Walking-distance introduced queueing model for pedestrian queueing system: theoretical analysis and experimental verification

We have introduced the effect of delay in walking from the head of a queue to the service windows in the queueing model and obtain a suitable type of queueing system under various conditions by both computational simulation and theoretical analysis. When there are multiple service windows, the queueing theory indicates that mean waiting time in a fork-type queueing system (Fork), which collects pedestrians into a single queue, is smaller than that in a parallel-type queueing system (Parallel), i.e., queues for each service window. However, in our walking-distance introduced queueing model, we have examined that mean waiting time in Parallel becomes smaller when both the arrival probability of pedestrians and the effect of walking distance are large. Moreover, enhanced Forks, which shorten waiting time by reducing the effect of walking distance, are considered, and parts of our results are also verified by real queueing experiments.