Much of queueing theory is very complex. Almost all of it relies heavily
on mathematics, especially statistics. This section investigates the mathematics
and theory of queueing theory, but much of the mathematics is formidable
(some of it beyond graduate mathematics level) and therefore beyond the
author. Thus, most important results will be stated, but not derived (where
possible, a source where a proof can be found will be included). The mathematics
for the M / M / 1 model will be worked through
partially, but results for many of the other queueing models will be summarised
in a table.