Minimizing Data Access Latencies for Virtual Machine Assignment in Cloud Systems

Cloud systems empower the big data management by providing virtual machines (VMs) to process data nodes (DNs) in a faster, cheaper and more effective way. The efficiency of a VM allocation is an important concern that is influenced by the communication latencies. In the literature, it has been proved that the VM assignment minimizing communication latency in the presence of the triangle inequality is 2-approximation. However, a 2-approximation solution is not efficient enough as data center networks are not limited to the triangle inequality. In this paper, we define the quadrilateral inequality property for latencies such that the time complexity of the VM assignment problem minimizing communication latency in the presence of the quadrilateral inequality is in P (polynomial) class. Indeed, we propose an algorithm for the problem of assigning VMs to DNs to minimize the maximum latency among allocated VMs in addition to DNs with their assigned VMs. This algorithm is latency optimal and 2-approximation for networks with the quadrilateral inequality and the triangle inequality, respectively. Besides, the extension of the proposed method can be applied to the cloud elasticity. The simulation results illustrate the good performance and scalability of our method in various known data center networks.