uber viele ....

....ahnlich wie ein kritischer Phasen ubergang verh alt; im Grenzwert unendlich kleiner Fluktuationen bei freiem Fahren ( Cruise Control Limit ) wird der Ubergang exakt kritisch [19, 20] Als Folge davon finden wir z.B. ein drastisches Absinken der Vorhersagbarkeit von Reisezeiten in diesem Bereich [21]. Zum Nachweis dieses Effektes dienen Simulationen eines geschlossenen Ssytems der L ange L und mit N = ae Delta L Fahrzeugen. Nach einer Relaxationszeit messen wir f ur alle N Fahrzeuge die Zeit T i (l) zum Durchfahren einer Me strecke l L=10. Der Mittelwert h T i = 1=N) P T i (l) und der ....

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Nagel K, Rasmussen S, Traffic at the edge of chaos, Brooks R, Maes P (eds.), Proceedings of the Alife 4 meeting, MIT press, Cambridge, MA, 1994.

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Kai Nagel & Steen Rasmussen (1994). Traffic at the edge of chaos. Rodney Brooks & Pattie Maes, eds., Artificial Life IV: 222--235. Cambridge, MA: MIT Press.

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