## 5 Summary and Conclusions  
This experimental study has provided a statistical analysis and statistical modeling of VR video freeze characteristics measured in a commercial TPCAST wireless VR solution together with an HTC Vive HMD. While bandwidth and latency characteristics have been extensively reported in literature for a variety of testbeds, this experimental study advances on the understanding of temporal disturbances with respect to video freezes and their lengths which both also affect the QoE of networked VR applications. The video freeze assessment has been conducted with respect to four room quadrants, aggregated over all quadrants, and each scenario for six transmitter-receiver distances. The statistical analysis of the measured VR video traces has been performed revealing the number of detected freezes, freeze intensities, histograms, and CCHs of the freeze length. This analysis has been serving as a basis for deriving statistical models capturing the underlying distributions of the freeze length characteristics. The obtained statistical models of the freeze characteristics may be used in wireless VR simulators to support the development of physical layer, medium access layer, and higher layer functionalities. They also may be used to generate realistic freeze events in wireless VR stimuli for VR QoE studies. The statistical results obtained from this experimental study, contributing to answering the two research questions posed in the introduction section, include the following insights:  
* The results obtained from the statistical analysis of the recorded VR traces for the different initial azimuthal angles, transmitter-receiver distances, and the four quadrants illustrate the dependence of the freeze characteristics on the topology of the multi-purpose lecture hall. * The number of freezes and freeze intensities commence to increase for distances \(d>5\,\mathrm{m}\). The quadrant-specific breakdown of the number of freezes and freeze intensities show also the dependence on the wall materials and room topology. * The obtained asymmetric unimodal right-skewed histograms indicate a few short freezes with tails being drawn out to the right. The tailedness of the histograms increases with distance and are induced by single occurrences of very long freezes. The central tendencies of the freeze length data in terms of skewness and kurtosis point to exponential and geometric distributions as basis for statistical modeling of the freeze length characteristics. * The quadrant-specific CCHs of freeze length show exponential progressions or corresponding geometric progressions with and without tails depending on the particular quadrant and distance. Similar initial drops by one order of magnitude can be seen for short freeze length \(x\leq 10\). The results also indicate the dominance of the contribution of quadrants Q3 and Q4 to the CCHs for freeze lengths \(x\geq 10\). * The statistical modeling of the freeze length characteristics returned two exponential functions, one for modeling the domain of short freeze lengths \(x\in\mathcal{X}_{\mathrm{s}}\) and the other modeling the subsequent domain of larger freeze lengths \(x\in\mathcal{X}_{\mathrm{t}}\) in the tails. The corresponding equivalent geometric distributions are also provided. A very good fitting performance has been obtained for these models with the majority of the adjusted coefficients of determination of the fits for the considered 21 scenarios being above 0.95. * Given that the chosen commercial TPCAST wireless VR solution resorts on beamforming, higher order modulation constellations, and millimeter wave technology in the 60 GHz band, similar as other systems such as WiGig, WirelessHD, 5G, and B5G that target ultra-reliable low latency communications, the results and statistical models may be considered as representative for the freeze characteristics in such settings.