Queue Under Controlled Admissibility Policy
Abstract: In this paper, we propose to study such a model which deals with the aspects concerning the control of the arrival process. The paper deals with Mx/G/1 queueing system with two types of heterogeneous services and Bernoulli vacation schedule under a controlled admissibility policy of arriving batches. There is a single server who provides two types of parallel general heterogeneous services (one of which has to be chosen by each customer) to the customer on FCFS basis. Before starting the service, each customer has option to choose first service with probability 1 or the second service with probability 2 . The server’s vacations are based on Bernoulli schedule under a single vacation policy where after completion of service (of any phase), the server either goes for a vacation of random length with probability or may continue to serve the next customer with probability (1) , if any. Under a controlled admissibility policy it is assumed that not all batches are allowed to join the system at all times. We obtain explicit queue size distribution at random epoch as well as at the departure epoch under the steady state conditions. In addition, some performance measures such as expected queue size and expected waiting time of a customer are also obtained. The numerical results for various performance measures are summarized displayed via graphs.