An agent-based day-to-day adjustment process for ridesharing matching markets

Motivation With advances in information and communications technologies (ICTs), alternative mobility systems (e.g. taxis, demand-responsive services, peer-to-peer ridesharing, carsharing) have garnered interest from both public and private sectors as potential solutions to address the last mile problem in public transit (Mulley and Nelson, 2009; Li and Quadrifoglio, 2010). Although there are a number of models to optimize flexible or dynamic transit operations (e.g. Horn, 2002; Jung and Jayakrishnan, 2011; Agatz et al., 2012; Hyytia et al., 2012), there has not been any methodology to evaluate the market equilibrium for these systems. The reasons for this gap are summarized by Djavadian and Chow (2014) [DC14] . The few studies that evaluate the effects of system operating designs on travel demand (Cortes et al., 2005; Jung and Jayakrishnan, 2014; Maciejewski and Nagel, 2013) assume fixed demand for the service. Furthermore, some assume that a day-to-day adjustment process (Cascetta and Cantarella, 1991; Yang and Zhang, 2009) would automatically apply to FTS. However, flexible transport services (FTS) inherently involve demand from a population that is dynamically random or unknown to the operator. As a result, FTS that allow real time or dynamic interactions with riders exhibit several properties that nullify conditions required for convergence to stable equilibria in other adjustment processes: 1) travelers only choose the route choice set simultaneously with other travelers from which the FTS selects an optimal route; the realized performance of the route depends heavily on the dynamic operating policy of the FTS; link costs do not necessarily increase monotonically with flow and are non-separable. An agent-based day-to-day rational behavior adjustment process (RBAP) was proposed in [DC14] (see Figure 1 ) that could converge to a stable state, which was shown to be equivalent to a dynamic user equilibrium. The method has not yet been defined to evaluate peer-based two-sided services where agents may choose to be a driver or a passenger, nor has the method been made operational in practice to evaluate the market equilibrium for some key operational models that are gaining interest in the public, e.g. two-sided ridesharing matching markets like UberX and Lyft or mobile-device data driven demand responsive transit like Helsinki’s Kutsuplus . This study addresses these gaps. Fig. 1. Key components of agent-based RBAP under FTS setting. (source: [DC14]) Study contributions We extend the agent-based RBAP under FTS setting developed in [DC14] to consider dynamic two-sided ridesharing under a decentralized dispatch system. The two-sided ridesharing modeling in the RBAP is based on the concept of matching theory, with examples of the theory in transportation provided by Matsushima and Kobayashi (2006), Yang et al. (2010), and Demirel et al. (2010). Each agent’s utility function is changed to include choices of other agents as well as themselves, as discussed by Cheng et al. (2014). The endogeneity issue (Manski, 1993) is handled with a two-stage method per Walker et al. (2011). In addition, we integrate a matching algorithm based on work by Abraham (2009) to identify a stable equilibrium. The extended method is applied to a real network case study in the town of Oakville (see Figure 2 ), using data from the Transportation Tomorrow Survey (DMG, 2011) and other sources. We compare the market equilibria of operating policy designs between a demand responsive shuttle service like Kutsuplus (using the original RBAP from [DC14]) and a two-sided ridesharing market like UberX and Lyft, and identify design parameters that yield equivalent welfare effects. Fig. 2. Oakville network on proprietary simulation platform for proposed agent-based RBAP. References Abraham, D.J., 2009. Matching markets: design and analysis. Ph.D. Dissertation, Carnegie Mellon University. Agatz, N., Erera, A., Savelsbergh, M., Wang, X., 2012. Optimization for dynamic ride-sharing: a review. EJOR 223(2), 295-303. Cascetta, E., Cantarella, G.E., 1991. A day-to-day and within-day dynamic stochastic assignment model. Trans. Res. A 25(5), 277-291. Cheng, S.F., Nguyen, D.T., Lau, H.C., (2014). Mechanisms for arranging ride sharing and fare splitting for last-mile travel demands. AAMAS-14 Cortes, C.E., Pages, L., Jayakrishnan, R., 2005. 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