Introduction to Management Science (10th Edition)

Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served . However, this does not mean that the service operation is understaffed or does not have the overall capacity to handle the influx of customers. In fact, most businesses and organizations have sufficient serving capacity available to handle their customers in the long run . Waiting lines result because customers do not arrive at a constant, evenly paced rate, nor are they all served in an equal amount of time. Customers arrive at random times, and the time required to serve them individually is not the same. Thus, a waiting line is continually increasing and decreasing in length (and is sometimes empty), and it approaches an average rate of customer arrivals and an average time to serve the customer in the long run. For example, the checkout counters at a grocery store may have enough clerks to serve an average of 100 customers in an hour, and in any particular hour only 60 customers might arrive. However, at specific points in time during the hour , waiting lines may form because more than an average number of customers arrive, and they make more than an average number of purchases.

Operating characteristics are average values for characteristics that describe the performance of a waiting line system .

Decisions about waiting lines and the management of waiting lines are based on these averages for customer arrivals and service times. They are used in queuing formulas to compute operating characteristics , such as the average number of customers waiting in line and the average time a customer must wait in line. Different sets of formulas are used, depending on the type of waiting line system being investigated. For example, a bank drive-up teller window that has one bank clerk serving a single line of customers in cars is different from a single line of passengers at an airport ticket counter that is served by three or four airline agents . In the next section we present the different elements and components that make up waiting lines before we look at queuing formulas in the following sections.