Performance analysis of a batch arrival retrial queue with Bernoulli feedback

This paper facilitates the performance prediction of an MX/G/1 retrial queue wherein the single server follows a modified vacation policy. We assume that the job who finds the server busy joins the retrial group (orbit) to get its service in random order and only the job at the head of the queue is allowed to receive service from the server first. As soon as the system becomes empty, the server leaves for at most J vacations of random length V each. When the server returns from the vacation and finds at least one job in the orbit, it renders service to these jobs otherwise it goes for next vacation. We assume that the service time, retrial time and vacation times are general distributed. The balking behaviour of the jobs is also taken into consideration. By using supplementary variable technique, we derive the formulas for system size distribution and mean system size at departure points and other performance measures. Numerical illustrations have been provided to validate the analytical results. In addition, by setting appropriate parameters, some special cases are deduced which tally with existing results. Tables and figures have been facilitated to examine the system behaviour with regard to different parameters.