| Summary: | Cloud computing has attracting more and more attention for its flexibility and economic benefits. To maintain the supply-demand relationship among different participants in cloud computing environment, the exchange of value is the inner drive. From the perspective of cloud service provider, its primary concern is to earn the profit, which can be obtained by finishing the tasks published from customers. In this paper, we consider each task consists of numbers of sub-tasks in the logical order, each sub-task corresponds to a type of service requests, which can be served in unique multi-server system. On this basis, we propose a profit maximization problem in the multistage multi-server queue systems, in which customers are served at more than one stage, arranged in a series structure. Moreover, a deadline constraint is taken into consideration, which demonstrates the maximum tolerance degree that the customers can wait. Therefore, how to configure the parameters in multistage multi-server queue systems to maximize profit on the premise of reducing the waiting times of customers is a critical issue for cloud service provider. To address this problem, we first discuss the probability distribution function of the waiting time for single multi-server system and multistage multi-server queue systems respectively, and then propose a profit maximization model under the deadline constraint. Due to the complexity of this model, the analytical solution can hardly be obtained, we study a heuristic method to search for the optimal solution. At last, a series of numerical simulations are implemented to describe the performance of the proposed profit maximization scheme, the results show that not only the profit can be maximized, but also the waiting time of customers have been reduced effectively.
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