1. A method, comprising: determining, by a processor, a first rate being a rate of change of an execution state of a virtual machine undergoing live migration from an origin host computer system to a destination host computer system; determining a second rate being a rate of transferring the execution state of the virtual machine from the origin host computer system to the destination host computer system; detecting an increase in the first rate; determining that a ratio of the first rate to the second rate exceeds a threshold convergence ratio; and reducing the rate of transferring the execution state of the virtual machine from the origin host computer system to the destination host computer system.