At the core of dynamic traffic assignment (DTA) we find the Dynamic Network Loading (DNL). The goal of the DNL is to find consistency between the propagation of traffic flows on the network and the constraints imposed by roads (e.g. maximum throughput, speed limits,...) or intersections (e.g. turning restrictions, obstructions by crossing traffic,...) by inflicting delays in the network. For solving practical DTA (or DNL) problems, a numerical discretization of the variables (traffic, space, time) is required. In our context:-Traffic: Individual vehicles are aggregated into a continuous vehicle flow represented by cumulative vehicle numbers (CVN) from which the fundamental traffic characteristics (speed, flow and density) can be derived (Newell, 1993). -Space: The link transmission model (LTM, Yperman, 2007) allows one to have discrete space intervals the size of homogeneous stretches of roads (links).-Time: The time discretization is depended on the level of the problem: for standard LTM and most other DNL's typically short (less than 1 min), for route choice models and origin destination flows a lot larger (typically around 15 min).For standard numerical schemes that solve DNL sequentially through the time domain, time steps are typically small (Courant Fraichant Lewy or CFL-condition), meaning that for each link in the network the update interval of the corresponding CVN cannot be larger than the minimum time it takes to propagate information over that specific link. This is of major importance for the efficiency of LTM (and other DNL) implementations, as computational resources are almost linearly dependent on the time update frequency. In this paper, we describe a variation on the basic LTM that avoids the CFL-conditions, which as a result allows for inherently faster numerical evaluation.
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