Methods for Shortening Waiting Time in Walking-Distance Introduced Queueing Systems

We have investigated the walking-distance introduced queueing theory and verified that the mean waiting time in a parallel-type queueing system, i.e., queues for each service windows, becomes smaller than that in a fork-type queueing system, which collects people into a single queue, when sufficiently many people are waiting in queues. In a fork-type queueing system, a person at the head of the queue, which is usually set at the end of the system, starts to move when one of the service windows become vacant. Since this walking time from the head of the queue to the windows increases the waiting time, we propose to set the head of the queue at the center of the system and keep one person waiting at each service window when it is occupied by other person. The validity of the methods is examined by the theoretical analysis, simulations, and experiments.