Search of arrivals of an m/g/1 retrial queueing system with delayed repair and optional re-service using modified bernoulli vacation

Single server queueing system in retrial is investigated, as well optional re-service,customer search and delayed repair. Furthermore, the permitted to take a vacation under Modified Bernoulli vacation. In this model, some of customer’s seek voluntary reservice for identical service taken, dissatisfied with first attempt without entering group (probability r1) or leaving area 1 – r1). The failing server's repair begins after an arbitrary length time termed delay has passed. supplementary variable technique used calculate orbit size, status, performance metrics. We explore several special situations our suggested model compare results previous research.