  Terahertz (THz) communications and reconfigurable intelligent surfaces (RISs)
have been recently proposed to enable various powerful indoor applications,
such as wireless virtual reality (VR). For an efficient servicing of VR users,
an efficient THz path allocation solution becomes a necessity. Assuming the RIS
component is the most critical one in enabling the service, we investigate the
impact of RIS hardware failure on path allocation performance. To this end, we
study a THz network that employs THz operated RISs acting as base stations,
serving VR users. We propose a Semi-Markov decision Process (SMDP)-based path
allocation model to ensure the reliability of THz connection, while maximizing
the total long-term expected system reward, considering the system gains, costs
of link utilization, and the penalty of RIS failure. The SMDP-based model of
the RIS system is formulated by defining the state space, action space, reward
model, and transition probability distribution. We propose an optimal iterative
algorithm for path allocation that decides the next action at each system
state. The results show the average reward and VR service blocking probability
under different scenarios and with various VR service arrivals and RIS failure
rates, as first step towards feasible VR services over unreliable THz RIS.
