Tajima, Y.; Takimoto, K.; Nagatani, T. Scaling of pedestrian channel flow with a bottleneck. (English) Zbl 0978.90016 Physica A 294, No. 1-2, 257-268 (2001). Summary: Pedestrian channel flow at a bottleneck is investigated under the open boundaries by using the lattice-gas model of biased random walkers. It is shown that a dynamical phase transition occurs from the free flow to the choking flow at a critical density \(p_c\) with increasing density. The flow rate saturates at higher density than the critical density. In the choking-flow region, a scaling behavior is found as follows: the saturated flow rate \(J_s\) scales as \(J_s\propto d^{0.93\pm 0.02}\) and the critical density \(p_c\) scales as \(p_c\propto(d/W)^{1.16\pm 0.02}\), where \(d\) is the width of the bottleneck and \(W\) is the width of channel. The plot of the rescaled flow rate against the rescaled density collapses onto a single curve. Cited in 21 Documents MSC: 90B20 Traffic problems in operations research 60G50 Sums of independent random variables; random walks Keywords:lattice-gas model; biased random walkers; dynamical phase transition PDFBibTeX XMLCite \textit{Y. Tajima} et al., Physica A 294, No. 1--2, 257--268 (2001; Zbl 0978.90016) Full Text: DOI References: [1] Chowdhury, D.; Santen, L.; Schadschneider, A., Phys. Rep., 329, 199 (2000) [2] Wolf, D. E.; Schreckenberg, M.; Bachem (Eds.), A., Traffic Granular Flow (1996), World Scientific: World Scientific Singapore [3] Helbing, D.; Herrmann, H. J.; Schreckenberg, M.; Wolf (Eds.), D. E., Traffic and Granular Flow ’99 (2000), Springer: Springer Berlin · Zbl 0942.00072 [4] Helbing, D., Verkehrsdynamik (1997), Springer: Springer Berlin [5] Kerner, B. S., Phys. World, 8, 25 (1999) [6] Nagel, K.; Schreckenberg, M., J. Phys. I, 2, 2221 (1992) [7] Treiber, M.; Hennecke, A.; Helbing, D., Phys. Rev. E, 62, 1805 (2000) [8] Lee, H. Y.; Lee, H. W.; Kim, D., Phys. Rev. E, 59, 5101 (1999) [9] Nagatani, T., Phys. Rev. E, 59, 4864 (1999) [10] Ben-Naim, E.; Krapivsky, P. L.; Redner, S., Phys. Rev. E, 50, 844 (1994) [11] Nagatani, T., Phys. Rev. E, 61, 3534 (2000) [12] Helbing, D.; Mulnar, P., Phys. Rev. E, 51, 4282 (1995) [13] Muramatsu, M.; Irie, T.; Nagatani, T., Physica A, 267, 487 (1999) [14] Muramatsu, M.; Nagatani, T., Physica A, 275, 281 (2000) · Zbl 1052.90530 [15] Muramatsu, M.; Nagatani, T., Physica A, 286, 377 (2000) · Zbl 1052.90530 [16] Fukui, M.; Ishibashi, Y., J. Phys. Soc. Jpn., 68, 2861 (1999) [17] Helbing, D.; Farkas, I.; Vicsek, T., Nature, 407, 487 (2000) [18] Tajima, Y.; Nagatani, T., Physica A, 292, 545 (2001) · Zbl 0972.90011 [19] Clement, E.; Reydellet, G.; Rioual, F.; Parise, B.; Fanguet, V.; Lanuza, J.; Kolb, E., (Helbing, D.; Herrmann, H. J.; Schreckenberg, M.; Wolf, D. E., Traffic and Granular Flow ’99 (2000), Springer: Springer Berlin) · Zbl 1007.62531 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.