Unreliable Server M/G/1 Queueing System with Bernoulli Feedback, Repeated Attempts, Modified Vacation, Phase Repair and Discouragement

This paper deals with unreliable M/G/1 queueing systemwith modified vacation, repeated attempts and K-phase repair. Thejobs arrive in Poisson fashion. On finding the server busy, undersetup, under repair or on vacation, the jobs either join to the orbit orbalk from the system. The jobs in the orbit repeat their request forservice after some random time. The inter retrial time of each job isgeneral distributed. The jobs are served according to FCFS discipline.After receiving the unsuccessful service, the job may immediately jointhe tail of the original queue with some probability p or may departfrom the system with probability q(= 1-p). Accidental (operational)breakdown of the server is also considered. There is a provision of kphaserepairs to restore the server to the state as before failure. Firstphase repair is essential whereas other (K-1) phases are optional. Therepairman, who restores the server, requires some time to start the firstphase of repair; this time is called as setup time. The service time,setup time and repair time of each phase are independent and generaldistributed. On finding the orbit empty, the server goes on at most Jvacations repeatedly until at least one job is recorded in the orbit. Theprobability generating function of steady state queue size at randomepoch is obtained using supplementary variable technique. Variousmodels studied earlier are discussed as special cases of our model, byappropriate choice of parameter values. Some queueing as well asreliability indices to predict the behaviour of the system are alsoderived. The effects of various system parameters on the systemperformance indices are also examined numerically.