## 4 Performance Evaluation
### Deployment Density Assessment  
Having solved the direct problem, we now proceed developing the algorithm for estimating the required mmWave NR BS deployment density satisfying a given enhancement layer drop probabilities, \(\vec{p}_{U}\).  
The proposed algorithm is presented in the form of pseudo-code in Algorithm 1. According to it, at step 1 we start with the maximum possible cell radius \(R=d_{E}\). Then, we define the appropriate antenna gain \(G_{A}\) to form beams (step 2) that allow serving an active session at the distance \(R\) even in LoS blocked conditions. Once we have the HPBW angle, we obtain the number of beams \(N\) needed to provide full coverage of the cell's sector at step 3. Note that some of the beams may not be effective, as they do not cover any users. To abandon the void beams, at step 4 we estimate the number of gaps between shadows, \(\Delta\), that are greater than the beamwidth as in (2). Afterward, we subtract these gaps from the number of beams to retain only \"active\" ones and calculate the amount of the required resource (step 5) for the base layer.  
Then, at steps 6-20, we estimate the amount of resources for the enhancement layers using Erlang-B formula. We first start with one server in the \(M/M/C\) queuing system and check whether it is enough to meet the QoS profile requirement defined by 8, i.e., whether the loss probability \(p_{C}(l)\) is lower than the share of users without successful layer delivery. If the condition is not satisfied, we increment the number of servers \(C_{l}\) (step 9) and perform the calculations again till the appropriate number of servers is found. Once \(C_{l}\) is obtained, it is treated as the mean number of active unicast sessions needed to deliver \(l\)-s layer to users, allowing us to estimate the total resource demand for \(l\)-s layer at step 19.  
Finally, if the calculated demands for all the layers fit into the given bandwidth (step 21), we conclude that the coverage radius and corresponding density (step 25) of BSs are optimal. However, if the demands are greater than the given resource, we reduce the coverage radius (step 22) and perform the algorithm once again.  
```
0:\(d_{E}\), \(\lambda\), \(\vec{\mu}\), \(\vec{p}_{U}\), \(\vec{b}\), \(Q\), \(p_{B,i}\)
0:\(\lambda_{A}\) Initialization:
1:\(R=d_{E}\), \(\vec{p}=\lambda/\vec{\mu}\), \(K=\sqrt{R^{2}-Q^{2}}\) Assessment of resource amount for base layer:
2:\(G_{A}=\frac{S_{1}(R)N_{0}WA}{P_{A}\tilde{\omega}_{R}^{-\frac{1}{2}}p_{B}(R)}\)
3:\(\xi=\frac{\alpha(G_{A})\pi R}{360}\), \(N=\left\lceil 120/\alpha(G_{A})\right\rceil\)
4:\(\Delta=\frac{\pi\lambda K^{2}}{3\left(e^{\frac{\pi\lambda K^{2}}{2K}}-e^{-\frac {\lambda K^{2}(k+1)}{2K}}\right.}\)
5:\(E[W]=b_{M}(N-\Delta)\) Assessment of resource amount for enhancement layers:
6:for\(l=2\) to \(L\)do
7:\(C_{l}=0\), \(p_{C}(l)=1\)
8:while\(p_{C}(l)>1-p_{U}(l)\)do
9:\(C_{l}=C_{l}+1\)
10:\(p_{0}(l)=1\)
11:for\(v=1\) to \(C_{l}\)do
12:\(p_{v}(l)=\frac{p_{v}(l)}{v+\theta\cdot p_{v-1}(l)}\)
13:endfor
14:\(G=\sum\limits_{v=0}^{C}p_{v}(l)\)
15:for\(v=1\) to \(C\)do
16:\(p_{v}(l)=\frac{p_{v}(l)}{G}\)
17:endfor
18:endwhile
19:\(E_{l}[U]=C_{l}\left(p_{B,i}b_{U_{l},B}+(1-p_{B,i})b_{U_{l},L}\right)\)
20:endfor
21:Stop criteria:
22:if\(\sum\limits_{l=2}^{L}E_{l}[U]+E[W]>B\)then
23:\(R=R-1\)
24:return to Step 6
25:else
26:\(\lambda_{A}=\left(\pi R^{2}\right)^{-1}\)
27:return\(\lambda_{A}\)
28:endif
```  
**Algorithm 1** NR BS Deployment Density Assessment