## 4 Proposed Resource Allocation Scheme
### Optimal Problem Formulation  
The computational resource allocation problem for the incoming requests from RRHs to BBUs is formulated as a multi-objective non-linear programming (MONLP) optimization problem, focusing on maximization of end-user Quality-of-Experience (QoE) as well as service provider profit. In order to initiate a radio communication service, soon after receiving the service requests from RRHs, a BBU must perform a specific task for each request to commence the corresponding radio access communication. The outcome of such tasks appear to the end users as the respective initial responses to the service requests. In this phase of this work, we target this sort of computation at the BBU pool. After the initialization of the service, radio communication will continue spontaneously. Here, the transmission delay is considered as the time required to send the request and receive the result, which depends on the connected network. Now, let the total time to get first response or the amount of time from when a request is submitted until the first response is produced from a BBU, \(b\in B\) to a RRH, \(h\in H\) after executing a request, \(r\in R\) can be defined as the summation of request processing time and waiting time, as shown in Equation (3):  
\[\tau_{r,b}=\zeta_{r,b}+\varpi_{r}, \tag{3}\]  
where \(\zeta_{r,b}\) denotes the time required to process the corresponding submitted request and \(\varpi_{r}\) represents the waiting time or the time count when a request arrives to the request queue until it goes for service. The _QoE and Profit-aware Resource Allocator_ always tries to allocate a specific BBU for a particular request, which can reduce the total response time to enhance the user's Quality-of-Experience (QoE). Let the total profit achieved by the service provider for executing a request, \(r\in R\), on a BBU, \(b\in B\), \(\rho_{r,b}\) be defined as follows,  
\[\rho_{r,b}=(d_{r}\times p_{d_{r}}+w_{r}\times p_{w_{r}})-(h_{b}+u_{b}), \tag{4}\]  
where \(h_{b}\) and \(u_{b}\) denote the monetary cost for renting BBU servers and other resource usage for processing a request on the BBU. Let \(p_{d_{r}}\) represent price per request with data to be processed \(d_{r}\) for executing the corresponding resource request, \(r\in R\), and \(p_{w_{r}}\) represents the additional unit price for executing a request with priority \(w_{r}\), provided by the _Pricing Policy Maker_. Theses values can be reactively determined based on the resource requirements as addressed in [19; 20]. Thus, the total profit gained by the service provider to allocate resource for requests can be calculated as in Equation (4). This value always ensures higher profit for the request with higher priority, as additional charge is required for executing a request with higher priority. The objective of our proposed methodology is to allocate a BBU, \(b\in B\) for each selected request, \(r\in R\) of an RRH, \(r\in R\) in such a way so that the total user QoE and the service provider's profit is maximized for executing all the selected service requests in a certain scheduling interval. Let \(O_{r}\)= \(\{\rho_{r,b},\tau_{r,b}\}\) be the set of objective parameters for executing a request \(r\), which consists of service provider's profit and request response time. As these two values belong to different units, the profit and response time are scaled within a range. Each element \(O^{i}\in O_{r}\) can be normalized as Equation (5), from which we get the normalized value of the service provider's profit, \(\hat{\rho}_{r,b}\) and response time, \(\hat{\tau}_{r,b}\) for executing an incoming request on a BBU:  
\[\hat{O^{i}_{r}}=\frac{cur(O^{i}_{r})-\min(O^{i})}{\max(O^{i})-\min(O^{i})} \tag{5}\]Here, \(cur(O_{r}^{i})\) represents the current value and the \(\max(O^{i})\) and \(\min(O^{i})\) are the maximum and minimum values of the corresponding objective parameters.