Virtual machine allocation in cloud computing for minimizing total execution time on each machine

This paper considers a virtual machine allocation problem. Each physical machine in cloud has a lot of virtual machines. Each job needs to use a number of virtual machines during a given and fixed period. The objective aims to minimize the cost induced by total execution time on each physical machine. This allocation problem is proved to be N P-hard. Additionally, three mixed integer linear mathematical models are constructed to represent and solve the problem. The performance comparison of the three proposed models is analyzed through some empirical results.