Jam formation with line changing at two tollgates on a highway

We present the stochastic model for queueing at two tollgates with line changing of vehicles to take into account fluctuating inflow and outflow. We study the jam formation and its transition in front of two tollgates on a highway. The line changing between two queues of vehicles has an important effect on the jam formation. The jams are classified into three kinds: (a) localized jam, (b) line-changing jam, and (c) growing jam. The jamming transitions among different jams occur at two stages with increasing inflow rate. At the first transition point, the jamming transition from the localized jam to the line-changing jam occurs. When the inflow rate is higher than the sum of outflow rates at two tollgates, two jams continue to grow and diverge with time. At the second transition point, the jamming transition from the line-changing jam to the growing jam occurs. The dependence of the transition points on the choice probability is clarified.