# Numerical Results

Firstly, we study the evolutionary behavior of users. We set the cloud resource size and the price of two brokers as E1 = E2 = 20 and p1 = 0.1, p2 = 0.5, respectively. Figure5.2 shows the convergence of the evolutionary behavior of users when the initial state of community is (x1t1, x1;2) = (0.4, 0.4). From Fig. 5.2, we can observe that both of utilities of users in community 1 and community 2 are converged to be optimal with several iteration steps. In addition, it can be known that the utilities of all users in both community 1 and community 2 are nearly identical.

Fig. 5.2 Convergence of the evolution among users to the equilibrium

Fig. 5.3 Best response of each broker on the size of cloud resource purchased from the media cloud. BR1 and BR2 represent the best response functions of broker 1 and broker 2

Fig. 5.4 Price of cloud resource determined by the media cloud versus iteration step. The initial prices po (0) are 0.1, 0.2, 0.4, 0.5, respectively

Figure 5.3 shows the best response of each broker on the size of cloud resource purchased from media cloud. We set p0 = 0.1 and choose two types of cloud service price for comparison, which are p1 = p2 = 0.3 and p1 = p2 = 0.5, respectively. From Fig. 5.3, when p1 = p2 = 0.5, if broker 2 has more cloud resource, broker 1 also has a larger size of cloud resource to be the best response. When p1 = p2 = 0.3, the best response of each broker firstly increases and then decreases. In addition, with each price, there is only one intersection point in Fig.5.3. It demonstrates the existence and uniqueness of the Nash equilibrium when the cloud service price is fixed.

Figure 5.4 shows the convergence of the price determined by media cloud. We set four different initial prices of the cloud resource determined by the media cloud for comparison. And we set E2 = 10 to study the influence between the price of cloud resource and the cloud resource demand of broker 2. From Fig. 5.4, we can observe that the price of cloud resource is converged to an optimal price with several steps.

In Fig. 5.5, we compare the proposed scheme with the existing approaches, which are Uniform Resource Allocation (URA) and Random Resource Allocation (RRA), respectively. In the URA, the total resource of media cloud is uniformly allocated

Fig. 5.5 Utility of each user in community 1, where the initial price of the resource determined by the media cloud is p(0) = 0.5

to all users in the network. In the RRA, each user can obtain cloud resource from the media cloud randomly. From Fig. 5.5, it can be known that the proposed scheme outperforms the other two existing approaches, where user can obtain the best utility. In the URA, as the cloud resource is uniformly allocated to users, too much resource may be allocated to someone whose demand is low, while users who need more resource can not obtain enough resource. In RRA, as the resource is allocated to users randomly, users cannot obtain the resource according to their needs. In the proposed scheme, users can obtain their wanted resource according to their demands. Furthermore, with the theoretical game model, the price gradually tends to be reasonable. Thus, all parties can possibly obtain the maximum utilities.

To test the performance with dynamical demands, Fig. 5.6 shows the utility of a user in community 1 when the value of in community 1 is changed from 2 to 3.5, which shows the variation of a userâ€™s resource demand [47]. From Fig.5.6, it can

Fig. 5.6 The utility of mobile user in community when the demand is changed

be observed that all utilities with dynamic demands decrease and reach to the stable finally. The user with higher demand has the higher utility. The reason is that the user with higher demand can be more sensitive to the resource than the one with lower demand.

We carry out the next experiment to evaluate the media quality of the proposed scheme. Based on [48], we define the metric to show the media quality as Media Response Ratio (MRR) = Media Runtime/Task Processing Time. The above metric can measure the quality of the media when delivering content to users through media cloud. With a given media runtime, if the task processing time is long, MRR becomes low when the playback speed of media content is slow and the media may be stunk. In opposite, if the task processing time is short, MRR becomes large where users can enjoy a high quality of media and content can be played fluently.

We compare the MRR of the proposed scheme with RRA, URA, and the local execution scheme. Here, the local execution scheme means that the mobile device does not connect to media cloud and processes the media data on local device. According to [48], in the experiment the file size of media is determined as 307MB and the runtime is 1291 s. Without the cloud, the task process rate of local device is 500tasks/s. For the task process rate of the proposed scheme, it is decided by the proposed algorithm. The task process rate of RRA and URA are determined randomly and uniformly, respectively. From Fig. 5.7, we can see that the proposed scheme can achieve the highest MRR compared to other schemes. The reason is that users can adjust the strategy to achieve the maximum revenue based on the social features in the community.

In the above experiments, it can be known that all users can choose the best strategies to obtain the optimal utility. Each broker can determine its optimal strategy on cloud service price and size to obtain the maximum utility. The price of cloud resource determined by media cloud is converged to the optimal. Therefore, the proposed resource allocation scheme is converged and the Stackelberg equilibrium exists. More details can be found in [49].

Fig. 5.7 Comparison of the media response ratio