## 4 Performance Evaluation  
In this section, we present the performance evaluation that shows how our resource consolidation algorithm allocates well in terms of deployment costs for both homogeneous (all cloud services require the same amount of computing resources and have the same network bandwidth) and heterogeneous (there are distinguishing cloud services that require different computing resources and have different network bandwidths) configurations. For the experiments, we consider the central cloud server and 10 edge servers in the system. When a user's request (_request\({}_{A}\)_) is performed in one of the edge servers for the first time, the related data should be downloaded to the edge server (case A). If the next request's service type is the same for _request\({}_{A}\)_, then the cost is minimized because the related data already have been downloaded to the edge server (case B). On the other hand, when a user's request is performed in the central cloud server (case C), the responsiveness of the service is longer than when it is performed in the edge server for the second time onwards (i.e., _cost\({}_{\textit{centralserver}}>{}_{\textit{cost}}{}_{\textit{daggererer}}\)_). For comparisons with existing approaches, we conduct experiments based on Google's cluster data set, which contains more than three million requests, and implement Belady [26], retrospective download with least recently used [27], and random methods (baseline). The Belady method uses the time-to-live approach to minimize the number of replacements provided that the future requests are known, while the retrospective download with least recently used method uses history information of the system with no assumption of request patterns. More specifically, when a new cloud task is requested and the edge servers have no empty task slots, the Belady method chooses the target task that will be used in the farthest future; the retrospective download with least recently used method applies two policies sequentially (retrospective download policy for the first part and a least recently used policy for the second part). The random method randomly chooses either the central cloud server or an edge server in the system when a user's request arrives. We show the results of the deployment cost of the four techniques for homogeneous and heterogeneous configurations in terms of edge servers' storage capacity and data download cost of service. Figure 3 shows the results of deployment costs for the homogeneous configuration. When the number of requests is 5 (Figure 3a), the deployment cost for the proposed method outperforms the Belady, retrospective download with least recently used, and random approaches. The average cost of the proposed resource consolidation algorithm is about 3.90, while those of the Belady, retrospective download with least recently used, and random approaches are about 4.20, 5.00, and 5.65, respectively. This result signifies that our resource consolidation algorithm effectively chooses the scheduling policy based on the hidden Markov model. When the number of requests is 10 (Figure 3b), the result of the proposed method is comparable to Belady, but our method is better than [PERSON]'s approach. The worst performance can be found in the retrospective download with the least recently used. The reason is that the retrospective download with the least recently used method requires some aging time since it utilizes the history information for previous requests. When the numbers of requests are 15 and 20 (Figure 3c,d), the performance ranking is the same as the previous experiment. The total costs for the homogeneous configuration are about 252, 382, 367, and 232, when the Belady, retrospective download with least recently used, random, and the proposed method are used, respectively. The cost of the proposed resource consolidation algorithm for the homogeneous configuration is about 61% over the retrospective download with least recently used, which indicates that our proposed technique effectively reduces the deployment cost.