Abstract : Cloud computing, the long-held dream of computing as a utility, has the potential to transform a large part of the IT industry, making software even more attractive as a service and shaping the way in which hardware is designed and purchased. In this thesis, we reviewed the new cloud computing technologies, and indicated the main challenges for their development in future, among which resource management problem stands out and attracts our attention. Combining the current scheduling theories, we proposed cloud scheduling hierarchy to deal with different requirements of cloud services. From the theoretical aspects, we have accomplished three main research issues. Firstly, we solved the resource allocation problem in the user-level of cloud scheduling. We proposed game theoretical algorithms for user bidding and auctioneer pricing. With Bayesian learning prediction, resource allocation can reach Nash equilibrium among non-cooperative users even though common knowledge is insufficient. Secondly, we addressed the task scheduling problem in the system-level of cloud scheduling. We proved a new utilization bound for on-line schedulability test, considering the sequential feature of MapReduce. We deduced the relationship between cluster utilization bound and the ratio of Map to Reduce. This new schedulable bound with segmentation uplifts classic bound which is most used in industry. Thirdly, we settled the comparison problem among on-line schedulability tests in cloud computing. We proposed a concept of test reliability to evaluate the probability that a random task set could pass a given schedulability test. The larger the probability is, the more reliable the test is. From the aspect of system, a test with high reliability can guarantee high system utilization. From the practical aspects, we have developed a simulator to model MapReduce framework. This simulator offers a simulated environment directly used by MapReduce theoretical researchers. The users of SimMapReduce only concentrate on specific research issues without getting concerned about finer implementation details for diverse service models, so that they can accelerate study progress of new cloud technologies.