Asymptotic analysis of retrial queueing system M/M/1 with non-persistent customers and collisions - Polkhovskaya, Anna (Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 20th International Conference, ITMM 2021, named after A. F. Terpugov, Tomsk, Russia, December 1–5, 2021 : revised selected papers)
A queuing system with repeated calls, one server, collisions (conflicts) of calls, H-persistence and rejections is considered. A call that found the device free occupies it, and service begins, which ends successfully if no other requests were received during it. If the server is busy, then a conflict (collision) arises between the call that have come for service and the ones being serviced, and in the general case, both calls instantly go to the orbit and repeat the attempt to successfully serve after a random time. In this article, in the event of a collision, one of the calls, for example, which was in service (on the device), goes into the orbit with probability H1, the other goes into orbit with probability H2, and with probability (1−H1) and (1−H2) respectively refuses service and leaves the system. The problem is to find asymptotic probabilities distribution of the calls number in the orbit.