Prism-based path set restriction for solving Markovian traffic assignment problem

Maximum likelihood estimation for randomized shortest paths with trajectory data

“…First, they can become computationally untractable when considering cycles on the network because of infinitely cumulating costs [46]. This problem has been alleviated, for instance, by restricting the path set to "efficient" paths [11], by constraining the path lengths [48], or by introducing a discount factor [46] that makes the model interpolate between unbiased and optimal behaviour similarly (but not equivalently) to the inverse temperature parameter β in the RSP model. A second criticism about logit assignment is that it has the independence from irrelevant alternatives (IIA) property [7], essentially meaning that an agent leaving from s to t according to the logit probabilities will more likely select an edge that leads to more alternative s-t-paths, even if those paths are almost identical (i.e.…”

“…Also, the dispersion-constrained model in [3] is based on a maximum-entropy approach similar to the RSP framework, and involves the estimation of a temperature parameter. Other works, such as [15,36,37,[46][47][48] focus, in various trafficrelated settings, on the problem of estimating parameters on edges or parameters associated to features on edges, which in some cases corresponds to the problem of estimating the inverse temperature and in some case to the problem of estimating edge costs in the RSP framework (the latter of which is addressed only briefly in the current work, in Section 2.4). The above cited works in logit assignment and related models is in many respects very close and similar to the RSP model.…”

Markovian Traffic Equilibrium Assignment based on Network Generalized Extreme Value Model

“…Because these problems are caused by the path set restriction to efficient paths, they cannot be alleviated even through the use of the NGEV route choice model. The MTA (Akamatsu, 1996;Baillon and Cominetti, 2008) is mathematically more preferable in terms of the solution properties, and it has an obvious similarity to the NGEV route choice model in the formulations Akamatsu, 2012, 2014;Mai et al, 2015;Mai, 2016;Oyama and Hato, 2019). Nevertheless, the algebraic relationship between them has never been investigated, and an efficient MTA algorithm for NGEV-based traffic assignment does not yet exist.…”

“…Although Dial can alleviate this problem, the convergence of equilibrium assignment with Dial to an exact solution is not ensured due to the definition of efficient paths (Akamatsu, 1997). Oyama and Hato (2019) proposed an efficient and flexible path restriction method based on the concept of choice-based prism, which alleviates the computational intractability of the MTA. They also provided an experiment to show that the method is well-suited for the NGEV assignment.…”

“…Rather, the use of Markovian traffic assignment (MTA) (Bell, 1995;Akamatsu, 1996), which is also an efficient network loading algorithm and implicitly considers a fixed path set, is mathematically convergent and preferable. One can also notice that the NGEV route choice model has an obvious similarity in its formulations to the MTA models (Akamatsu, 1996;Baillon and Cominetti, 2008;Fosgerau et al, 2013;Oyama and Hato, 2019). Nevertheless, the algebraic relationship between them has never been investigated, and an efficient and convergent algorithm does not exist for NGEV-based network loading.…”