This paper shows that an appropriate choice of the transport protocol, either TCP or UDP, in video streaming services can effectively improve the efficiency of the network resources. The proposed algorithm compares the available network capacity with the rate that is required to transmit the video content. In particular, the study focuses on video streaming by means of DASH standard, so that a new video chunk is selected according to the estimated network capacity. We use a simulation study, carried out over the ns-3 platform, to assess the performance of our proposal. The results show that by using a cross-layer technique for the transport protocol selection, we can maintain the Quality of Experience perceived by the end-users, while reducing the number of transmissions that are required in the uplink, which effectively improves the resources usage.