Round trip delays constitute the basic network measure that can be obtained by end systems without any network support. Our aim is to design measurement-based admission control strategies for streaming applications based on such minimal feedback on network state. To this end we discuss simple statistical models of packet round trip delays accross either local or wide area networks. We observe that the delay component due to queueing scales like the reciprocal of the spare capacity, at least in a ‘heavy traffic’ regime where spare capacity is scarce. Our models also allow to capture the correlations between consecutive measurements. Based on these results we propose a two-stage strategy for inferring spare capacity along a network path. We show consistency of this estimate, and analyse its asymptotic variance when the number of samples becomes large. We have experimented these strategies in a local network environment. We observe a good match between theory and practice for switched Ethernets. Surprisingly, the match deteriorates only slightly when the network path comprises hubs, although the theoretical models seem to be less applicable to such technology.