ABSTRACT

In our everyday life, there are many so-called “waiting line systems”; for example, customers waiting in the checkout line in a grocery store, passengers waiting in line to go through the security checkpoint at an airport, and customers calling customer service and waiting in a queue to be answered in the order received. If the demand for processing exceeds the capacity of serving units, we often encounter a “wait line” system. If you look at these systems, it is not difficult to find the common features involved in these systems; (1) there is a demand for service and the demand is stochastic, that is to say, the time when a customer arrives is somewhat random and unpredictable; (2) there are limited resources (or servers) to fulfill the demand; when there are more customers than the available servers, waiting occurs and the order of being served follows a predetermined rule, usually the first-in-first-out (FIFO) order. In systems operations and processes, it is very common to observe the characteristics of waiting line systems, such as in manufacturing systems; raw materials waiting in the queue to be processed, machines in queues to be serviced, and finished products waiting in line to be shipped out; in service systems, entities (such as customers) forming a line, waiting for their turn to be served. As system designers, we are tasked to control the length of the waiting line; on the one hand, entities that request processing and service need to have shorter waiting times, but, on the other hand, we need to control the number of process/service channels to make sure they provide enough capacity with the most cost efficiency. In waiting line system design, the objective is to optimize the number of service channels to achieve the desired systems performance. The mathematical models addressing the waiting line system behaviors are called queuing theory and models.