We propose a scheme to schedule the transmission of data center traffic to guarantee a transmission rate for long flows without affecting the rapid transmission required by short flows. We call the proposed scheme Deadline-Aware Queue (DAQ). The traffic of a data center can be broadly classified into long and short flows, where the terms long and short refer to the amount of data to be transmitted. In a data center, the long flows require modest transmission rates to keep maintenance, data updates, and functional operation. Short flows require either fast service or be serviced within a tight deadline. Satisfaction of both classes of bandwidth demands is needed. DAQ uses per-class queues at supporting switches, keeps minimum flow state information, and uses a simple but effective flow control. The credit-based flow control, employed between switch and data sources, ensures lossless transmissions. We study the performance of DAQ and compare it to those of other existing schemes. The results show that the proposed scheme improves the achievable throughput for long flows up to 37% and the application throughput for short flows up to 33% when compared to other schemes. DAQ guarantees a minimum throughput for long flows despite the presence of heavy loads of short flows.