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