Volume-Delay Function (VDF) is a key input in several tasks including traffic assignment and trip distribution estimation. However, there is no clear framework to identify the VDF formula and parameters. Furthermore, the VDF performance in the oversaturated condition is uncontrolled. In this paper, most VDF-related aspects are investigated, including the key attributes, traffic model and VDF formulas, oversaturated condition assumptions, and optimization techniques. In each aspect, different methods are compared for best performance, while a new procedure is introduced, if necessary. The best traffic model and VDF formulas are nominated to satisfy a set of logic and statistical conditions, while a new optimization technique is presented. Furthermore, a new realistic assumption to control the VDF performance is discussed. This framework is applied on 32 worldwide roads of different categories and characteristics, which indicates accurate and realistic results. The results encourage for further investigation of the VDF performance in future work.
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