TL;DR: In the formulation of I, even the system with a single server is non-trivial for the authors are concerned not just with the queue length at the first server but with the joint probability distribution of D0(t) and D1(t).
Abstract: In the formulation of I, even the system with a single server is non-trivial for we are concerned not just with the queue length at the first server but with the joint probability distribution of D0(t) and D1(t), or equivalently, the joint distribution of D0(t) or D1(t) and the queue length D0(t) − D1(t).