Traffic jam at adjustable tollgates controlled by line length

We present the stochastic model for the jam formation at the tollgates of which the number is adjusted by synchronizing with the jam's length. We study the jam formation and its fluctuation in front of the adjustable tollgates on a highway. Controlling the number of tollgates has an important effect on the jam formation. The jams are classified into three kinds: (a) localized jam, (b) synchronized jam, and (c) growing jam. The jamming transitions from the localized jam, through the synchronized jam, to the growing jam occur with increasing inflow probability. At an intermediate inflow, the jam fluctuates largely by synchronizing with the number of tollgates. When the inflow probability is higher than the sum of outflow probabilities at tollgates, the jam continues to grow and diverge with time. The dependence of the fluctuating jam on the inflow probability is clarified.