In this paper, we mathematically model the multi-hop Peer-to-Peer (P2P) ride-matching problem as a binary program. We formulate this problem as a many-to-many problem in which a rider can travel my transferring between multiple drivers, and a driver can carry multiple riders. We propose a pre-processing procedure to reduce the size of the problem, and devise a decomposition algorithm to solve the original ride-matching problem to optimality by means of solving multiple smaller problems. We conduct extensive numerical experiments to demonstrate the computational efficiency of the proposed algorithm and show its practical applicability to reasonably-sized dynamic ride-matching contexts. Finally, in the interest of even lower solution times, we propose heuristic solution methods, and investigate the trade-offs between solution time and accuracy.

Real-time peer-to-peer ridesharing is a promising mode of transportation that has gained popularity during the recent years, thanks to the wide-spread use of smart phones, mobile application development platforms, and online payment systems. An assignment of drivers to riders, known as the ride-matching problem, is the central component of a peer-to-peer ridesharing system. In this paper, we discuss the features of a flexible ridesharing system, and propose an algorithm to optimally solve the ride-matching problem in a flexible ridesharing system in real-time. We generate random instances of the problem, and perform sensitivity analysis over some of the important parameters in a ridesharing system. Finally, we introduce the concept of peer-to-peer ride exchange, and show how it affects the performance of a ridesharing system.

The solution algorithms for the family of flow distribution problems, which include (1) the trip distribution problem of travel forecasting, (2) the OD estimation from link counts problem, and (3) the trip matrix disaggregation problem, are usually based on the Maximum Entropy (ME) principle. ME-based optimization problems are hard to solve directly by optimization techniques due to the complexity of the objective function. Thus, in practice, iterative procedures are used to find approximate solutions. These procedures, however, cannot be easily applied if additional constraints are needed to be included in the problem. In this paper a new approach for balancing trip matrices with application in trip matrix disaggregation is introduced. The concept of generating the most similar distribution (MSD) instead of the Most Probable Distribution of Maximum Entropy principle is the basis of this approach. The goal of MSD is to minimize the deviation from the initial trip distribution, while satisfying additional constraints. This concept can be formulated in different ways. Two MSD-based objective functions have been introduced in this paper to replace the ME-based objective function. One is the Sum of Squared Deviations MSD (SSD-MSD), and the other is Minimax-MSD. While SSD-MSD puts more emphasis on maintaining the base year trip shares as a whole, Minimax-MSD puts more emphasis on maintaining the share of each individual element in the trip table. The main advantage of replacing the entropy-based objective functions with any of these functions is that the resulting problems can include additional constraints and still be readily solved by standard optimization engines. In addition, these objective functions could produce more meaningful results than entropy-based functions in regional transportation planning studies, as shown in the case study and some of the examples in the paper. Several examples and a case study of the California Statewide Freight Forecasting Model (CSFFM) are presented to demonstrate the merits of using MSD-based formulations.

Peer-to-peer (P2P) ridesharing is a relatively new concept that aims to provide a sustainable method for transportation in urban areas. Previous studies have demonstrated that a system that incorporates both P2P ridesharing and transit would enhance mobility. We develop schemes to provide travel alternatives, routes and information across multiple modes, which includes P2P ridesharing, transit, city bike-sharing and walking, within the network. This study includes a case study of the operation of the multimodal system that includes P2P ridesharing participants (both drivers and riders), the Los Angeles Metro Red line subway rail, and the Los Angeles downtown bike-share system. The study conducts a simulation, enhanced by an optimization layer, of providing travel alternatives to passengers during morning peak hours. The results indicate that a multi-modal network expands the coverage of public transit, and that ride- and bike-sharing could be effective transit feeders when properly designed and integrated into the transit system.