In packet-switched networks, a packet delay channel, we refer to it as delay channel later, uses different delays between packets as media to carry messages. Because the delays between packets are not normal media for the network communications, the delay channels can penetrate most of network firewalls and then leaks sensitive information without being noticed. Therefore, the delay channels are popular in the areas of covert communication and packets flow watermarking. Because of such an unusual communication method, the delay channels are labeled as unstable channels. To the best of our knowledge, no work has been done to scale the robustness of the delay channels. We treat the lengths of the delays as the amplitudes of carrier waves and then propose a mathematical model for the delay channels through the theory of amplitude modulation. Furthermore, the different kinds of noise for the delay channels are modeled by different distribution functions. Subsequently, using probability theory, the robustness of the delay channels is quantified from the aspects of channel capacity and channel transmission error rate, etc. Both simulation and experimental results show the soundness of our works.