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 the design of telecommunications systems, from data networks to call centers.

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. By applying queuing theory, a business can develop more efficient queuing systems, processes, pricing mechanisms, staffing solutions and arrival management strategies to reduce customer wait times and increase the number of customers that can be served.

Queuing theory as an operations management technique is commonly used to determine and streamline staffing needs, scheduling and inventory, which helps improve overall customer service. It is often used by Six Sigma practitioners to improve processes.

For example, a 2003 paper by Stanford School of Business professor Lawrence Wein et al. used queuing theory to analyze the potential effects of a bioterrorism attack on U.S. soil and propose a system to reduce wait times for medications that would decrease the number of deaths caused by such an attack.

There are free queuing theory calculators available, where a user can choose a specific queuing model. Queuing Systems is a peer-reviewed scientific journal that covers queuing theory.

The origin of queuing theory can be 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.