On the buffers overfill probability between two interconnected repairable servers

The stationary operating mode is discussed for a service system of two servers, each capable of serving both its customers and those arriving from the overfilled buffer of the other in the case of buffer overfill through a switching channel. The customers arrive by a Poisson law and the service time has an exponential distribution. The proposed model decoupling technique leads to very simple expressions for computing the buffer overfill probability. The results of a simulation experiment confirm the sufficient accuracy of the approximations. A system of two servers can be thoroughly described by a vector model.