  In this paper, the queue-aware simultaneously transmitting and reflecting
reconfigurable intelligent surfaces (STAR-RIS) assisted non-orthogonal multiple
access (NOMA) communication system is investigated to ensure the system
stability, where the long-term stability-oriented problem is reformulated to
maximize the per-slot queue-weighted sum rate (QWSR) of users based on the
Lyapunov drift theory. By jointly optimizing the NOMA decoding order, the
active beamforming coefficients at the BS, and the passive transmission and
reflection coefficients at the STAR-RIS, three STAR-RIS operating protocols are
considered, namely energy splitting (ES), mode switching (MS), and time
switching (TS). For ES, the blocked coordinate descent and the successive
convex approximation methods are invoked to handle the highly-coupled and
non-convex problem. For MS, the proposed algorithm is further extended to a
penalty-based two-loop algorithm to solve the binary amplitude constrained
problem. For TS, the formulated problem is decomposed into two subproblems,
each of which can be solved in a similar manner to ES. Simulation results show
that: i) our proposed STAR-RIS assisted NOMA communication achieves better
performance than the conventional schemes; ii) the reformulated QWSR
maximization problem confirms the system stability; and iii) TS achieves
superior performance with respect to both the QWSR and the average queue
length.
