# ARAAC: A Rational Allocation Approach in Cloud Data Center Networks
## 2 ARAAC: A Rational Allocation Approach in Cloud-Service Networks
### Definitions and Mathematical Modeling  
ARAAC assumes the game players to all be _rational_ in that they always aim to maximize their own profits [9]. In this context, cloud-DCN providers aim to maximize their collected profits from those chosen service-tenants. However, to achieve such high profits, the provider needs to deliver acceptable service levels with competing service prices. In the same way, service-tenants also seek to maximize their profits. This is achieved when the required resources are fully granted, and satisfy their QoS requirements in low price-units. Accordingly, the objectives of the cloud-DCN providers and the service-tenants are formed by maximizing their utilities, which are defined as follows:  
* **Definition 1:** (Provider's Utility.) The utility of the cloud-DCN provider in such a game is represented in the charges collected from the cooperative tenants nominated for allocation. In ARAAC, this is calculated as shown in Equation (1), which adds the different charges collected per accepted request \(i\), \(\forall\;i\in N\): \[U_{\mathrm{P}}=\sum_{i=1}^{N}s_{i}.{p_{i}}^{*}\] (1) where \(s_{i}\) refers to the requested resource units by bidder \(i\), and \({p_{i}}^{*}\) is the price-unit chosen by the pricing policy of the cloud-DCN provider. This function is bounded by the following **constraints**:
* **Behavior-Based Threshold:** For each bidder \(i\), an identification reference \(d_{i}\) is used to link \(i\) to a database that collects information related to the bidder's previous history, in regard to its resource utilization behavior \(e_{i}\) throughout a certain time window predefined by the market providers. For bidder \(i\) to be listed among the candidates for allocation, its behavior score \(e_{i}\) needs to pass the behavioral threshold value \(E_{t}\). At each auction round \(t\), the threshold value may be revised by the providers according to the market state. The formulation of this constraint is given by: \[e_{i}\geq E_{t}\qquad;\forall\;i\in N\] (2)
* **Leasing Price-unit Threshold:** For each bidder \(i\), to be considered for allocation among the set of candidates, its offered price-unit \(p_{i}\) needs to be higher than or at least equal a predefined price-unit threshold \(P^{*}_{t}\). The process of defining such threshold follows the providers' profit objectives and market state at the allocation period \(t\). With such threshold, ARAAC allows to maintain the providers' profit objectives and avoids losses. Such constraint is given by: \[p_{i}\geq P^{*}_{t}\qquad;\forall\;i\in N\] (3)
* **Resource Availability:** To control the allocation decision, those bidders who satisfy the aforementioned two constraints are sorted in \(N\) according to their offered price-units \(p_{i}\). After having the bidders sorted, and according to their required resource units \(s_{i}\), for each bidder \(i\), the provider checks if it has sufficient resource capacities for allocation in accordance to the residual resources \(\alpha_{t}S_{t}\) after previous allocations. At each auction round \(t\), the cloud-DCN provider defines the portion of the resources available for allocation \(S_{t}\). Hence, each candidate bidder \(i\) needs to pass the following: \[\sum_{i=1}^{N}s_{i}\leq\alpha_{t}S_{t}\] (4) Those bidders who pass the aforementioned three constraints are stored in the candidate list \(C\), and thus are charged for their granted services according to the pricing policy set by the cloud-DCN providers. In ARAAC, the model chooses the SBP policy to set the charges for its service tenants. * **Definition 2:** (Tenants' Utility.) The utility of the service-tenants (i.e., the bidders) in the allocation game is represented by the gain a tenant can collect from participating in the auction.