Asymptotic analysis of a Bernoulli vacation non-Markovian queuing system in air traffic control system

We examine a single server queue arriving with Poisson batches of varying sizes. When the system starts the service, it provides service to all the arriving customers on a first come first served basis. Before the first service starts after each system downtime, the server provides general services to the client for a specified time of random duration, known to be a set-up time stage. If the server is affected by random crashes, a delay time occurs before the commencement of repair process. If there are no clients in the queue after the service is complete, the server takes a Bernoulli vacation. Two new parameters, reneging and restricted admissibility happen during the process of vacation and repair process respectively. For the defined queuing issue, we find the length of the duration of the steady state of different states of the system according to the probability generating function. Other queue performance metrics are also exported. In addition, the disposal is legalised through a digital scheme and graphic representation. This model means that supervisors are aware of the structural difficulties of the client-server framework and the basic rules of investigation.