In this paper, information theoretic methodology for
system modeling is applied to investigate the probability density function
of the busy period in M/G/1 vacation models operating under the N-, T- and
D-policies. The information about the density function is limited to a few
mean value constraints (usually the first moments). By using the maximum
entropy methodology one obtains the least biased probability density
function satisfying the system's constraints. The analysis of the three
controllable M/G/1 queueing models provides a parallel numerical study of
the solution obtained via the maximum entropy approach versus “classical”
solutions. The maximum entropy analysis of a continuous system descriptor
(like the busy period) enriches the current body of literature which, in
most cases, reduces to discrete queueing measures (such as the number of
customers in the system).