Design and Analysis of a Vacation Model for Two-phase Queueing System with Gated Service

This paper mainly deals with a two phase service queueing model with gated service vacation. In this gated service vacation model, only those customers who are present in the queue when the server starts a batch mode service are taken into the batch. We have derived probability generating functions of the system size and the orbit size. We have investigated the conditions under which the steady state exists. Some useful performance measures are also obtained. The service to further arrivals is deferred until the server completes the second phase individual service to the batch. Based on the numerical calculations and graphical representations it reveals the fact that this type of modelling helps in analyzing certain situations in which customers require service in two stages of which the first stage of service is essentially of gated type.