Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Mechanical Engineering


In today's world, the waiting lines or queues formed by people, machines, or other units are common and occur whenever the temporary demand for a service exceeds the capacity to provide it. These values may be the costs associated with idle production equipment and personnel or the lost sales due to unsatisfied customers. If one designs for sufficient facilities so that no queue builds up, then the operation is likely to be uneconomical due to excessive idle time at the service facility. If one designs the facility so that there is never any idle time at the service facility, then an unmanageable queue and many lost customers may result. A systems analyst must design a practical system so as to balance these costs at some optimal point. Classical queueing problems may be found in many areas. In the transportation field, one must decide the optimal number of aircraft flights to schedule into a particular city to handle individual requests for freight and passenger service. In machine interference, when one operator is assigned to two or more machines, there is a possibility that one machine may require his services while he is working with the other. As the number of machines per operator is increased, the probability of one machine interfering with the normal operation of another is similarly increased. In a supermarket system, one must know the number of checkout counters to be provided. In a medical facility, one would want to know how many physicians should be assigned to an outpatient clinic. Physically a queueing system is composed of two parts: a waiting line and a service facility. A complete description of a particular queueing system is dependent on the input process, service mechanism, queue discipline, station configuration, and population. Another way to designate queueing problems is by consideration of their properties. Thus, problem areas may be grouped into operational, statistical, and behavioral problems. Operational problems include all problems that are inherent in the operation of a real queueing system. For example, in a supermarket, a manager must know the number of customers he is willing to have waiting in line for service before an additional checkout-counter is opened. He is attempting to optimize between the costs of lost customers who fail to wait and the cost of providing additional service facilities.

Library of Congress Subject Headings

Queuing theory
System analysis



Number of Pages



South Dakota State University