Theoretical and experimental study on excluded volume effect in pedestrian queue

We have introduced excluded volume effect, which is a significant factor to model a realistic pedestrian queue, into queueing theory. The model has been exactly solved. Concretely, probability distributions and means of the number of waiting pedestrians, length of a queue, and waiting time, have been derived. Due to the excluded volume effect, the process of closing up and interval distance between pedestrians are included in our new model, so that it becomes more realistic than previous model and has reproduced the results of our queueing experiment.