The objective function is formulated as an integer programming (IP) problem problem problem to optimize the system revenue of the entire system for network
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function, \(Z_{\text{IP}}\), comprises the values corresponding to the maximum tasks assigned to subtract the setup cost of servers in C-RAN. The first term of the objective function represents the total values of served tasks in the system. \(V_{i}\) is the reward rate of task \(i\). A task blocking variable, \(b_{i}\), is set for the task rejection into the system in the second term of the objective function. The penalty, \(N_{i}\), is considered if a task is not admitted to be processed due to the task requests are not entirely served by task assignments. The penalty values are set to be higher than the values of the reward rate. There are three types of cost: initial cost rate \(A_{s}\), reopening cost \(E_{s}\), and migration cost \(F_{i}\). \(A_{s}\) is the estimated cost per unit time for server \(s\). The total initial cost is estimated based on the on-going time slots, which is referred to Amazon EC2 operation. \(E_{s}\) is charged for a server to be switched on one at a time after server initialization. The value of \(E_{s}\) is designed to be greater than that of \(A_{s}\) in the experiments. The migration cost occurs when a VM process migrates to other servers. It represents a type of overhead of computational resource disturbances. The difference between time index \(\tau\) and \(\pi\) is the time scale, and \(\tau\) is a superset  
(C. 15) : \(a_{\pi is}\leq\alpha_{\pi is},\text{for}_{\pi-1}<t_{\tau}<t_{\pi}\), \(\forall\tau\in T\), \(\forall i\in I\), \(\forall s\in S\), \(\forall\pi\in\Pi\), (C. 16) : \(\sum_{s\in S}\alpha_{\pi is}\leq 1\), \(\forall\pi\in\Pi\), \(\forall i\in I\), (C. 17) : \(\alpha_{\pi is}-\alpha_{(\pi-1)is}\leq\eta_{\pi i}\), \(\forall\pi\in\Pi\), \(\forall i\in I\), \(\forall s\in S\). where (C. 1)-(C. 8) are task assignment constraints, (C. 9)-(C. 10) are capacity constraints, and (C. 11)-(C. 17) are switching constraints. For task assignment constraints, the admitted task \(i\) should be assigned to one of the servers. The summation of \(a_{\pi is}\) overall servers should not be greater than one, as shown in constraint (C. 1). Constraint (C. 2) represents that the processing time slot requested by task \(i\) should be satisfied. The total assignment time slots are equal to the requested time slot. Constraint (C. 3) implies that only if task \(i\) is assigned to server \(s\), server \(s\) must be switched on. Accordingly, both decision variables \(a_{\pi is}\) and \(x_{\pi s}\) are set to one. If task \(i\) is not assigned to any server, \(a_{\pi is}\) is set to zero, and \(x_{\pi s}\) can be a free variable. Constraint (C. 4) and (C. 5) imply that time is assigned for task \(i\) in chronological order. More precisely, task \(i\) should be processed after it arrives and needs to be earlier than its deadline. The deadline is presented by the delay tolerance, which begins in arrival time. Constraints (C. 6) and (C. 7) represent the correlation between task required time slot for assignments and the task blocking decisions. The blocking decision \(b_{i}\) is set to one when the requested time slots of \(\gamma_{i}\) of processing are not satisfied. Otherwise, the decision is set to zero. Constraint (C. 8) presents that the total rate of blocking tasks should not exceed that of the system requirement. \(K\) represents the system requirement of total task-blocking rate, for example, 3%, which implies that fewer than 3% tasks will be blocked. For capacity constraints, constraint (C. 9) and (C. 10) are intuitively obtained by the total requirements of tasks aggregated in server \(s\). The aggregated traffic should not exceed the server capacity. To put it another way, if a new amount of traffic load (CPU or memory) is arriving and is assigned to server \(s\). After that, it should not be greater than either the remaining CPU or memory capacities of server \(s\)[28].