Queueing System with Single Vacation and Single Service with Feedback

For a bulk arrival queueing system takes into consideration with 2 kinds of service patterns and single vacation. When a length of the queue is $\geq b$ least of batch length ‘b’, a bulk service will be supplied; moreover, a single vacation or service will be supplied. A bulk service is over, if a queue length is smaller than ‘ $\mathbf{b}$ ‘, a server goes to single vacation. A single vacation is over and queue length is $\geq \mathbf{b}$, a server will be provided bulk service; moreover, a server goes on a single service. A batch or single service is over, if customers are unsatisfied with the service, they will rejoin the queue with probability p. Using probability generating function (PGF), this type of queuing model was analyzed and some performance measures were also obtained. Lastly, graphical representation and tables are used to display the numerical data.