Virtual machine (VM) migration is a widely used technique in cloud computing systems to increase reliability. There are also many other reasons that a VM is migrated during its lifetime, such as reducing energy consumption, improving performance, maintenance, etc. During a live VM migration, the underlying VM continues being up until all or part of its data has been transmitted from source to destination. The remaining data are transmitted in an off-line manner by suspending the corresponding VM. The longer the off-line transmission time, the worse the performance of the respective VM. The above is because during the off-line data transmission, the VM service is down. Because a running VM's memory is subject to changes, already transmitted data pages may get dirtied and thus needing re-transmission. The decision of when suspending the VM is not a trivial task at all. The above is justified by the fact that when suspending the VM early we may result in transmitting off-line a significant amount of data degrading thus the VM's performance. On the other hand, a long waiting time to suspend the VM may result in re-transmitting a huge amount of dirty data, leading in that way to waste of resources. In this paper, we tackle the joint problem of minimizing both the total VM migration time (reflecting the resources spent during a migration) and the VM downtime (reflecting the performance degradation). The aforementioned objective functions are weighted according to the needs of the underlying cloud provider/user. To tackle the problem, we propose an online deterministic algorithm resulting in an strong competitive ratio, as well as a randomized online algorithm achieving significantly better results against the deterministic algorithm.