Complementarity models for traffic equilibrium with ridesharing

Convergence Properties of a Second Order Augmented Lagrangian Method for Mathematical Programs with Complementarity Constraints

“…MPCCs are also present in many applications like urban traffic control, economy, problems arising from the electrical sector, etc. See [18,25,41,42,51] and references therein.…”

A Side-Constrained Peer-to-Peer Carpooling Stochastic User Equilibrium Model

“…In actual P2P carpooling, the drivers often take detours to pick up or drop off riders, indicating that the drivers and riders often have inconsistent OD pairs. In view of this shortage, Xu et al [20] set up a traffic equilibrium model based on P2P carpooling, transformed the model into a hybrid complementary model, and applied the hybrid model to several cases with different network structures. The case study shows that more travellers prefer to act as carpooling drivers at a high price of P2P carpooling.…”

“…minimum of linear constrained minimization. According to Theorem 2, Theorem 6.3.3 of Bazaraa et al and Theorem 6.3.1 of Bazaraa et al, it is known that y(λ) is unique, and L(λ) is continuous differentiable and concave[20].The KKT conditions of Lagrange duality are as follows:…”

A Multi-Modal Route Choice Model with Ridesharing and Public Transit

“…Recently, there is a small but growing body of studies with respect to ridesharing activities to explain travel behavior within the transportation domain. Some researchers have conducted empirical studies [8,11,[20][21][22][23][24][25][26][27][28]; some researchers have studied travelers' route choice and mode decision making process when ridesharing activities are incorporated into the morning commute problem [29][30][31] and the traffic assignment problem [32][33][34][35][36][37]. As for empirical studies, for instance, Morency [8] used travel data from four large-scale origin-destination (OD) surveys to study the evolution of the ridesharing market in the Greater Montreal Area, and found that commuters were at one time more inclined (or forced) to share car seats and then less people chose to share rides with others (because travelers wanted more freedom to travel as they wish with the rapid urban development and economic growth); Caulfield [20] conducted a logistic regression analysis to examine the characteristics of the individuals that rode shares in Dublin, and found that females and those in couples were most likely to rideshare; Erdogan et al [21] studied the demand for ridesharing in a university campus context by using a commuter survey data, developed ordered probit models to investigate interest in ridesharing, and found that taste heterogeneity significantly affected propensity to rideshare; Lee et al [25] conducted a self-reported online survey among Uber users in Hong Kong, used the structural equation modeling technique to analyze the empirical results, and found that perceived risks, perceived benefits, trust in the platform, and perceived platform qualities significantly influenced users' intention to participate in Uber; Stiglic et al [26] used an extensive computational study to investigate the potential benefits as well as synergies of the seamless integration of ride-sharing and public transit, and found that such a system could significantly enhance mobility and increase the use of public transport.…”

“…The advent of a ridesharing program provides travelers more travel modes (i.e., sharing a ride as a driver, sharing a ride as a rider) and makes the traffic assignment model add car capacity constraints, the goal of the traffic assignment model with ridesharing is to determine travelers' path and mode choices to minimize their generalized path travel cost (not their actual path travel cost on account of the car capacity constraints). At a ridesharing user equilibrium (RUE) state, no traveler can improve his or her generalized travel cost by either unilaterally changing his or her routes or travel modes [32,33,35,36].…”