Effect of the trip-length distribution on network-level traffic dynamics: Exact and statistical results

This paper presents additional results of the generalized bathtub model for urban networks, including a simpler derivation and exact solutions uniformly distributed trip lengths. It is shown that in steady state this trip-based equivalent to more parsimonious accumulation-based model, trip-length distribution has merely transient effect on traffic dynamics, which converge same point macroscopic fundamental diagram (MFD). To understand statistical properties system, queueing approximation method proposed compute network accumulation variance. found (i) variance much larger than predicted by traditional models, due nonlinear dynamics imposed MFD, (ii) no variance, indicating formula might be universal, (iii) system exhibits critical behavior near capacity where diverges. indicates tools from phenomena phase transitions useful congestion cities.