An optimization model for line planning and timetabling in automated urban metro subway networks

In this paper we present a Mixed Integer Nonlinear Programming model that we developed as part of a pilot study requested by the R&D company Metrolab in order to design tools for finding solutions for line planning and timetable situations in automated urban metro subway networks. Our model incorporates important factors in public transportation systems from both, a cost-oriented and a passenger-oriented perspective, as time-dependent demands, interchange stations, short-turns and technical features of the trains in use. The incoming flows of passengers are modeled by means of piecewise linear demand functions which are parameterized in terms of arrival rates and bulk arrivals. Decisions about frequencies, train capacities, short-turning and timetables for a given planning horizon are jointly integrated to be optimized in our model. Finally, a novel Math-Heuristic approach is proposed to solve the problem. The results of extensive computational experiments are reported to show its applicability and effectiveness to handle real-world subway networksComment: 30 pages, 6 figures, 9 table

An approach to Handling Irregular Oversaturation in Urban Subway Stations

Train timetable, Passenger waiting time, Oversaturated condition, Genetic algorithmThis Theses presents a data-based approach for a train scheduling that aims to minimize passenger waiting time by controlling train departure time and the number of skipped trains. In contrast to existing approaches that rely on a statistical model of passenger arrival, we develop a model based on real-world automated fare collection (AFC) data from a metro line in Daegu, a Korean city. The model consists of decomposing the travel time for each passenger into waiting, riding, and walking times, clustering of passengers by trains they ride and calculating the number of passengers in each train for any given time. Based on this, for a given train schedule, the passenger waiting time of each passenger for the entire AFC data period can be calculated. The problem is formulated using the model under realistic constraints such as headway, the number of available trains, and train capacity. To find the optimal solution, we employed a genetic algorithm (GA). The results demonstrate that the average waiting time is reduced up to 56% in the highly congested situation. Moreover, letting the trains directly go to the congested station by skipping previous stations further reduces the maximum waiting time by up to 19%. The effect of the optimization varies depending on the passenger arrival pattern of highly congested stations. This approach will improve the quality of the subway services by reducing passenger waiting time.openⅠ. INTRODUCTION 1 II. RELATED WORK 4 2.1. Passenger Volume Estimation 4 2.2. Train Scheduling Optimization 5 III. PROPOSED APPROACH 6 3.1. Overview 6 3.2. Dataset 8 3.3. Scenario Analysis 9 3.3.1 Peak Hours Scenario 10 3.3.2 Congested Off-Peak Hours Scenario 10 IV. PROBLEM FORMULATION 13 4.1. Assumptions 13 4.2. Train Capacity 15 4.3. Passenger Volume Estimation 15 4.3.1. Passenger Volume on the Train 16 4.3.2. Passenger Volume on the Platform 20 4.4. Timetable Optimization Model 20 4.4.1. Train Departure Time Control 21 4.4.1.1. Passenger Waiting Time Minimization Problem 21 4.4.1.2. Oversaturation Time Minimization Problem 24 4.4.2. Train Skip Plan Control 24 4.5. Genetic Algorithm 27 V. EVALUATION 29 5.1. Peak Hours Scenario 30 5.2. Congested Off-peak Hours Scenario 32 5.2.1 Single Peak Oversaturation 32 5.2.2 Double Peak Oversaturation 36 5.2.3 Box-shaped Peak Oversaturation 40 5.3. Discussion 43 VI. CONCLUSION AND FUTURE WORK 44 REFERENCES 46 APPENDIX A. Optimization Results 48 요약문 81도시 지하철은 도로교통 상황의 영향을 크게 받지 않으며 대용량의 교통 수요를 처리할 수 있어 많은 승객들에게 이용된다. 혼잡한 지하철은 승객들에게 불편을 야기하며, 승객들의 승강장에서의 대기시간을 증가시킨다. 본 논문은 열차 출발 시간과 역들을 건너 뛴 열차 수를 조절하여 승객 대기 시간을 최소화하는 것을 목표로 한 열차 시간표 최적화 방안을 제시한다. 승객 도착 통계 모델에 의존하는 기존의 접근 방식과 달리, 이 연구는 대구의 지하철에서 수집된 교통카드 데이터들을 기반으로 하는 최적화 모델을 만든다. 모델은 각 승객의 여행 시간을 차량 대기 시간, 차량 탑승 시간 및 보행 시간으로 구분하고, 탑승한 기차에 따라 승객들을 군집화 시킨 후 각 차량마다 승객 수를 추정하는 것으로 구성된다. 이를 바탕으로 주어진 열차 스케줄에 대해 모든 승객 각각의 대기 시간들을 계산할 수 있다. 최적화 문제는 이용 가능한 열차 수, 열차가 수용 가능한 최대 승객 수, 폐색구간과 같은 현실적인 제약 조건 하에서 구성된다. 최적의 시간표를 찾기 위한 방법으로 유전자 알고리즘이 사용되었다. 그 결과 승객 평균 대기 시간은 최대 56%까지 단축되었으며, 열차 출발시간 뿐만 아니라 일부 역을 건너뛰는 열차의 수까지 최적화하면 매우 혼잡한 상황에서 승객의 차량 대기 시간을 더욱 줄일 수 있었다. 혼잡한 상황에서 기차가 일부 역을 건너뛰었을 때, 그렇지 않을 때보다 승객 최대 대기 시간은 19%, 승객 평균 대기 시간은 15% 정도 더욱 단축되었다. 또한 혼잡한 상황에서 승객 도착 패턴에 따라 최적화의 효율이 달라진다는 것을 확인하였다. 본 방안은 승객 평균 대기시간을 감소시킴으로써 지하철 서비스를 향상시킬 것이다.MasterdCollectio

Feasibility evaluation and critical factor analysis for subway scheduling

In strategic subway scheduling stage, the conflict sometimes comes from different requirements of the subway operator. This study aims to investigate the significant factors concerning strategic subway scheduling problem and to develop an automatic procedure of feasibility analysis in subway scheduling. To this end, accurate simulation of train movement (via a simulator, named HAMLET) is applied first by considering the line geography, train performances, actual speed restrictions, etc. The critical elements of subway scheduling and their correlations are then studied and a bound structure of the critical factors is established. The feasibility of primary plan requirements is analysed with the restrictions of the bound structure. Infeasible aspects and possible adjustments are shortly discussed. Finally, the subsequent applications including schedule generation and optimization according to various objectives are indicated as well

Optimization Methods in Modern Transportation Systems

One of the greatest challenges in the public transportation network is the optimization of the passengers waiting time, where it is necessary to find a compromise between the satisfaction of the passengers and the requirements of the transport companies. This paper presents a detailed review of the available literature dealing with the problem of passenger transport in order to optimize the passenger waiting time at the station and to meet the requirements of companies (maximize profits or minimize cost). After a detailed discussion, the paper clarifies the most important objectives in solving a timetabling problem: the requirements and satisfaction of passengers, passenger waiting time and capacity of vehicles. At the end, the appropriate algorithms for solving the set of optimization models are presented