This paper considers a retrial tandem queue with single orbit, Poisson arrivals of incoming calls and without intermediate buffer. The first server provides services for incoming calls for an arbitrary random time, while the second server does for an exponentially distributed random time. Blocked customers at either the first server or the second server join the orbit and stay there for an exponentially distributed time before retrying to enter the first server again. Under an asymptotic condition when the mean of retrial intervals is extremely large, we derive a diffusion limit, which is further utilized to obtain an approximation to the number of customers in the orbit in stationary regime.
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. Cham, 2022. P. 131-143