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.