A study on MX/GB/1 retrial queueing system with Bernoulli vacation schedule and variable server capacity

In this paper, we have investigated bulk retrial queueing system with Bernoulli vacation schedule and variable server capacity. According to the variable server capacity bulk service rule, the server can serve a minimum of one customer and a maximum of B customers in a batch. After completion of a batch of service, if the orbit is empty, then the server will go for a vacation. After completion of each batch of service, if the orbit is non-empty, then the server either go for a vacation with probability p or resumes its service with probability p. If arriving customers finds the server is busy with service or on vacation, they are grouped and it termed as unsatisfied customers or orbit. Unsatisfied customers will retry its appeal for service after some time. We have presented steady state system equations for the proposed model. Also, we have obtained some important performance measures for this system. Further, we have given numerical justification for this queueing system.