When allocating network bandwidth to multiple classes of applications in inter-data center communication, coordi nation always yields a better utilization of the backbone network. Yet, it often comes at a prohibitively heavy computational and communication cost, making it thus far not a practically viable approach. SDN helped in bridging the communication cost gap by enabling centralized control, and SDN has been recently applied in such inter-DC traffic management. However, the computational cost is still an issue as the efficient and fast response of the centralized traffic engineering algorithm has become crucial to the practicality of such SDN-based approach. In this paper, we present MCTEQ, a utility-optimization-based joint-bandwidth al location for inter-DC communication with multiple traffic classes, that handles priorities between traffic classes in a soft manner and explicitly considers the delay requirement of Interactive flows.MCTEQ being NP-hard, we apply approximation techniques to lean on the mature and efficient LP solver and obtain fast and accurate approximations. We demonstrate via experiments with Google's inter-DC backbone topology that MCTEQ achieves about 160 Gbps higher network utilization than the existing SWAN solution, yet runs 2.5 times faster. In particular, MCTEQ guarantees that the allocated bandwidth for Interactive flows strictly meets their end-to-end delay requirements.