Predicting the matching probability and the expected ride/shared distance for each dynamic ridepooling order: A mathematical modeling approach

Abstract

The popularity of smartphones and the advent of GPS positioning and wireless communication technologies in the recent decade have facilitated large-scale implementations of dynamic ridepooling services, such as Uber Pool, Lyft Line, and Didi Pinche. As in such services trips usually start before the appearance of pooling partners, knowing the probability of getting matching with another order (i.e., matching probability), the expected detour distance, and the expected shared distance before the start of each trip is essential for passengers to evaluate their willingness to pool and for ridepooling platforms to offer attractive discounts. In this paper, assuming that every ridepooling passenger shares vehicle space with at most one another during the entire trip, and ridepooling orders in each (origin-destination) OD pair appear following a Poisson process with a given rate, we propose a mathematical modeling approach to predict the matching probability, the expected ride distance, and the expected shared distance of each order under a first-come-first-serve strategy in dynamic ridepooling service. The method defines unmatched passengers at different locations along the exclusive-riding path of each OD pair into different seeker- and taker-states, formulates the complex interdependency of the matching probabilities, matching rates and arrival rates of (unmatched) passengers in different states into a system of nonlinear equations, and generates the matching probabilities and expected ride/shared distances of all OD pairs simultaneously. Under the same first-come-first-serve strategy, we simulated the occurrence, movements and state transitions of ridepooling orders based on a 30*30 grid network and the real network of Haikou City in China. In comparison with simulation results, we show that the method proposed in this paper can generate fairly satisfactory predictions under diverse matching conditions and demand intensities.