Mathematics for all Queueing Models
There is some simple mathematics which can apply to all queueing models.
It is outlined below. Firstly, It is obvious from the definitions
of
and that:
Also, generalised equations are available which apply to any queueing
model:

It has been shown that in a steadystate queueing system, that .
This is known as Little's Law, as it was discovered by John D. C. Little.
A proof can be found in [LITT61]. Little
also managed to show that .
If the arrival rate of customers is not independent of the size of the
queue, then the symbol
in Little's Law can be replaced with ,
which denotes the average customer arrival rate over a long period of time.

If one assumes that the expected service time is as indicated as above,
then it follows from the definition of W and W_{q},
Last Updated: 14th June 1999