## 3 System Model and Assumptions
### Proposed Slice Allocation System
#### 3.2.2 Proposed Adaptive Slice Allocation System (ASA)  
The drawback of the above SSA system is that it guarantees the QoS requirements of each slice at the expense of efficient system utilization. Therefore, we propose an ASA system that considers the aforementioned drawback and provides an efficient resource allocation that satisfies the minimum QoS requirements of network slices while maintaining slice isolation and increasing system utilization. Figure 4 shows the system model for the ASA system. In the ASA system, each slice request has its own queue, and all slice requests share the available RBs. In addition, each slice request has a predefined virtual resource partition specified as \(R^{1}_{v}\) RBs for URLLC slice, \(R^{2}_{v}\) for eMBB slice, and \(R^{3}_{v}\) RBs for mMTC slice, so that \(R^{1}_{v}+R^{2}_{v}+R^{3}_{v}=R\). Each queued request of slice \(i\) is assigned an adaptive slicing priority (ASP) that is dynamically calculated based on the predefined virtual resource partition value, \(R^{i}_{v}\), and the current total cell load, \(R^{i}_{c}\). The predefined resource partition for each slice request \(R^{i}_{v}\) is used only to maintain the ASP for each slice request, which means that it is not used to statically partition the resources into three separate partitions. For low-to-moderate traffic loads, all RBs are available for slices requests to increase system utilization. However, at high traffic loads, the ASP is used to differentiate between queued requests. The priority is modified adaptively so that if a slice's request \(i\) currently occupies fewer RBs than its predefined virtual resource partition (\(R^{i}_{v}\)) it will be given a higher priority. Therefore, slice isolation is guaranteed such that slices with a lower priority are not affected by other slices with a higher priority [36]. Figure 3: The system model for the SSA system. The system can be described as follows: the total number of RBs is divided into three non-overlapping partitions, with one partition per slice traffic, which can be expressed as. The system procedure can be stated as follows:  
1. The arrived slice's request \(i\) is accepted if the following criterion is satisfied: \[R_{c}+\Delta R_{i}\leq R\] (15)
2. When all system RBs are utilized, an arriving slice's request \(i\) is inserted into its corresponding queue or blocked if it is full. 3. If a slice's request \(i\) exceeds its queuing time limit, it will be dropped from its queue. 4. When a slice's request \(i\) departs, its corresponding occupied RBs are released, and the ASP is computed for all queued slices requests that have non-empty queues. Then, the queue with the lowest ASP value, which indicates that it has the highest priority, is served first based on the FIFO policy. The ASP value for a slice's request \(i\) used in step 4 of the above procedure, is calculated using the following: 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 _ith_ slice, denoted as \(R_{v}^{i}\) Therefore, the ASP value for slice's request \(i\) is given by \[ASP_{i}=\frac{R_{c}^{i}}{R_{v}^{i}}\] (16)  
The ASP of each request \(i\) depends on the value of its slice priority ratios. Table 5 shows the ASP of each slice's request \(i\) in the ASA system. The slice's request \(i\) with the lowest ASP value will be given the highest priority in receiving the service. The value of the predefined virtual resource partition (\(R_{v}^{i}\)) for each slice has a significant impact on determining its priority level. Therefore, the URLLC slice has the highest \(R_{v}^{i}\) value, which raises its priority. Figure 4: The system model for the ASA system.