The literature on queueing theory is already very large. It contains
more than a dozen books and about a thousand papers devoted exclusively
to the subject; plus many other books on probability theory or
operations research in which queueing theory is discussed. Despite this
tremendous activity, queueing theory, as a tool for analysis of
practical problems, remains in a primitive state; perhaps mostly because
the theory has been motivated only superficially by its potential
applications. People have devoted great efforts to solving the 'wrong
problems. ' Queueing theory originated as a very practical subject. Much
ofthe early work was motivated by problems concerning telephone traffic.
Erlang, in particular, made many important contributions to the subject
in the early part of this century. Telephone traffic remained one of the
principle applications until about 1950. After World War II, activity in
the fields of operations research and probability theory grew rapidly.
Queueing theory became very popular, particularly in the late 1950s, but
its popularity did not center so much around its applications as around
its mathematical aspects. With the refine- ment of some clever
mathematical tricks, it became clear that exact solutions could be found
for a large number of mathematical problems associated with models of
queueing phenomena. The literature grew from 'solutions looking for a
problem' rather than from 'problems looking for a solution.