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


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.


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