Impact of Trip Distance Distribution Time Dependency and Aggregation Levels in Bathtub Models -- A Comparative Simulation Analysis

TL;DR

The paper addresses how different bathtub (MFD-based) formulations respond to static and dynamic trip distance distributions (TDD) across networks with varying connectivity. It systematically compares accumulation-based, M-model, and two trip-based approaches (event-based and fixed-time-step) against a macroscopic dynamic traffic assignment baseline on Delft-derived and toy networks, incorporating dynamic TDD and multiple aggregation levels. Key findings show dynamic TDD generally increases errors for trip-based methods, while accumulation-based approaches perform better in the Delft networks; the M-model underperforms with the optimized alpha, and the benefits of reduced TDD aggregation are most pronounced during demand transitions. These results highlight the influence of network state transition speeds and suggest directions for enhancing bathtub models to capture dynamic TDD effects and congestion transitions more robustly.

Abstract

Bathtub models are used to study urban traffic within a certain area. They do not require to take into account the detailed network topology. The emergence of different bathtub models has raised the question of which model can provide more robust and accurate results under different demand scenarios and network properties. This paper presents a comparative simulation analysis of the accumulation-based model and trip-based models under static and dynamic trip distance distribution (TDD) scenarios. Network accumulation was used to validate and compare the performance of the bathtub models with results from the macroscopic traffic simulation with dynamic traffic assignment. Three networks were built to explore the effect of network properties on the accuracy of bathtub models. Two are from the network of Delft, the Netherlands, and one is a reference toy network. The findings show that the time dependency of TDD can increase the errors in bathtub models. Using TDD in different aggregation levels can significantly influence the performance of bathtub models during demand transition periods. The state transition speed of networks is also found to be influential. Future research could explore the effects of dynamic TDD under congested situations and develop enhanced bathtub models that can better account for different network state transition speeds.

Figures (9)

• Figure 1: Road networks used for macroscopic traffic simulation. Stars represent centroids of zones and the connectors are represented by dashed links. (a) Delft network with freeways (DF); (b) Delft urban network (DU); (c) Toy network (T).
• Figure 2: Speed MFD fitting results for three cases. (a) Delft network with freeways (DF); (b) Delft urban network (DU); (c) Toy network (T).
• Figure 3: Conditions in different simulation scenarios. (a) Two demand profiles; (b) Coefficients for time-dependent OD matrices; (c) Delft network with freeways (DF): static TDD; (d) Delft urban network (DU): static TDD; (e) Toy network (T): static TDD; (f) Delft network with freeways (DF): dynamic TDDs; (g) Delft urban network (DU): dynamic TDDs.
• Figure 4: Accumulation comparison between models in different scenarios with static TDD. (a,b) Delft network with freeways (DF); (c,d) Delft urban network (DU); (e,f) Toy network (T).
• Figure 5: Accumulation comparison between models in different scenarios with dynamic TDD. (a,b) Delft network with freeways (DF); (c,d) Delft urban network (DU).