# Modeling and Analyzing Preemption-Based Service Prioritization in 5G Networks Slicing Framework
## 2 System Model  
Consider a Fifth Generation (5G) Base Station (BS) at which operate customizable and logical Network Slice Instances (NSIs). Let \(C\) represent the total network capacity of the 5G BS measured in some capacity units. For simplicity, assume that constant network capacities and service requirements for a NSI are measured in bps, i.e., these can be given in other capacity units by applying the radio channel model for the Radio Access Technology (RAT) in use. Let \(\mathcal{S}\) represent the finite set of NSIs at the 5G BS, i.e., \(\mathcal{S}\subset\mathbb{N}\setminus\{0\}\) with \(S=|\mathcal{S}|\) representing the number of NSIs. Let \(C_{s}\) represent the overall network capacity of the \(s^{\text{th}}\) NSI, \(s\in\mathcal{S}\), under the condition  
\[C_{1}+\ldots+C_{S}\geq C. \tag{1}\]  
Suppose that the overall network capacity \(C_{s}\) of the \(s^{\text{th}}\) NSI includes a guaranteed network capacity [26; 31]. Thus, let \(Q_{s}\) represent the guaranteed network capacity of the \(s^{\text{th}}\) NSI, i.e., \(Q_{s}\leq C_{s}\), under the condition  
\[Q_{1}+\ldots+Q_{S}\leq C. \tag{2}\]  
The above conditions suggest that when no requests are servicing at the \(s^{\text{th}}\) NSI, the guaranteed network capacity \(Q_{s}\) is available to service arriving requests at the other NSIs. In that case, these arriving requests become violators of the isolation of the \(s^{\text{th}}\) NSI. At those moments, arriving requests at the \(s^{\text{th}}\) NSI become competent to free the necessary resources from the violators servicing at the other NSIs. Various approaches are used to determine the number and the emplacement of the violators that must be discarded to free resources [32]. Some approaches suggest discarding the last admitted violator, and others propose discarding the violator with the longest remaining service time. Our paper proposes a Pre-emption-based Prioritization (PP) scheme for randomly discarding first the violators servicing at the NSI with the lowest priority until the necessary resources are freed up.  
Consider the Poisson arrival process of a unique request type with rate \(\lambda_{s}\), \(s\in\mathcal{S}\), at the \(s^{\text{th}}\) NSI. Suppose that the arriving request at the \(s^{\text{th}}\) NSI requires for starting service \(b_{s}\) capacity units, i.e., \(b_{s}\leq Q_{s}\). Assume the average service time for a request at the \(s^{\text{th}}\) NSI to be exponentially distributed, with the mean \(\mu_{s}^{-1}\) that corresponds to scenarios with real-time applications.  
Give a summary of the proposed system main notations in Table 1.  
Organize the radio admission control (RAC) scheme so that upon arrival at the \(s^{\text{th}}\) NSI, \(s\in\mathcal{S}\), the arriving request is bound to one path: blocking, direct admission, or via pre-emption admission. The blocking path is followed when the number \(n_{s}\) of servicing requests at the NSI is greater than or equal to \(\lfloor Q_{s}/b_{s}\rfloor\) and the amount of available capacity units at the 5G BS is less than \(b_{s}\). The direct admission path is followed when the number \(n_{s}\) of servicing requests at the NSI is less than \(\lfloor C_{s}/b_{s}\rfloor\) and the amount of available capacity units at the 5G BS is greater than or equal to \(b_{s}\). The via pre-emption admission path is followed when the number \(n_{s}\) of servicing requests at the NSI is less than \(\lfloor Q_{s}/b_{s}\rfloor\) and the amount of available capacity units at the 5G BS is less than \(b_{s}\). In that case, the arriving request is competent to discard a number of violators servicing at the \(s^{\text{th}}\) NSI, \(\hat{s}\in\mathcal{S}\setminus\{s\}\). Consideration of Service Prioritization appears with the dilemma of choosing the violator(s) that must be discarded in the cases of three and more NSIs at the 5G BS. Such cases are outlined below. Therefore, develop a Discard or Preemption scheme, starting with cases of the system where two and three NSIs operate.