ESTIMATION OF ROUTE-LEVEL TRANSIT OD MATRIX USING BOARDING AND ALIGHTING DATA

Abstract

Transit OD matrix is a fundamental element of service planning and operation.As it provides information about passenger trips between each pair of stops, OD matrix can be crucial for route designing, route modification (extending or splitting), transit/crew scheduling, vehicle composition, etc. Transit origin-destination matrices can be generated at route or network-level. At route-level, no transfers are considered and trips are assumed to be independent of each other, whereas working at network-level necessitates dealing with trip interchanges, which makes the estimation process more complicated. Traditionally, transit OD matrices are generated by conducting on-board surveys. Such surveys are labor-intensive, time consuming and highly expensive. Therefore, utilizing the readily available data in the estimation process has been the subject of many research for the past few decades. Owing to the popularity of automatic systems such as Automatic Fare Collection (AFC) , Automatic Passenger Count (APC) and Automatic Vehicle Location (AVL) systems in public transport, it is more convenient now to collect large-scale information about passengers’ mobility. The data obtained from such systems have been widely used to study the mobility pattern of passengers in public transport. Most recent studies used smart card data to infer passengers’ boarding and alighting stations using trip chaining algorithm. The problem of estimating OD matrix using boarding and alighting data is ill-posed in nature. That is, there can be more than one possible solutions to the problem. To reduce the degree of ill-posedness, previous methods such as Iterative Proportional Fitting (IPF) and Maximum Likelihood Estimation (MLE) used a seed matrix and tried to improve the seed matrix through an iterative process. However, a base O-D matrix is usually not available. In such cases, these methods fail to generate reliable results. This study focuses on the estimation of transit OD matrix using boarding and alighting counts. We have evaluated four different methods namely IPF, Markov Model, Uncertainty Maximization and Compressed Sensing using true matrices obtained from the literature. We found that the IPF and Markov models generate almost the same results. Compressed sensing approach, on the other hand, forces the solution to be sparse. This approach is more suitable for trip-level OD estimation and may result in significant errors if used for daily ridership data. Furthermore, we introduced a new model for route-level transit OD estimation . Unlike compressed sensing, the proposed model employs ℓ∞ norm regularizer instead of Euclidean norm (ℓ2) and requires spot information about the critical cell in each direction. Python API of CVXPY was used to solve the formulated convex optimization problem. Our proposed model was found to outperform the existing methods when tested for RMSE value and trip length distribution. In the most favorable scenario, the RMSE value was found to be 18 compared to 145 and 95 for compressed and IPF, respectively. Lastly, we considered the case study of the Haridwar-Rishikesh metro corridor, which is at the planning phase yet. We obtained the boarding and alighting data for this line from ICRA Management Consulting Services Limited, which is hired by the Delhi Metro Rail Corporation Limited for this project. The OD matrices for both directions of the corridor were estimated and the results from different methods were analyzed for different OD flows. Overall, it can be seen from the results that the proposed approach can generate OD matrices of comparatively higher accuracy than all four methods. Our proposed methodology will enable transportation agencies to easily update old OD matrices or generate new ones with high computational efficiency and minimal requirements for prior information.