Increasing demands on mobile networks to provide high speed data rates has led to fifth generation wireless networks. Essential to achieving the high frequencies of operation and powers required are gallium nitride (GaN) high-electron mobility transistors (HEMTs), because of their high efficiency, relatively high voltage breakdown and power handling. As a comparatively young technology, computer modelling is essential to developing and optimizing GaN HEMTs, and current two-dimensional (2D) modelling techniques struggle to efficiently link process parameters to DC and RF performance. Modern undoped devices based on InAlN/GaN heterostructures put further demand on computer models, as they rely on polarisation effects as the main contributors to the current-carrying two-dimensional electron gas channel, rather than doped donor layers found in previous GaAs and GaN devices. The new quasi-two-dimensional physical model presented in this research covers all these issues to accurately simulate device performance from DC to mm-wave. It includes an appropriate treatment of the electric field in the gate region and transport models for hot electron effects such as velocity overshoot, as well as handling electron transport in InAlN alloys, polarisation effects and the effects of undoped and doped layers. It is the first model to account for hot electron effects for undoped GaN-based HEMT devices. The model is used to demonstrate the link between process parameter variation and small-signal performance.