Queueing Model of a Cell Operation with Retrials and State-Dependent Rate of Requests

In this paper, we consider a queue, where the first block is an infinite-server queue, and the second is a retrial one. Customers in the first block generate requests for service to the retrial queue while being served in the first block, and they are lost when the service is over. Therefore, we have a retrial queue having several input flows, which number is the number of customers in the first service block. The queue is Markovian and we use asymptotic analysis under low rate of retrials condition to derive the probability distribution of the system state.