Journal of Advanced Transportation

Volume 2019, Article ID 5174961, 11 pages

https://doi.org/10.1155/2019/5174961

## A Real-Time Timetable Rescheduling Method for Metro System Energy Optimization under Dwell-Time Disturbances

Correspondence should be addressed to Feng Zhang; nc.ude.utjs@gnahzf

Received 15 April 2019; Accepted 17 August 2019; Published 2 December 2019

Academic Editor: Rakesh Mishra

Copyright © 2019 Guang Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Automatic Train Systems (ATSs) have attracted much attention in recent years. A reliable ATS can reschedule timetables adaptively and rapidly whenever a possible disturbance breaks the original timetable. Most research focuses the timetable rescheduling problem on minimizing the overall delay for trains or passengers. Few have been focusing on how to minimize the energy consumption when disturbances happen. In this paper, a real-time timetable rescheduling method (RTTRM) for energy optimization of metro systems has been proposed. The proposed method takes little time to recalculate a new schedule and gives proper solutions for all trains in the network immediately after a random disturbance happens, which avoids possible chain reactions that would attenuate the reuse of regenerative energy. The real-time feature and self-adaptability of the method are attributed to the combinational use of Genetic Algorithm (GA) and Deep Neural Network (DNN). The decision system for proposing solutions, which contains multiple DNN cells with same structures, is trained by GA results. RTTRM is upon the foundation of three models for metro networks: a control model, a timetable model and an energy model. Several numerical examples tested on Shanghai Metro Line 1 (SML1) validate the energy saving effects and real-time features of the proposed method.

#### 1. Introduction

With rapid development of intelligent transportation, Automatic Train Systems (ATSs) have attracted much attention in recent years. A reliable high-level ATS ensures the entire railway network to function safely, cost-effectively and efficiently under sudden disturbances [1]. Disturbances in metro networks such as temporary platform blockages make offline schedules suboptimal for use. Hence, various methods of Train Timetable Rescheduling (TTR) [2–6] have been proposed to handle unforeseen events which may disturb timetable. Prevailing methods for timetable rescheduling can be classified into two categories: passenger-oriented and train-oriented. The passenger-oriented research focuses on minimizing the total delay time of passengers [4], while the train-oriented research focuses on minimizing the overall delays of all trains [7, 8]. However, short delays in one train may not necessarily arouse block conflicts of the route ahead, still, it will inevitably affect the energy consumption of the overall metro network. Since a metro network consumes a large amount of electric energy every day, there is tremendous potential of energy conservation in metro transportations. So far, there is little research that mentions the topic on how to save energy when a metro network encounters disturbances.

Different from the traditional TTR problem, the energy-efficient TTR problem consists of two steps. The first step is to build an offline timetable for optimal use of the total energy of the metro network, which is called Energy-Efficient Train Timetabling (EETT) [9]. In this step, all trains in the network run with confirmed dwell time and no emergencies happen [8]. The second step is to build a real-time timetable to cope with sudden disturbances. In this step, proper travel time in different sections and different trains will be determined and modified in real time to minimize the system energy consumption after disturbances happen.

Energy-efficient TTR problem is a challenging task because of its real-time demand and randomness of disturbances. Any disturbance in a metro network can bring a series of chain reactions that make the offline schedule not optimal any more. Rescheduling timetable is a good solution to avoid the chain reactions and save more energy. EETT methods that are nonreal-time methods cannot be used in the energy-efficient TTR problem. Moreover, disturbances occur randomly at different stations on different trains, and the length of delay is also stochastic. It requires the method having a self-adaptability that makes the appropriate choice presciently according to the disturbances.

Energy-efficient TTR problem has been rarely mentioned in recent years. Gong et al. [10] proposed an integrated Energy-efficient Operation Methodology (EOM) to compensate dwell time disturbances in real-time. By reducing the travel time of the delaying train in the section following a disturbance, the schedule can be recovered to the original one which is optimized by GA. The cost of EOM is that more energy will be consumed before the recovery of the schedule.

In this paper, a real-time timetable rescheduling method (RTTRM) for energy optimization is proposed. Different from EOM, this method reschedules all trains in the network after a disturbance happens, rather than reschedules the delaying train only. The proposed method can finish making decisions immediately after a disturbance happens, attributed to the combinational usage of GA and DNN. Firstly, GA provides a series of corresponding energy-optimal timetables for random disturbances. Then, a decision system based on DNN learns from the connection between the random disturbances and the optimal timetable which are deduced by GA. Finally, the well trained decision system provides proper solutions in different cases of disturbances in real-time.

The remainder of the paper is organized as follows. Section 2 reviews the previous contributions related to TTR and EETT problem. Section 3 presents the description of a control model, a timetable model and an energy model in metro system. Section 4 introduces GA and a decision system to solve the energy-efficient TTR with dwell-time disturbances. In section 5, several experiments based on a real-world network of Shanghai Metro Line 1 (SML1) is presented to validate the proposed method. The final section concludes the paper.

#### 2. Literature Review

Pioneering theoretical works related to TTR problem were first carried out by Carey’s group [11–13]. They eliminated the distribution and propagation of the train delay by using the sequential solution procedures. Törnquist and Persson [14] presented a Mixed Integer Programming (MIP) model that took into account the reordering and rerouting of trains. D’Ariano et al. [15] computed a conflict-free train timetable compatible with the actual status of the railway network and proposed a branch-and-bound algorithm for minimizing the global secondary delay. Khan and Zhou [16] developed a stochastic optimization formulation with the purpose of minimizing the total trip time in a published timetable and reducing the expected schedule delay. Cacchiani and Toth [17] classified approaches of timetable rescheduling into six categories: stochastic optimization [18], light robustness [19], recovery robustness [20], delay management [21], bicriteria and Lagrangian-based approaches [22] and meta-heuristics [23]. Dündar and Sahin [24] developed a Genetic Algorithm (GA) to reschedule the trains on a single track railway line in Turkey and determined the meets and passes of the trains in the opposite direction. They designed benchmarking experiments among an Artificial Neural Network (ANN), a MIP model and two kinds of GA. They also validated that GA outperforms the other methods. Šemrov et al. [25] used a rescheduling method based on reinforcement learning, more specifically Q-learning, on a real-world railway network in Slovenia. They illustrated that Q-learning leaded to rescheduling solutions that were at least equivalent and often superior to the simple First-In-First-Out (FIFO) method and the random walk method. Xu et al. [7] proposed a Mixed-Integer Linear Program (MILP) model for the quasi-moving block signaling system to reduce the final delay and to solve a real-world instance in China. They optimized traffic in transition from a disordered condition to a normal condition and analyzed delays in different transition phases. Ortega et al. [4] proposed a biobjective optimization method for timetable rescheduling during the end-of-service period of a subway, in order to minimize the total transfer waiting time for all transfer passengers and the deviation from the scheduled timetable.

Albrecht and Oettich [26] first discussed EETT problem. They used a Dynamic Programming (DP) to calculate the optimal timetable. The quality criteria of the multiobjective optimization function were the overall waiting time and the energy consumption. Albrecht [27] considered to change the additional running time to the synchronize acceleration and the regenerative braking in order to minimize total energy consumption and power peaks. It was the first to study EETT with the regenerative braking. Yang et al. [28] first described EETT problem in a mathematical programming mode and solved this problem by maximizing time overlaps of nearby accelerating and braking trains. Sun et al. [29] developed a bi-objective timetable optimization model to minimize the total passenger waiting time and energy consumption.

#### 3. Formulation of Model for Metro Network

In this section, three models are formulated: a control model, a timetable model, and an energy model, all of which are used to describe the operation process for a metro network. For the single-train control model, state variables of trains, such as the position and the speed, are formulated. For the timetable model, the departure time and the arrival time for each single train are calculated. For the energy model, energy exchange among trains running in the same network is formulated.

##### 3.1. Parameter and Variable

The notation system which includes parameters and variables, is presented as follows:

: conversion efficiency of the train traction system (from electricity to mechanical energy). : conversion efficiency of the train braking system (from mechanical energy to electrical energy). : feedback coefficient on braking energy. : total number of trains in the metro network. : total number of stations. : index for train, . : index for station, . : dwell time of train at station . : departure instants of train at station . : headway of train . : interstation running time of train running from station to station . : total travel time. , constant traction force in the constant force accelerating phase. : constant braking force in the constant force braking phase. : speed in switching point (from the constant force accelerating phase to the constant power accelerating phase). : speed in switching point (from the constant power braking phase to the constant force braking phase). : cruising speed of train running from station to station . : the maximum speed limit between stations. : the pull-in speed limit and the pull-out speed limit. : spacing of the section . : current position of train . : current time of train . : current driving speed of train . : traction or braking force per unit mass of train . : resistance per unit mass. : gravity per unit mass.##### 3.2. Assumptions

(i) The network in the model has narrow spacing (for example Shanghai Metro Line 1). Trains drive in each section in a sequence of accelerating-cruising-braking, without the repeated accelerating and braking.(ii) The adjacent trains run with enough spacing, so we do not consider the blocking conflict during operation.(iii)The disturbances are small enough which will not lead to network disruption.(iv) Only one disturbance happens during a complete test procedure from the first train’s departure to the last train’s arrival.(v)The disturbances will not happen at the starting station.##### 3.3. Control Model for a Single Train

When driving a train from to , according to Newton’s Second Law, the motion equations are

where for and . In Equation (2), meets Davis’s Equation [30]

where , and are constant parameters. represents the gravity per unit mass, which is a piecewise linear function. represents the force per unit mass or acceleration. We assume that is positive in the acceleration phase and negative in the braking phase. Figure 1 shows the bound curves of , where is the lower bound and is the upper bound.