Abstract
An important class of models for macroscopic dynamic network loading (DNL) and dynamic traffic assignment (DTA) is based on treating link travel times as a function of link occupancy. However, these models suffer from some problems or deficiencies namely (a) the link outflows can violate first-in-first-out (FIFO), (b) the link outflows can exceed the link outflow capacities, (c) the link inflows can exceed the link inflow capacities, and (d) the link occupancies can exceed the link occupancy capacities. In this paper we introduce methods to overcome each of these problems.To remove problems (a) and (b) we extend the link travel-time model to better reflect behaviour when traffic flow is varying over time. To remove problems (c) and (d) we introduce more substantial changes in the model, to introduce capacities, spillback and queues compatible with the model. These extensions strengthen the realism, behavioural basis and usability of the link travel-time model and the DNL and DTA models that are based on it. They have no obvious adverse implications or side effects and require little additional computational effort. The original model is a special case of the new/extended model: the above extensions are activated if and only if any of the problems (a)–(d) arise, otherwise the new model reduces to the original model.
Highlights
In most of this paper we focus on single links and, in that case, the distinction between dynamic network loading (DNL) and dynamic traffic assignment (DTA) is not so important
The conditions (5) and (6) use an upper bound on inflows or outflows (Bin or Bout) but, in the standard forms of the macroscopic DNL model based on travel-time functions s(x(t)), there are no explicit or implicit upper bounds such as Bin or Bout on link inflows or outflows and no mechanisms for imposing such bounds
Since x varies over time in these models, the travel-time functions can be rewritten as s(x(t)), where t can represent discrete or continuous time
Summary
We deal with two of these, namely (a) and (b). These problems reflect ways in which the model can deviate from the behaviour of real traffic and to remedy these deviations we need to first discuss how they occur and what adjustments or extensions to the model are needed to overcome or eliminate them. When the original model would yield sðtÞ 6 sðt À 1Þ, we will reset the exit flow rate e(t) to equal the flow capacity Bout, which ensures s(t) > s(t À 1). There is a second problem that arises even if there are no FIFO violations so that the above problems do not arise This problem is that the original model allows the link exit flow rate (10) to exceed the maximum (capacity) flow rate for the link. In that case (10) yields an outflow rate e(t) that far exceeds the link exit flow capacity Bout. (a) Since all terms on the right hand side of (120) are positive, (120) reduces to snewðtÞ P snewðt À 1Þ, which is the FIFO condition for traffic entering the link at times t À 1 and t. Continuing in this way we see that enew(t) and snew(t) depend on all previous values of x(t). h
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
