Abstract
We introduce the effect of delay in walking from the head of the queue to the service windows in the queueing theory and analyze queueing systems under various conditions. When there are plural service windows, the queueing theory indicates that a fork-type queue, which collects people into a single queue, is more efficient than a parallel-type queue, i.e., queues for each service windows. However, in the walking-distance introduced queueing theory, we find that the parallel-type queue is more efficient when sufficiently many people are waiting in queues and service time is short against walking time.
