Modeling decisions for the time-dependent optimal lane configuration policy with queueing theory and mathematical programming

We provide mathematical models to operate a toll plaza with the time-dependent lane configuration policy. To formulate toll operations in the problem we use the queueing theory and mathematical programming. The queueing theory is utilized to obtain the stability condition which requires the mean arrival rate less than the mean service rate in each lane and compute the mean waiting time in the queue. The mathematical programming is used to determine the time-dependent lane configuration to minimize the total waiting and operation costs. In order to apply the introduced mathematical models in real world problem, we provide a case study based on the actual traffic data collected and show how the time-dependent lane configuration policy can be achieved in each time period. By numerical evaluation we demonstrate the electronic toll collection (ETC) is an intelligent transportation system which achieves high throughput and maintains almost no wait time.