Analytical models play a crucial role in evaluating Alternative Intersections and Interchanges (AIIs) and developing their signal plans. A key application is comparing O-D movement delays to measure the operational benefits of AIIs over conventional intersections. However, existing models often fail to account for time-varying arrival patterns and the segregation of O-D movements within the same lane group. This paper addresses these gaps by proposing new appropriate delay models that incorporate the Queue Accumulation Polygon (QAP) concept for uniform delay calculations. The QAP enables realistic modelling of arrival patterns and segregates delays by queues formed from different movements. Other delay terms are also developed to reflect AII operating conditions. Validation using various AIIs and traffic scenarios shows the proposed models align with field observations and movement-specific microsimulation results, outperforming widely used U.S. analytical models. These improvements enhance the accuracy of delay estimation and support better AII design and analysis.