Using time‐varying tolls to optimize truck arrivals at ports

An analytical point‐wise stationary approximation model is proposed to analyze time‐dependent truck queuing processes with stochastic service time distributions at gates and yards of a port terminal. A convex nonlinear programming model is developed which minimizes the total truck turn time and discomfort due to shifted arrival times. A two‐phase optimization approach is used to first compute a system‐optimal truck arrival pattern, and then find a desirable pattern of time‐varying tolls that leads to the optimal arrival pattern. Numerical experiments are conducted to test the computational efficiency and accuracy of the proposed optimization models.