Development of a New Methodology to find the Expected Busy Periods for Controllable M/G/1 Queueing Models Operating under the Multi-variable Operating Policies: Concepts and applications to the dyadic policies

In this paper, steady-state controllable M/G/1 queueing systems operating under the dyadic policies are considered. A new method to obtain the expected busy period when the D-policy is involved in system operation, is developed. This new method requires derivation of so called 'the pseudo probability density function' of the busy period for the system under consideration, which is completely different from its actual probability density function. However, the proposed pseudo probability density function does generate the correct expected busy period through simple procedures.