Constructing a cell transmission model solution adhering fully to first-in-first-out conditions. (July 2022)

• Record Type: Journal Article
• Authors: Bar-Gera, Hillel; Carey, Malachy
• Is Part Of: Transportation research. Volume 161(2022)
• Page Start: 247
• Page End: 267
• Publication Date: 2022-07
• Subjects: Continuous time network flow models -- Cell transmission model -- CTM -- First-in-first-out -- FIFO -- Dynamic network loading -- DNL -- Flow merges -- Flow diverges -- Exit priorities; Transportation -- Research -- Periodicals; Transportation -- Mathematical models -- Periodicals
• DOI: 10.1016/j.trb.2022.04.002
• Languages: English
• ISSNs: 0191-2615

Abstract

Highlights: Continuous flow network models, especially cell transmission model (CTM) are widely used in modelling time-varying flows on traffic networks. These approximate first-in-first-out (FIFO) behaviour, but allow deviations from FIFO not observed or possible in practice and deviations can cumulate over time. This paper adapts the CTM to ensure, for the first time, perfect adherence to FIFO. The proposed methods are computationally intensive, hence suitable for small to medium size problems. Can produce accurate benchmark solutions, to measure/ assess FIFO violations, performance, and implications for other CTM models and methods. Partial adoption of proposed ideas could yield new algorithms that approximate FIFO better than existing methods. 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.