The a priori vacation probability in the M/G/1 single vacation models Original Research Article

In the paper we focus on the class of M/G/1 single vacation models, where a server takes exactly one vacation immediately after service completion and there are no items available in the system. This vacation model class includes model types with different vacation disciplines and, particularly, the exhaustive service model, gated non-exhaustive model, model with fixed vacation policy. Here we investigate the models that are characterized by the dependence of the item waiting time on the model parameters gained analytically or with the help of simulation. It is assumed that at the moment an item arrives into the system, there exists the probability, denoted as the a priori probability, that, according to some vacation discipline, the server takes a vacation after this item service completion. So we aim at deriving this a priori probability. To achieve the goal, we present some special M/G/1 model, which is equivalent to the mentioned above models, as far as the item waiting time is concerned. Within this special model the item flow is divided according to the Bernoulli recurrence operation with the parameter, associated with the a priori probability. Following this approach, the mentioned above models are differentiated from each other only by the a priori probability value. We introduce the examples of analytical and simulation approach for the a priori probability definition. The gained results widen the possibilities for analyses of the models being considered.