Abstract
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 is included in our new model, so that the mean number of pedestrians increases as pedestrian arrival probability (λ) and leaving probability (μ) increase even if the ratio between them (i.e., ρ = λ/μ) remains constant. Moreover, interval distance between pedestrians is included in our model because of the excluded volume effect, thus, length of a queue is considered more realistically than previous model. A queueing experiment is also performed to verify the validity of our model.
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Yanagisawa, D. et al. (2010). Excluded Volume Effect in a Pedestrian Queue. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds) Cellular Automata. ACRI 2010. Lecture Notes in Computer Science, vol 6350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15979-4_56
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DOI: https://doi.org/10.1007/978-3-642-15979-4_56
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