A FIFO Rule Consistent Model for the Continuous Dynamic Network Loading Problem

This paper presents a first-in-first-out (FIFO) rule consistent model for the continuous dynamic network loading problem. The model calculates the link travel time functions at a basic finite set of equally spaced times that are used to interpolate a monotone spline for all the other times. The model assumes a nonlinear link travel time function of the link volumes, but some corrections are made to satisfy the FIFO rule at the basic set. Furthermore, the use of monotone cubic splines preserving monotonicity guarantees that the FIFO rule is satisfied at all points. The model consists of five units: 1) a path origin flow wave definition unit; 2) a path wave propagation unit; 3) a congestion analysis unit; 4) a network flow propagation unit; and 5) an inference engine unit. The path flow intensity wave, which is the basic information, is modeled as a linear combination of basic waves. Next, the individual path waves are propagated throughout the paths by using a conservation equation that stretches or enlarges the wave lengths and increases or reduces the wave heights, depending on the degree of congestion at different links. Then, the individual path waves are combined together to generate the link and node waves. Finally, the inference engine unit combines all information items to make them compatible in times and locations using the aforementioned iterative method until convergence. The method is illustrated by some examples. The results seem to reproduce the observed trends closely. The required CPU times oscillated between seconds and a few minutes.