## 3 System Model and Assumptions
### Proposed Slice Allocation System
#### 3.2.3 Proposed Delay Aware Adaptive Slice Allocation System (DA-ASA)  
The second system we propose is a delay-aware ASA (DA-ASA) system. This system adds maximum time delay tolerance as a new parameter in ASP calculations. It assigns a high-priority value to a slice's request \(i\) when the difference between the pre-defined maximum tolerable delay \(MTD_{i}\) and the current delay of the slice request, \(D_{i}\) (i.e., \(MTD_{i}-D_{i}\)), decreases. Figure 7 shows the system model for the DA-ASA system. \begin{table}
\begin{tabular}{l c} \hline \hline
**Arrival Event of Request \(i\)** & **Departure Event of Request \(i\)** \\ \hline
**if (\(R_{c}+\Delta R_{i}\ \leq R\))** & **if (\(Q_{i}\)  is full)** \\  Admit request \(i\) & Set ASP(i) = \(\frac{R_{c}^{i}}{R_{v}^{i}}\) \\
**else** & **Select** \(Q_{i}\)  with the lowest ASP value. \\
**if (\(Q_{i}\)  not reaches its limits)** & **if (\(R_{c}+\Delta R_{i}\ \leq R\))** \\  & Admit request \(i\) \\  & **else** \\  Insert in \(Q_{i}\) & Release the resource. \\
**else** & **end if** \\  & **else** \\  & **Reject request i** & Release the resource \\
**end if** & **end if** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The arrival and departure procedures in the ASA. ```
1:procedureERRIVAL(0)
2:Server \(\leftarrow\) IDLE;
3:if(Q(i) > 0)then
4:Server \(\leftarrow\) BUSY; //if there are req. of same slice waiting in queue
5:endif
6:\(\Delta R_{i}\) = criteria (i); //calculate the number of resources needed by this req. 7:if(\(R_{c}+\Delta R_{i}>R\))then
8:Server \(\leftarrow\) BUSY;
9:endif
10:if(Server = BUSY)then
11:if(Q(i) >= Q. Limit(i))then
12:Drop (i); //dropping because the queue is full
13:else
14:insert in Q(i);
15:endif
16:else
17:Admit (i); //the Sever is IDLE
18:endif
```  
**Algorithm 1** Pseudocode for Arrival event of request \(i\) algorithm. Figure 5: Arrival event of request \(i\). Figure 6: Departure event of request \(i\). The procedure for this system is the same as that of the ASA system, except that the ASP is calculated using:  
1. The total number of RBs that are currently utilized by all active users of the \(i^{th}\) slice, denoted as \(R_{c}^{i}\). 2. The number of RBs that are virtually reserved for the \(i^{th}\) slice, denoted as \(R_{v}^{i}\). 3. The maximum tolerable delay limit for a user request in the \(i\)_th_ slice, denoted as \(MTD_{i}\). 4. The current delay for a request in the \(i^{th}\) slice, denoted as \(D_{i}\). Therefore, the ASP value for slice's request \(i\) is calculated as follows: \[ASP_{i}=\frac{R_{c}^{i}}{R_{v}^{i}}\times(MTD_{i}-D_{i})\] (17)  
Table 7 shows the ASP of each slice's request \(i\) of the DA-ASA system. In (17), if a slice's request \(i\) has a large queuing delay, the difference between its maximum tolerable delay \(MTD_{i}\) and its current request delay \(D_{i}\) decreases, resulting in a lower ASP value. Therefore, when the ASP value of the slice's request \(i\) decreases, its priority in obtaining the service increases. At high traffic load, the delay parameter maintains slice isolation by preventing the slices from negatively affecting each other. For example, suppose the DA-ASA system receive requests from each slice. The URLLC slice's \(R_{v}^{i}\) value is 50 RBs, the current \(R_{c}^{i}\) value is 25 RBs, the MTD is 1 ms, and the current delay of a queued URLLC request is 0.9 ms. The eMBB slice's \(R_{v}^{i}\) value is 35 RBs, the current \(R_{c}^{i}\) value is 5 RBs, the MTD is 4 ms, and the current delay of a queued eMBB request is 1 ms. The mMTC slice's \(R_{v}^{i}\) value is 15 RBs, the current \(R_{c}^{i}\) value is 10 RBs, the MTD is 7 ms, and the current delay of a queued mMTC request is 6 ms. As previously stated, when calculating the ASP, the DA-ASA takes into account the difference between the slice's \(MTD_{i}\) and the current request delay. Using Equation (17), the ASP value for the URLLC slice is 0.7, 1.2 for the eMBB slice, and 0.6 for the mMTC slice. As a result, the