Microscopic approach for the distribution of the system size in M/G/1 with vacations

Abstract

The Distribution of the system size in M/G/1 with vacations is analyzed in this thesis. While traditional analysis suggests Laplace-stiltjes transform for the system size distribution as the results, microscopic approach used in this thesis results in explicit and transform-free distribution of system size in M/G/1 with vacations. The method used in this thesis has different point of view comparing to the traditional approach. The traditional approach considers waiting space as a whole. Contrarily, the approach used in this thesis investigates waiting space as a separate component of the system, which is why the latter is called by microscopic approach. Microscopic approach can not only show most of results derived through traditional approach but it also allows us to understand and examined the behavior of the queueing system thoroughly. Even though microscopic approach gives simple and explicit expressions of the distribution of system size of vacation models, it contains unknown parameter. However, the results of microscopic approach are still useful since the property of the unknown parameter can be analyzed. Analysis on vacation model causes one additional part comparing to M/G/1 without vacation(Standard M/G/1). However, the additional part can be analyzed exactly through cycle analysis. Accordingly, the vacation model can be evaluated if the results of M/G/1 is known. Thus, Microscopic approach has shown the system behavior explicitly as well as in detail.