Over the past decade there has been a growing demand for interactive multimedia applications deployed over public IP networks. To achieve acceptable Quality of Ser- vice (QoS) without significantly modifying the existing infrastructure, the end-to-end applications need to optimize their behavior and adapt according to network char- acteristics. Most existing application optimization techniques are based on reactive strategies, i.e. reacting to occurrences of congestion. We propose the use of predic- tive control to address the problem in an anticipatory manner. This research deals with developing models to predict end-to-end single flow characteristics of Wide Area Networks (WANs). A novel signal, in the form of single flow packet accumulation, is proposed for feedback purposes. This thesis presents a variety of effective predictors for the above signal using Auto-Regressive (AR) models, Radial Basis Functions (RBF) and Sparse Basis Functions (SBF). The study consists of three sections. We first develop time- series models to predict the accumulation signal. Since encoder bit-rate is the most logical and generic control input, a statistical analysis is conducted to analyze the effect of input bit-rate on end-to-end delay and the accumulation signal. Finally, models are developed using this bit-rate as an input to predict the resulting accu- mulation signal. The predictors are evaluated based on Noise-to-Signal Ratio (NSR) along with their accuracy with increasing accumulation levels. In time-series models, RBF gave the best NSR closely followed by AR models. Analysis based on accu- racy with increasing accumulation levels showed AR to be better in some cases. The study on effect of bit-rate revealed that bit-rate may not be a good control input on all paths. Models such as Auto-Regressive with Exogenous input (ARX) and RBF were used to develop models to predict the accumulation signal using bit-rate as a modeling input. ARX and RBF models were found to give comparable accuracy, with RBF being slightly better.