In recent years, virtualization is playing an increasingly important role in the cloud environment, as it allows service providers to create an abstraction of the physical servers running on data centers. In this way services can be directly hosted on these abstract entities, which are then called Virtual Machines (VMs). The direct result of service virtualization is the ability to move services hosted on VMs, from a data center to another, hence, to perform VM migration. Efficient strategies for VM migrations bandwidth provisioning in an inter-data centers scenario are needed as a considerable use of network resources (available bandwidth, especially) is required, and the impact of live VM migrations on the underlying optical transport network has not been extensively investigated. In this paper we propose Routing and Bandwidth Allocation (RBA) algorithms for the live migration of VMs in a distributed DC infrastructure, focusing our attention on the live VM migration technique under dynamic traffic conditions. In order to evaluate the performance of the RBA algorithms in terms of migration blocking probability and network resource occupation we developed a discrete event-based simulator. We find that assigning a bandwidth to the VM migration request in proportion to the path length could improve the network performance