An M/M/1-Type Queue with an Individual Deterministic Retrial Rate

Consider a system where customers arrive to a single-server queue according to a Poisson process with rate λ. The service times are independent and exponential distributed with rate μ. A customer who arrives when the server is busy is blocked and goes to orbit. Each orbit customer then every T units of time to re-enter the system. If he is blocked again, he will keep trying every T units of time. Balking is not allowed. In this paper, we consider retrial policy with deterministic T and we calculate the expected number of customers in orbit (without using balance equations).