queueing theory Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...

, a discipline within the mathematical

theory of probability Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...

, Kendall's notation (or sometimes Kendall notation) is the standard system used to describe and classify a queueing node. D. G. Kendall proposed describing queueing models using three factors written A/S/''c'' in 1953 where A denotes the time between arrivals to the queue, S the service time distribution and ''c'' the number of service channels open at the node. It has since been extended to A/S/''c''/''K''/''N''/D where ''K'' is the capacity of the queue, ''N'' is the size of the population of jobs to be served, and D is the queueing discipline. When the final three parameters are not specified (e.g.

M/M/1 queue In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single server, where arrivals are determined by a Poisson process and job service times have an expon ...

), it is assumed ''K'' = ∞, ''N'' = ∞ and D = FIFO.

A: The arrival process

A code describing the arrival process. The codes used are:

S: The service time distribution

This gives the distribution of time of the service of a customer. Some common notations are:

''c'': The number of servers

The number of service channels (or servers). The

has a single server and the

M/M/c queue In queueing theory, a discipline within , the queue (or Erlang–T model) is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a , there are servers, and job service t ...

''c'' servers.

K: The number of places in the queue

The capacity of queue, or the maximum number of customers allowed in the queue. When the number is at this maximum, further arrivals are turned away. If this number is omitted, the capacity is assumed to be unlimited, or infinite. : Note: This is sometimes denoted ''c'' + ''K'' where ''K'' is the buffer size, the number of places in the queue above the number of servers ''c''.

N: The calling population

The size of calling source. The size of the population from which the customers come. A small population will significantly affect the

effective Effectiveness is the capability of producing a desired result or the ability to produce desired output. When something is deemed effective, it means it has an intended or expected outcome, or produces a deep, vivid impression. Etymology The ori ...

arrival rate Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the ...

, because, as more customers are in system, there are fewer free customers available to arrive into the system. If this number is omitted, the population is assumed to be unlimited, or infinite.

D: The queue's discipline

The Service Discipline or Priority order that jobs in the queue, or waiting line, are served: :Note: An alternative notation practice is to record the queue discipline before the population and system capacity, with or without enclosing parenthesis. This does not normally cause confusion because the notation is different.

References

{{Queueing theory Mathematical notation Single queueing nodes