Technical Note—Conical Volume-Delay Functions

The widely used BPR volume-delay functions have some inherent drawbacks. A set of conditions is developed which a “well behaved” volume delay function should satisfy. This leads to the definition of a new class of functions named conical volume-delay functions, due to their geometrical interpretation as hyperbolic conical sections. It is shown that these functions satisfy all conditions set forth and, thus, constitute a viable alternative to the BPR type functions.