Analysis of bulk arrival queueing system with batch size dependent service and working vacation

This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least ‘a’. On the other hand the server provides fixed batch service if the queue length is at least ‘k’ (k > a). Batch service is provided with some fixed batch size ‘k’. After completion of service if the queue length is less than ‘a’ then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.This paper concentrates on single server bulk arrival queue system with batch size dependent service and working vacation. The server provides service in two service modes depending upon the queue length. The server provides single service if the queue length is at least ‘a’. On the other hand the server provides fixed batch service if the queue length is at least ‘k’ (k > a). Batch service is provided with some fixed batch size ‘k’. After completion of service if the queue length is less than ‘a’ then the server leaves for working vacation. During working vacation customers are served with lower service rate than the regular service rate. Service during working vacation also contains two service modes. For the proposed model probability generating function of the queue length at an arbitrary time will be obtained by using supplementary variable technique. Some performance measures will also be presented with suitable numerical illustrations.