An M/G/1 retrial G-queue for balking, reneging, subject to modified Bernoulli vacation, starting failure

A study of retrial G-queue with balking and reneging, subject to modified Bernoulli server vacation, starting failure is analyzed. The positive arrival in the service area follows Poisson stream. When the assistance is inactive, one of the positive arrivals comes for service and the remaining add into the retrial group. During the assistance period of a positive customer, the arrival of the negative customer will eliminate the positive occurrence in-service they come in a retrial group and make an effort next time. Balking (or reneging) may occur during the entry of positive customers with probability 1-b and leaves the service area at specific times with probability b. To proceed further at the end of assistance for each positive arrivals, the server goes for vacation accompanying probability a and remains in the service area for assisting the next arrivals accompanying probability 1-a. The entire equations, solved by applying supplementary variable method to predict system capacity, orbit size are obtained. Further Performance features and several special cases of this suggested model are presented and arrived through MATLAB.