At present, the amount of data from users is increasing exponentially, and most of the data is stored in data centers distributed in different geographic locations. The cost of transferring large amounts of data across geographically distributed data centers can become prohibitive. Therefore, to shorten the data transmission time and reduce the cost of data transmission bandwidth and maintain the load balance of the geographically distributed cloud system, an optimal data placement strategy considering capacity limitation and load balancing in a geographically distributed cloud is proposed. Firstly, the capacity limitation, load balancing, and bandwidth cost of each cloud data center in the geographically distributed cloud are considered, and the data placement problem in the geographically distributed cloud is mathematically modeled. Secondly, the Floyd algorithm is used to model the cost of data transmission bandwidth and find the minimum transmission bandwidth cost. Finally, the Lagrangian relaxation method is used to obtain the optimal data placement scheme for the transmission time. To show the performance advantages of the proposed algorithm, comparative experiments are carried out. When the bandwidth is 15 Mbps, in terms of the Load Balancing Degree ($LBD$), the proposed algorithm is 40.3% higher than the Hash on average, 35.6% higher than the Closest on average, and 25.7% higher than the CRANE on average. Moreover, the experimental results show that the proposed algorithm can reduce the data transmission cost, and improve the load balancing in a geographically distributed cloud system.

目前，来自用户的数据量呈指数级增长，大部分数据存储在分布在不同地理位置的数据中心。跨地理分布的数据中心传输大量数据的成本可能变得过高。因此，为了缩短数据传输时间，降低数据传输带宽成本，保持地理分布式云系统的负载均衡，提出了一种考虑地理分布式云中容量限制和负载均衡的最优数据放置策略。首先考虑地理分布式云中各云数据中心的容量限制、负载均衡和带宽成本，对地理分布式云中的数据放置问题进行数学建模。其次，Floyd 算法用于对数据传输带宽成本进行建模，并找到最小传输带宽成本。最后，利用拉格朗日松弛法得到传输时间的最优数据放置方案。为了展示所提出算法的性能优势，进行了对比实验。当带宽为 15 Mbps 时，负载均衡度 ($升乙D$)，所提算法平均比Hash高40.3%，比Clestest平均高35.6%，比CRANE平均高25.7%。此外，实验结果表明，该算法可以降低数据传输成本，提高地理分布式云系统中的负载均衡。