On Single Server Vacation Queues with Deterministic Service or Deterministic Vacations

We study two models of a single server queue with vacations. In model A, we study an M ⁄ M ⁄1 queue with deterministic vacations and designate it as M⁄M⁄D⁄l queue and in model B we study an M⁄D⁄1 queue with exponential vacations and designate it as M⁄D⁄M⁄1 queue. We obtain time dependent as well as steady state probability generating functions for both the models. For the steady state, we obtain explicit results for the mean number in the system and the mean waiting times for both models. All known results of the M ⁄ M ⁄1 and the M⁄D⁄1 queues are derived as special cases.