M/G/1 Multiple Vacation Model with Balking for a Class of Disciplines

In this paper an M/G/1 multiple vacation model with balking is considered. In this model the probability of joining to the system upon arrival depends on the number of customers at previous (customer or vacation) start epoch. The distribution of the joining probabilities is general, i.e. it is not limited to any class of distributions. The model enables a wide range of service disciplines including the exhaustive, the non-exhaustive, the semi-exhaustive, the gated, the G-limited and the E-limited ones. We establish stationary relationships between the number of customers in the system at different characteristic epochs. This leads to a system of linear equations for the stationary number of customers in terms of unknown probabilities. We provide the solution for these unknown probabilities on discipline specific way for all the above listed disciplines. Additionally the stability, the special case of state independent joining probabilities and the numerical solution are also discussed.