## 2 Related Work
### Time-Dependent Modeling  
Performance analysis of 5G/6G mmWave/sub-THz cellular systems with directional antennas, blockage, and micro-mobility has been conventionally performed by assuming static locations of UE and blockers, see, e.g., [7; 13; 18; 19]. The rationale is that this greatly simplifies that analysis using the tools of stochastic geometry. From the technology point of view, the assumption of the periodic beam tracking utilized in systems with directional antennas [20] with a rather short time between tracking events (up to 512 ms in 5G NR) makes the static analysis appropriate as neither micro- nor macro-mobility may lead to drastic beam misalignment over these intervals [21; 22].  
The beam tracking operation has been recently shown to drastically degrade the energy efficiency of UEs. Specifically, by performing the system-level analysis, the authors in [23; 24] demonstrated that 5G UEs operating in the mmWave frequency band are much more energy inefficient as compared to LTE UEs and characterized by a significantly smaller UE lifetime. To this aim, the recently introduced RedCap UEs utilize the RRM Relaxation feature that allow them to skip beam tracking events for a much larger time as compared to the standard procedure defined for 5G NR UEs [25]. In [26], the authors proposed a pragmatic approach to activate the RRM Relaxation mechanism for RedCap UEs that considers different mobility patterns. To determine the stationarity of UEs, they applied grouping that is based on geographical location and beam characteristics. It was shown that the UE can reduce the energy consumption caused by unnecessary detection and measurement and be adjusted in a timely and flexible manner according to different situations. When such UEs are subject to micro- or macro-mobility, this may, however, lead to drastic performance degradation due to antenna misalignment between UE and BS. The choice of the optimal RRM relaxation period naturally requires models allowing for the prediction of time-dependent performance measures, including signal-to-noise ratio (SNR), spectral efficiency, and attained rate.  
Time-dependent 5G/6G mmWave/NR systems performance has been conventionally evaluated by utilizing system-level simulation (SLS) studies. The rationale is that mathematical performance modeling requires not only the methods of stochastic geometry to estimate performance metrics, but also random walks theory [27]. The latter is utilized to track the current position of the UE with respect to the BS and thus explicitly defines the performance measures as a function of time. Joining the tools of stochastic geometry and random walk to specify a unified time-dependent framework for the performance evaluation of 5G/6G mmWave/sub-THz systems is a complex task. The only study we are aware of is [28], proposing new strategies for energy consumption and user aggregation based on a random walk mobility pattern. The result showed that it is possible to achieve up to a 16.1% and 20% energy reduction in the case of uniform and non-uniform distributions. However, that study is also performed by utilizing computer simulations. In addition to inherent dynamism, one also needs to account for mmWave/sub-THz specifics, including directional antennas and blockage. On top of this, the time-dependent metrics of interest also depend on the micro-mobility process that potentially also has quite complex characteristics, as discussed in [6]. As a result, no attempts to provide such frameworks have been made so far.