S. Yukawa et al., DYNAMICAL PHASE-TRANSITION IN ONE-DIMENSIONAL TRAFFIC FLOW MODEL WITHBLOCKAGE, Journal of the Physical Society of Japan, 63(10), 1994, pp. 3609-3618
Effects of a bottleneck in a linear trafficway is investigated using a
simple cellular automation model. Introducing a blockage site which t
ransmit cars at some transmission probability into the rule-184 cellul
ar automation, we observe three different phases with increasing car c
oncentration: Besides the free phase and the jam phase, which exist al
ready in the pure rule-184 model, the mixed phase of these two appears
at intermediate concentration with well-defined phase boundaries. Thi
s mixed phase, where cars pile up behind the blockage to form a jam re
gion, is characterized by a constant flow. In the thermodynamic limit,
we obtain the exact expressions for several characteristic quantities
in terms of the car density and the transmission rate. These quantiti
es depend strongly on the system size at the phase boundaries; We anal
yse these finite size effects based on the finite-size scaling.