An M/G/l Vacation Model with Two Service Modes

Abstract

Consider an M/G/1 type queueing system with two service modes: regular speed and high speed. The service rule is characterized by two switch-over levels nR and nH, where nR and nH are given integers with 0 ≤ nH < nR. The server switches from regular speed mode to high speed mode when the number of customers present at a service completion epoch is equal to or larger than nR and switches from high speed mode to regular speed mode when the number of customers present decreases to nH. A key feature of the model is that the server takes a vacation for setup operations before a new service mode is available. This paper derives for the general model an expression for the generating function of the equilibrium queue-length distribution in terms of the switch-over levels. Two unknown parameters appear in the generating functions. Using a recursive method, we solve these unknown parameters and obtain a computationally tractable algorithm for the steady-state probabilities.