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Long queues of vehicles are often found at various traffic light intersection in cities. Such situation is caused by many factors, including the duration of traffic lights that do not match with the arrival of the vehicles. In this article, we propose a model of queue at a road intersection with traffic lights where it can be determine the appropriate traffic light duration based on the arrival of the vehicle, so that the queue waiting time can be obtained that is as far as possible under the driver's time stress threshold. The waiting time in the queue is very dependent on the accuracy of the traffic light time duration setting, both red and green lights on all intersection lines. The research method that will be carried out is firstly to determine the vehicle waiting time model in the queue at the red light phase, followed by the waiting time model in the green light phase with the arrivals by Poisson process with M/M/1 queuing model, then, the …