While delay-critical applications typified by online multimedia communication are growing rapidly, the end-to-end (E2E) delay behavior in the Internet remains poorly understood. This paper proposes a stochastic process model, in which E2E delay alternations are classified into two categories, jump and perturbation, according to whether the statistical characterizations alter or not. As the chief type of majority delay alternations, perturbations generally occur continuously in a period, and can be analogous to an ergodic stationary process. The authenticity of the model is verified with real life delay measurements in the Internet collected by all pairs pings (APP) project through months from PlanetLab nodes. Based on the model, several delay estimation algorithms are comparatively analyzed, and the experimental results demonstrate that in terms of minimizing the mean squared error, the most accurate delay prediction is the minimum of the two most recent measurements.