Retrial Queue M^(∣x])/G/C With Bernoulli’s Vacation, Repair, Service And Re-Service In Orbit

Abstract

This paper focused on a back - end system for periodic testing with modified Bernoulli’s vacation on each service includes additional service after breakdowns and repairs by the method of supplementary variable techniques. Further vacation repair and vacation interruption on queues and orbit is discussed simultaneously. Upon arrival, if the server is busy, serviced, or on vacation, then the entire queue (batch wise) joins in the orbit. In general all the customers require and expect the regular service and appropriate re-service, but only some customers require additional service and re-service. At the end of each service few exceptional case of re-service is available with probability . This reliability measured was examined through various numerical parameters. To implement these concepts we build a mathematical model using the complementary variable method and obtained a function that gives the probabilities for the number of customers in the system when the server is free or on repair or on vacation.