In this paper, we describe a software defined networking (SDN) approach to traffic engineering in inter-data center communication; then present $\mathrm{MCTEQ}$, a constrained utility-optimization formulation of the joint-bandwidth allocation problem for multiple classes of traffic in inter-data center communication. $\mathrm{MCTEQ}$ handles priorities between traffic classes in a soft manner and explicitly considers the delay requirement of $\mathrm{Interactive}$ flows. $\mathrm{MCTEQ}$ being NP-hard, we construct a new approximation to be able to lean on the mature and efficient linear programming solvers to obtain fast and accurate approximations. We demonstrate via numerical experiments with two realistic inter-data center network topologies that $\mathrm{MCTEQ}$ achieves considerably more network utilization than the best known solutions from the literature, while running at least twice faster. We also show via ns-2 packet level simulation that with $\mathrm{MCTEQ}$ traffic engineering, end-to-end packet delay requirements of $\mathrm{Interactive}$ flows are indeed guaranteed for in-profile traffic, which is not the case for alternative approaches.