Designing method for large queueing system by walking-distance introduced queueing theory

The queueing theory has been extended for designing large queueing systems. In the large queueing systems, walking time from the head of the queue to the service windows is too large to ignore. Thus, we introduce the effect of delay in walking in the queueing theory, and obtain the suitable type of queueing system 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 shorter than walking time. We also consider the situation where there are two kinds of people, whose service time is short and long. The analytical result says that we can decrease peoplepsilas waiting time and their stress by setting up queues for each kind of people separately.