A Vectorized Formulation of the Cell Transmission Model for Efficient Simulation of Large-Scale Freeway Networks

Macroscopic traffic flow models are powerful tools for assessing the level of service on freeway segments. One popular model is the Cell Transmission Model (CTM) proposed by Daganzo. The US highway capacity manual (HCM) operationalizes this model in the form of the simulation tool FREEVAL for assessing sequences of freeway segments. The conceptual CTM also supports networks of freeway segments. In the literature this was implemented and applied to a mid-scale freeway network of 340 km. However, the literature lacks research in efficient implementations of CTM, which becomes relevant when applying it to large-scale networks at national scale like the German Autobahn with a length of 260 000 km.
In this paper we propose a vectorized formulation of the CTM for networks. Boolean vectors are employed for vectorized case distinction. Furthermore, we exploit the properties of adjacency matrices to achieve shifting operation on complex network structures. To evaluate the vectorized CTM implementation, we simulate synthetic freeway network grids of varying size and complexity for different simulation periods. The results show that the network complexity has no influence on computation time, while it scales linear in simulated hours. ... mehrA quadratic regression was applied to the measured computation times over varying network sizes. For large network sizes, the vectorized CTM implementation achieves a speedup factor of 9 compared to a sequential implementation. When simulating 2880 kilometers of freeway, the computation time of 2.3 hours is reduced to 16 minutes.