Köteori

Køteori, or køteori in Norwegian and Danish, is the branch of mathematics and operations research that studies waiting lines and service systems. It analyzes how items such as customers, data packets, or jobs arrive, wait, and are served, with the goal of predicting performance measures like average waiting time, queue length, and server utilization.

The framework of koteori includes the arrival process, service process, number of servers, and the rule by which items are chosen for service (the queue discipline). Common modeling assumptions use stochastic processes, often with Poisson arrivals and various service-time distributions. A standard tool is Kendall notation, which describes a system as A/S/c with A representing the arrival process, S the service-time distribution, and c the number of servers. Finite-capacity systems are denoted with an additional K. Classic models include M/M/1, M/M/c, M/G/1, and GI/G/1, as well as networks of queues such as Jackson networks.

Key results in koteori include Little’s Law (L = λW), which relates average numbers in the system to arrival rate and waiting time, and stability conditions that ensure the system does not grow without bound. Analyses often yield performance metrics such as expected waiting time, service level, and utilization, guiding design and staffing decisions.

Applications span telecommunications, manufacturing, computer networks, and service industries. The field has historical roots in early 20th-century work on telephone traffic and was formalized in the mid-20th century through development of standard notations and models. See also queueing theory, operations research, and performance modeling.