Dynamic Traffic Assignment

DTA is an important problem as its models have many applications in transportation planning, transportation policy evaluation and real-time traffic control and management. A comprehensive literature review on this problem area includes articles by Cascetta and Cantarella (1993), Peeta and Ziliaskopoulos (2001), Boyce, Lee, and Ran (2001), Szeto and Lo (2005a, 2005b), Jeihani (2007) and Szeto (2013).

Problem Definition

DTA is a generalisation of static traffic assignment. In simple terms, static traffic assignment is a problem of determining the number of vehicles entering each highway in a specific area per hour (i.e. the vehicular traffic flow or flow pattern on each highway), given the vehicular demand for travel from each of the origins to each of the destinations in the area. In other words, the problem is to assign traffic to different highways according to certain behavioural rules. However, this problem cannot capture the realistic changes in the number of vehicles on the highways over time or the departure time choices of travelers. Therefore, DTA generalises static traffic assignment to determine the time-varying flow on each highway over a study period, given the overall demand for vehicular travel.

DTA problems can be roughly divided into day-to-day adjustment (or dynamic) problems (e.g. Ben-Akiva, de Palma, & Kaysi, 1991, and Cascetta, 1989; Horowitz, 1984) and within-day DTA problems (e.g. Chang & Mahmassani, 1988; Friesz, Bernstein, Smith, Tobin, & Wie, 1993, 2013; Lam & Huang, 1995; Long, Huang, Gao, & Szeto, 2013; Ran & Boyce, 1996). Day-to-day adjustment problems are concerned with how the travel decisions of travelers change over days (or periods) and how their route or departure time choices on a particular day (or period) depend on their experience obtained in previous days (or periods). Within-day DTA problems include pure departure time choice problems, pure route choice problems, and simultaneous route and departure time choice problems, in the sense that the travel decision is considered in a typical day and there is no day-to-day adjustment.

The solution of a within-day DTA problem can also be viewed as the final state solution of a day-to-day adjustment problem, where no traveler can make a better decision than their current one.

For pure route choice problems, they can be further classified into the en route adjustment model or the reactive DTA problems (e.g. Ben-Akiva et al., 1991; Pel & Bliemer, 2009; Kuwahara & Akamatsu, 1997) and no en route adjustment problems or the predictive DTA problems (e.g. Friesz, Tuque, Tobin, & Wie, 1989, 1993; Lo & Szeto, 2002a; Sumalee, Zhong, Pan, & Szeto, 2011; Szeto, Jiang, & Sumalee, 2011; Szeto & Lo, 2006). The en route adjustment problems allow drivers to switch their routes during their trips in response to having more updated traffic information. For example, a driver will switch to another route if he/she realizes that there is a heavy traffic jam ahead on his/her originally planned route. This adjustment problems contrast with the no en route adjustment problem, which assume that choices do not change during trips and that travelers select routes based on pre-trip information and predicted travel times.

The focused problem in this chapter is actually within-day DTA problems with no en route adjustment consideration, but the literature review also includes those related to day-to-day DTA problems and en-route adjustment problems. Unless specified otherwise, DTA in the rest of this chapter, except the section of literature review (i.e. Section 8.3), refers to within-day DTA problems without en-route adjustment consideration.