What Is Queuing Theory?

Queuing theory is the mathematical study of the congestion and delays of waiting in line. Queuing theory (or "queueing theory") examines every component of waiting in line to be served, including the arrival process, service process, number of servers, number of system places, and the number of customers—which might be people, data packets, cars, etc.

As a branch of operations research, queuing theory can help users make informed business decisions on how to build efficient and cost-effective workflow systems. Real-life applications of queuing theory cover a wide range of applications, such as how to provide faster customer service, improve traffic flow, efficiently ship orders from a warehouse, and design of telecommunications systems, from data networks to call centers.

How Queuing Theory Works

Queues happen when resources are limited. In fact, queues make economic sense; no queues would equate to costly overcapacity. Queuing theory helps in the design of balanced systems that serve customers quickly and efficiently but do not cost too much to be sustainable. All queuing systems are broken down into the entities queuing for an activity.

At its most elementary level, queuing theory involves the analysis of arrivals at a facility, such as a bank or fast food restaurant, then the service requirements of that facility, e.g., tellers or attendants.

The origin of queuing theory can be traced back to the early 1900s, found in a study of the Copenhagen telephone exchange by Agner Krarup Erlang, a Danish engineer, statistician and, mathematician. His work led to the Erlang theory of efficient networks and the field of telephone network analysis.