# Kendall's Notation for Classification of Queue Types

There is a standard notation for classifying queueing systems into different types. This was proposed by D. G. Kendall. Systems are described by the notation:

A / B / C / D / E

where:

 A Distribution of interarrival times of customers B Distribution of service times C Number of servers D Maximum total number of customers which can be accommodated in system E Calling population size

A and B can take any of following distribution types:

 M Exponential Distribution (Markovian) D Degenerate (or Deterministic) Distribution Ek Erlang Distribution (k = shape parameter) G General Distribution (arbitrary distribution)

Notes: If G is used for A, it it sometimes written GI. C is normally taken to be either 1, or a variable, such as n or m. D is usually infinite or a variable, as is E. If D or E are assumed to be infinite for modelling purposes, they can be omitted from the notation (which they frequently are). If E is included, D must be, to ensure that one is not confused between the two, but an infinity symbol is allowed for D.

## Examples

• D / M / n - This would describe a queue with a degenerate distribution for the interarrival times of customers, an exponential distribution for service times of customers, and n servers.
• Ek / El / 1 - This would describe a queue with an Erlang distribution for the interarrival times of customers (with a shape parameter of k), an exponential distribution for service times of customers (with a shape parameter of l), and a single server.
• M / M / m / K / N - This would describe a queueing system with an exponential distribution for the interarrival times of customers and the service times of customers, m servers, a maximum of K customers in the queueing system at once, and N potential customers in the calling population.

Last Updated: 6th June 1999
Written by: Andrew Ferrier