Constructing a cell transmission model solution adhering fully to first-in-first-out conditions

Abstract

Multi-commodity continuous flow network models, especially the cell transmission model (CTM) and the link transmission model, have been widely used in theory and practice for dynamic network loading (DNL), as well as for computing dynamic user equilibria (DUE). These models attempt to follow a first-in-first-out (FIFO) priority rule at various levels of approximation. However, previous studies have shown that these existing models and implementations do not fully ensure FIFO. Also, they allow deviations from FIFO that are not observed or permitted or physically possible in practice and these deviations can cumulate over time. A benchmark is needed for assessing the implications of FIFO violations in these models and methods, preferably over a wide range of instances. For this purpose, we propose here the first solution method that ensures perfect adherence to FIFO at the network-wide level.For clarity of exposition, the specific methods are presented here within the CTM framework. Variants of the principles presented here can be used to develop methods for ensuring FIFO for other DNL models. The proposed method is computationally intensive, and therefore suitable for small to medium size problems. As such, this method may not be applicable to large scale problems, which are considered fairly often in practice. The main value of the proposed method is therefore in the ability to produce a set of benchmark solutions, to evaluate the FIFO performance of other methods or the implications of FIFO violations in other methods. In addition, partial adoption of the ideas proposed here could lead to new efficient algorithms that approximate FIFO better than existing methods.