Stochastic equilibrium assignment with variable demand: literature review, comparisons and research needs

Abstract

The aim of this paper is threefold: (1) propose a detailed literature review; (2) compare existing approaches and (3) discuss the main research needs. The literature review is structured with respect to (a) solution approaches: optimization, variational inequalities and fixed-point (internal and external approaches). (b) choice dimensions taken into account, (c) solution algorithms. The comparison is aimed at highlighting the transportation problems that each approach is able to address and to highlight the most effective approach within a specific problem and/or the most performing solution algorithm within the same approach. Finally, a sort of research "road-map" is drawn in order to emphasize research needs and research perspectives.

Stochastic equilibrium assignment with variable demand: Theoretical and implementation issues

“…Among them, the most interesting one are (for a complete review the reader may refer to Cantarella, de Luca, Di Gangi, & Di Pace, 2013) : Fernandez, Florian, De Cea, and Cabrera (1994); Nagurney, Ramanujam, and Dhanda (1998); Lundqvist and Abrahamsson (1999); May and Milne (2000); De Cea and Fernandez (2001); Clegg, Smith, Xiang, and Yarrow (2001); Yildirim and Hearn (2005); Zhou, Chen, and Wong (2009); D'Acierno, Gallo, and Montella (2006); Meng and Liu (2012). Alternative and interesting approaches are presented by Wong (1998) and Wichiensin, Bell, and Yang (2007).…”

Approaches for solving the stochastic equilibrium assignment with variable demand: internal vs. external solution algorithms

“…Alternative step size or alternative step techniques have been proposed for solving constant demand assignment problems (see for instance, [68,21,24]). A different averaging scheme on arc costs (MSA-CA) was proposed in [13], and investigated in depth in [15,19] where a systematic comparison between the MSA-FA and the MSA-CA was carried out.…”

“…The internal approach may be addressed by three main methods (a synopsis is proposed in Table 1; for an extended review of literature the reader may also refer to [15]): optimisation (OPT), variational inequality (VI) and F-P.…”

Consistent formulation of network equilibrium with stochastic flows

“…While there exist a variety of general-purpose algorithms for solving fixed point problems in transportation networks (e.g. Liu et al, 2009;Cantarella et al, 2013), which might be applied to problem (2), an attractive and efficient alternative for practical applications is a formulation as a convex optimization problem. Since some of the proposed models presented in Section 3 may be formulated as convex optimization problems, we discuss these below.…”