Multiple control policy in unreliable two-phase bulk queueing system with active Bernoulli feedback and vacation

Abstract

In this paper, a bulk arrival and two-phase bulk service with active Bernoulli feedback, vacation, and breakdown is considered. The server provides service in two phases as mandatory according to the general bulk service rule, with minimum bulk size ' a ' and maximum bulk size ' b '. In the first essential service (FES) completion epoch, if the server fails, with probability 'delta ' , then the renewal of the service station is considered. On the other hand, if there is no server failure, with a probability ' 1 - delta ' , then the server switches to a second essential service (SES) in succession. A customer who requires further service as feedback is given priority, and they join the head of the queue with probability beta. On the contrary, a customer who does not require feedback leaves the system with a probability ' 1- beta '. If the queue length is less than ' a ' after SES, the server may leave for a single vacation with probability ' 1 - beta '. When the server finds an inadequate number of customers in the queue after vacation completion, the server becomes dormant. After vacation completion, the server requires some time to start service, which is attained by including setup time. The setup time is initiated only when the queue length is at least ' a '. Even after setup time completion, the service process begins only with a queue length 'N' (N > b). The novelty of this paper is that it introduces an essential two-phase bulk service, immediate Bernoulli feedback for customers, and renewal service time of the first essential service for the bulk arrival and bulk service queueing model. We aim to develop a model that investigates the probability-generating function of the queue size at any time. Additionally, we analyzed various performance characteristics using numerical examples to demonstrate the model's effectiveness. An optimum cost analysis was also carried out to minimize the total average cost with appropriate practical applications in existing data transmission and data processing in LTE-A networks using the DRX mechanism.