Passenger Behavior Simulation in Congested Urban Rail Transit System: A Capacity-Limited Optimal Strategy Model for Passenger Assignment

Optimal strategy, one of the main transit assignment models, can better demonstrate the flexibility for passengers using routes in a transit network. According to the basic optimal strategy model, passengers can board trains based on their frequency without any capacity limitation. In the metropolitan cities such as Beijing, Shanghai, and Hong Kong, morning commuters face huge transit problems. Especially for the metro system, there is heavy rush in metro stations. Owing to the limited train capacity, some passengers cannot board the first coming train and need to wait for the next one. To better demonstrate the behavior of passengers pertaining to the limited train capacity, we consider capacity constraints for the basic optimal strategy model to represent the real situation. We have proposed a simulation-based algorithm to solve the model and apply it to the Beijing Subway to demonstrate the feasibility of the model. The application of the proposed approach has been demonstrated using the computational results for transit networks originating from practice.

Designing Zonal-Based Flexible Bus Services Under Stochastic Demand

In this paper, we develop a zonal-based flexible bus services (ZBFBS) by considering both passenger demands’ spatial (origin-destination or OD) and volume stochastic variations. Service requests are grouped by zonal OD pairs and number of passengers per request, and aggregated into demand categories which follow certain probability distributions. A two-stage stochastic program is formulated to minimize the expected operating cost of ZBFBS, in which the zonal visit sequences of vehicles are determined in stage 1, whereas in stage 2, service requests are assigned to either regular routes determined in stage 1 or ad hoc services that incur additional costs. Demand volume reliability and detour time reliability are introduced to ensure quality of the services and separate the problem into two phases for efficient solutions. In phase 1, given the reliability requirements, we minimize the cost of operating the regular services. In phase 2, we optimize the passenger assignment to vehicles to minimize the expected ad hoc service cost. The reliabilities are then optimized by a gradient-based approach to minimize the sum of the regular service operating cost and expected ad hoc service cost. We conduct numerical studies on vehicle capacity, detour time limit and demand volume to demonstrate the potential of ZBFBS, and apply the model to Chengdu, China, based on real data to illustrate its applicability.

Morning Peak-Period Pricing Surcharge of Elderly Passengers Taking Express Buses

This study deals with the elderly fare pricing issue for taking express buses in the morning peak period. As many elderly passengers are not commuters, fare discount policy may not be an opportune option when buses get overcrowded. Imposing surcharge on the elderly becomes a potentially beneficial measure that encourages an appropriate number of elderly passengers to circumvent the most crowded buses. The elderly pricing surcharge problem is formulated as a bilevel model, in which the upper-level model is to make the pricing surcharge decision, and the lower-level model is the equilibrium passenger assignment that represents passengers’ bus choice behavior. It is classified into the special case and the generic case depending on the number of buses that impose surcharge. Several useful properties of two cases are analyzed, and a trial-and-error solution method is later developed to solve these two cases. Numerical experiments show that the elderly pricing surcharge scheme is not always applicable to all the demand scenarios, which owns a certain effective interval.

A Benders Decomposition Algorithm for the Passenger Train Service Planning

Railway transport becomes a more popular transportation in many countries due to its large transport capacity, low energy consumption, and benign environment. The passenger train service planning is the key of the rail operations system to balance the transport service and the passenger demand. In this paper, we propose a mixed binary linear programming formulation for the passenger train service planning to optimize the train route, frequency, stop schedule, and passenger assignment simultaneously. In addition, we analyze the computational complexities of the model and develop a Benders decomposition algorithm with valid inequalities to solve this problem. Finally, our model and algorithm are tested on a real-world instance of the Beijing-Shanghai high-speed railway line. The computational results show that our approach can solve these problems within reasonable solution time and small optimality gaps (less than 2.5%).

The Depth-First Optimal Strategy Path Generation Algorithm for Passengers in a Metro Network

Passenger behavior analysis is a key issue in passenger assignment research, in which the path choice is a fundamental component. A highly complex transit network offers multiple paths for each origin–destination (OD) pair and thus resulting in more flexible choices for each passenger. To reflect a passenger’s flexible choice for the transit network, the optimal strategy was proposed by other researchers to determine passenger choice behavior. However, only strategy links have been searched in the optimal strategy algorithm and these links cannot complete the whole path. To determine the paths for each OD pair, this study proposes the depth-first path generation algorithm, in which a strategy node concept is newly defined. The proposed algorithm was applied to the Beijing metro network. The results show that, in comparison to the shortest path and the K-shortest path analysis, the proposed depth-first optimal strategy path generation algorithm better represents the passenger behavior more reliably and flexibly.

A Matheuristic Iterative Approach for Profit-Oriented Line Planning Applied to the Chinese High-Speed Railway Network

In this paper, a matheuristic iterative approach (MHIA) is proposed to solve the line planning problem, also called network design problem, and frequency setting on the Chinese high-speed railway network. Our optimization model integrates the cost-oriented and passenger-oriented objectives into a profit-oriented objective. Therefore, the passenger travel time is incorporated in the ticket price using a travel time value. As a result, transfers and detours will result in lower ticket prices and thus lower revenues for the operator. When evaluating the performance of a given line plan, the way in which passengers will travel through the network needs to be modelled. This passenger assignment is typically a time-consuming calculation. The proposed line planning approach iteratively improves the line plan using easy-to-determine indicators. During the process, a mixed integer linear programming model addresses the passenger assignment and optimizes the frequency setting in order to maximise the operational profit. Extensive computational experiments are executed to show the effectiveness of the proposed approach to deal with the real-world railway network line planning problem. Through extensive computational experiments on the small example network and real-world-based instances, the results show that the proposed model can improve the profits by 22.4% on average comparing to their initial solutions. When comparing to an alternative iterative approach, our proposed method has advantage of obtaining high quality of solutions by improving the profit 10.8% on average. For small, medium, and large size networks, the obtained results are close to the optimal solutions, when available.