Queueing theory

Queueing theory is the mathematical study of waiting lines and congestion. It models arrivals and service to estimate delays, queue lengths, and system performance.

Poisson process: A counting process with independent increments and Poisson-distributed event counts, often used to model random arrivals. Its memoryless event structure makes it a standard model for arrivals.
Arrival rate: The average number of customers or jobs entering a system per unit time. It measures demand against which service capacity is evaluated.
Call centre: A centralized operation that handles large volumes of telephone or digital customer contacts. Models estimate staffing needs and callers' waiting times under changing demand.
Discrete-event simulation: A simulation method that advances a model from one event to the next. It can estimate queue performance when analytic formulas are unavailable or assumptions are complex.
Exponential distribution: A continuous probability distribution with a constant hazard rate and the memoryless property. It models memoryless service times and underlies many tractable queueing models.
Service rate: The average number of customers or jobs a server completes per unit time. It sets the pace at which a queue can be cleared.
Packet switching: A method of transmitting data by dividing it into packets that share network links. Packets queue at network devices when traffic approaches link or processing capacity.
Operations research: The discipline of using mathematical methods to support decisions about complex systems. Queueing theory is one analytical toolkit within this broader decision-science field.
Kendall's notation: A notation that classifies queues by arrival process, service-time distribution, server count, and other features. It compactly specifies the assumptions behind a queueing model.
Traffic intensity: A measure of offered workload relative to service capacity, commonly expressed as a ratio. As workload approaches capacity, delays and queue lengths can rise sharply.

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