Analysis of Poisson repeated queue general service with set up time and different vacation policies

This paper deals with unreliable M/G/1 queueing system with different vacation policies, nonpersistent customers and repeated attempts. The jobs arrive in Poisson fashion. On finding the server busy, under setup, under repair or on vacation, the jobs either join to the orbit or balk from the system. The jobs in the orbit repeat their request for service after some random time. The inter retrial time of each job is general distributed. The jobs are served according to FCFS discipline. If the primary call, on arrival finds the server busy, it becomes impatient and leaves the system with probability (1 ) and with probability , it enters into an orbit. The server provides preliminary first essential service (FES) and followed by second essential service (SES) to primary arriving calls or calls from the retrial group. On completion of SES the server may go for i th (i = 1,2,3··· ,M) type of vacation with probability i(i = 1,2,3,...,M) or may remain in the system to serve the next call, if any, with probability 0 where P M=0 i = 0.