Variance of the Number of Departed Messages in a Simple Queueing System

We study a simple queueing facility consisting of two servers in tandem, separated by a finite buffer. The servers are independent and their sequences of up/down modes are Bernoullian. The input flow is deterministic (one new message per time unit). We compute explicitly the coefficient $A$ in the asymptotics $\mathbf D(T)\sim AT$ of the covariance of the number of departed messages per interval $[0,T]$.