Simulation-Based Schedule Optimization for Virtual Coupling-Enabled Rail Transit Services with Multiagent Technique

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Introduction
It is recognized that railroads are cost efective, energy efcient, environmentally friendly, and safer.However, under the conventional railway system, dynamic and fexible scheduling is relatively difcult, especially for the large volume of passenger travel demand at peak hours in megacities.It is necessary to make up trains dynamically according to the diverse and uneven operation demand, e.g., increasing capacity supply at peak hours, decreasing capacity at nonpeak hours, matching passenger fow and train trafc more precisely, and implementing energyefcient train control, by using next generation signalling systems such as virtual coupling (abbreviated as VC).Te ever-increasing demand for railway services requires train-centric railway operations shifting from traditional railway signalling infrastructure, i.e., a paradigm towards such a train-to-train communication as the VC technique, and even new methods and advanced models to maintain stable and safe train trafc.Te performance and efectiveness of the railway system [1], e.g., infrastructure occupation, feasibility, stability, resilience, robustness, journey time efciency, and energy efciency, corelate highly to the quality of the train operation plan and schedule/timetable.
Te phenomenon that trains do not follow their initial schedule/timetable takes place frequently due to multiple reasons, which requires a more fexible or dynamic schedules for these train operations, so as to efciently and proactively manage such dynamics in the complex railway systems [2], to achieve a mobile and intelligent railway transport system, and to bridge between practice and research closer.For sound train operation, e.g., best running time, no conficts on the lines, free tracks in all the stations, avoidance of the phenomenon of passengers left behind, the schedule/timetable, or train operation plan is always positioned as the heart of the railway system to control/ optimize the rail operation and to create "high value slots" [3], which is surrounded by several other essential elements, e.g., service goals, network capacity, rolling stock, and infrastructure, in a coordinated and iterative point of view.
Dynamic and automatic timetabling/scheduling is the key part of the intelligent transport organisation, with regard to the determination of the train formation, departure/arrival time, and dwell time dynamically.By using certain commercial or academic railway computer programs/software, e.g., OpenTrack, RailSys, Planning Timetable Generator, DONS, Capacity Management Systems, and OpenTimeTable, it is not difcult to automatically generate and assess timetables rapidly [4].With regards to the key issues for establishment and success of the railway operation organisation, certain essential elements have to be addressed, e.g., trafc and slots organisation for scheduling, which can be realized by using the slot search engine embedded in RailSys [5].
In general, the main tasks of train scheduling can be categorized as real-time train operation planning, train operation controlling, of-line train timetabling, and train rescheduling [6].By using the VC-enabled technique, the main motivation of this study is to design the demandsensitive and fexible train operation plan or schedule to meet passenger demand, enhance passenger riding comfort degree, reduce passenger travel cost (e.g., waiting time and transfer time) and train operation cost, decrease infrastructure occupation (optimize interdeparture time or headway time), and improve capacity utilization, through reconciling fexibility with practical applicability, so as to improve the efciency and quality of train operation plan and schedule, as well as the self-adaptability of the railway capacity system.
Tere are two general philosophies of railroad operation: improvised (corresponding to real-time scheduling) and structured (corresponding to master scheduling).Te operating philosophy afects the use of simulation in determining the infrastructure that is appropriate for the desired trafc [7].In normal conditions, scheduling/timetabling is the procedure of allocating track capacity and time slots for operational train trafc.Te improvised operating philosophy is a kind of ad hoc planning (i.e., real-time rescheduling), which includes all changes, e.g., rerouting, retracing, retiming, and reordering, to the timetable that are taken after the disruptions happened in the rail system.In contrast, the structured operating philosophy is a kind of predefned and completed timetabling.In our study, the semistructured train operations' philosophy is adopted, which lies in between the improvised one and the structured one.It is also a part of automation of rail transport to increase the system robustness, demand adaptability [8], service quality, capacity fexibility, and operation reliability, and reduce the gap between daily operational trafc and timetable planning.
In order to improve the fexibility and capacity of European freight railways, Köni and Herbst [9] frst proposed the concept of VC train operation.Under the future railway background, Meo et al. [10] proposed the VC technique under ERTMS L3, so as to reduce the train interval and increase capacity by using train-to-train communication.Te VC technique is ascribed to the third generation of coupling technology [11], which is based on the ETCS-3 signalling system and an additional layer for V2V communication.VC can enable the train to couple/decouple at station or on-the-run in track section without stopping when necessary, i.e., virtual coupling is a train-centric signalling system, which can enable multiple trains to operate in a formation just like one train or decouple separately onthe-run in the track section (or at station) fexibly (or as planned).For platooning, trains can join in and split from a platoon as planned.Te railway trafc planning and management system will be afected by the introduction of VC.Te VC technique can realize a very high degree of fexibility and self-organisation, since it allows the train convoys to be coupled and decoupled anywhere and anytime, even on-the-run [12].
Besides the published article by Park et al. [13] provided a behavioral control mechanism, few studies have been taken into account for concrete operating strategies for VC, particularly, towards merge and separation, which is a kind of self-organising behavior of intelligent trains.Te VC technique enables a dynamic on-demand use of automatic train units without a fxed schedule or static timetable.It has been recognized that automated technologies, e.g., automated vehicles (AVs), are one of the largest innovations in transportation research.A large proportion of the signifcant costs in the rail system will be saved due to process automation in the area of planning and operations, which can keep the railways more competitive in the future.Te advantage of automation lies in its highly precision and efciency.With multitrain information synchronization, under the condition of train-to-train communication, VC-enabled trains autonomously recognize each other, i.e., including those ahead of and behind them [14].Multiple trains are formed to run in formation in the VC scheme.As one of the key railway system components, undoubtedly, the technique of railway trafc planning and management would be affected by the introduction of the VC technique [12].Te dynamics of the VC-enabled schedule mainly refects on decisions about the coupling/decoupling (i.e., variation of the number of train units in the virtually coupled train set) and interdeparture time/headway time, according to the near real-time passenger demand, which are the key motivations of this study.
Te aim of this study is to derive optimal dynamic schedule for VC-enabled rail transit services using the multiagent simulation technique on the NetLogo platform, i.e., to optimize interdeparture time or headway time, to improve the onboard passengers' riding comfort, and to minimize the passenger travel cost and the train operation cost.Terefore, the study gives the following contributions to the literature: (1) Representation of VC-enabled rail transit entity for agent-based simulation, including representation of VC-enabled train unit, representation of VC-enabled train convoy, representation of passenger attributes and behavior in VC-enabled environment, and development of the mathematical formula for calculation of the train operation cost and passenger travel cost, as well as passengers riding comfort degree (2) Defning operational principles for fexible and self-organisingVC-enabled trains (3) For the frst time, the VC-enabled train centric, passenger demand-driven, and agent-based simulation fow and algorithms are developed (4) Te proposed representation method, operational principles, simulation fow, and algorithms are applied on the computational experiments for optimal schedule simulation with NetLogo Te article outline is as follows.In Section 2, a literature review on VC-enabled train services is provided.Section 3 describes the problem of schedule optimization for VCenabled rail transit services considered in this study in detail.Te representation of VC-enabled rail transit entity for agent-based simulation is demonstrated in Section 4. Section 5 defnes operational principles for fexible and self-organisingVC-enabled trains.VC-enabled train-centric, passenger demand-driven, and agent-based simulation fow and algorithms are developed in Section 6. Section 7 demonstrates the application of the proposed representation method, operational principles, and simulation fow and algorithms on the computational experiments for optimal schedule simulation with NetLogo.Finally, the conclusions are provided in Section 8.

Literature Review
Integrated automatic and dynamic timetabling models can provide fast solutions which allow analyses of multiple operational scenarios.Cacchiani and Toth [15] reported an extensive review of timetabling models.Bešinović et al. [16] introduced deterministic microscopic models for computing accurate track blocking times that can support macroscopic models to build acceptable, feasible, and stable timetables.For completely automated generation of timetable, the microscopic models have been incorporated in a multilevel timetabling framework, i.e., efcient automatic conversion between microscopic and macroscopic networks.
For VC in railway operations, the constant distance gap policy is not applicable [12] due to the relative distance depending on speed, although for a given (cruising) speed, a constant time gap policy can provide a constant distance.Under VC, due to incorporation of relative braking distances between trains and therefore reduction of path conficts, certain changes have taken place when planning the railway trafc, comparing with the conventional railway trafc planning and management, especially for platoon's planning.So, there exists a necessary and practical requirement to develop dynamic schedule for virtual coupling.
Most of the existing literature about VC and automation focused on the optimal design of the train control system from the perspective of safety constraints for local and string stability [17] in infnite time or neglecting the temporal dimension, e.g., adaptive cruise control (ACC), cooperative adaptive cruise control (CACC) [18][19][20], leading-follower trains' gap control based on sliding mode control with a nonlinear and uncertain train model [13], model predictive control approach [21], Lagrangian control of trafc fow [22], the intra-platoon car-following gaps of VC-enabled trains and the inter-platoon car-following gaps of coupling trains, trajectory planning, and dynamic train following behavior and mechanism [23], under the connected and automated environment, considering the possibility of chain collisions or collision avoidance.Even most of their topics are control oriented rather than trafc fow theory or operation planning.And most of the VC cases description referred to only one leading train and one following train, despite the relative concepts and principles can be extendible to multiple trains.Few existing literature have been found about VC-enabled train operation planning or scheduling, e.g., the number of train units in one virtually coupled train formation [24,25] (in operational practice, the allowable maximum length of train is limited by the factors such as the signalling system, the length of platform, and the length of siding line), when to recouple or decouple the dynamic train headway.It is necessary to introduce or study the train operation plan, the scheduling and rescheduling mechanism for the VC-enabled multitrain communication-based control systems, order optimization of heterogeneous train units in the train convoy [26], possible VC of passenger trains with heterogeneous speed, and VC of mixed passenger and freight trains.
Under VC, the virtually coupled train set (VCTS) or train convoy based on vehicle-to-vehicle communication is viewed as one train by the interlocking systems [12]; trains are required to complete the coupling/decoupling process and reach a new state, e.g., coupled state, within a specifed distance or time [27], which implies that the entire coupling/ decoupling procedure for every train must be concerned particularly by the operational strategies, and the conventional static preprogrammed strategies or timetables may fail to meet these variant operating conditions.
Platoon is one of the cooperative VC modes and diferent from the train convoy or VCTS.To certain extent, VCTS has a similar platoon concept to the connected autonomous vehicle platoon, in that the desired distance between the trains in the platoon, e.g., maintaining the safe spacing and consistent running speed, is explored to ensure the stability and efciency of the train platoon [28].Compared with the fxed train formation, VCTS can meet the operational demands of a tidal passenger fow much better, under the limited track and train resource conditions, because the number of train units in one VCTS can be adjusted fexibly to match the variable-capacity supply with the passenger demand.For train trafc conficts of mainline railways forecasting and control in real time, Muniandi [26] proposed a novel blockchain-enabled VC of automatic train operation, e.g., architecture of the autonomous confict control system centering on blockchain infrastructure database and Journal of Advanced Transportation blockchain train database, and also described seven variants of VC strategies.
Besides the reduced service headway, VC railway signalling technology could potentially enable a service more in line with the passenger demand pattern, especially for the reason that trains move in a much more predictable environment than cars.Van Aken et al. [25] discussed how to determine the best number of trains to group together in case of temporarily unavailable tracks.VC-enabled train services [29], i.e., virtually coupled train sets/formations or train convoys, are with variable train length of several multiple units (MUs); particularly, they are worth applying to address massive demand in dense areas and making the railway market more attractive with provision of on-demand train services.Te number of vehicles of each MU can be fxed or variable.Aoun et al. [29] analysed three maneuvers for investigating the benefts of VC over conventional railway signalling systems according to nonstopping cases and stopping cases and considered 80 operational scenarios in total.Cao et al. [30] explained and simulated the operation mode of VCTS.In this study, we also use the multiagent simulation technique on the NetLogo platform.For more details about the multiagent technique, one can refer to the literature review section in [31].

Problem Statement
It is believed that when the cooperative movement of trains are optimized, the gap between these trains in diferent directions can be shortened to the minimum, along with the simultaneous increment of train trafc density and fow rate [32].Te problem of schedule optimization for VCenabled rail transit services considered in this study is as follows: (1) By considering the dynamic passenger demand and operation procedure of virtually coupled-enabled trains, taking fexible variable-capacity operation (provision) into account, the main objective of this study is to decrease infrastructure occupation (i.e., optimize interdeparture time or headway time) and enhance capacity utilization and target to maintain the train always running in the optimal state, improve the on-board passengers' riding comfort, and minimize the passenger travel cost and the train operation cost, so as to provide on-demand and fexible variable-capacity rail transit service by adopting near batch-matching policy.(2) Te key variables considered in this study include headway time and fexible variable-capacity of trains (i.e., variation of the number of train units in a virtually coupled train formation) (3) How the railway's capacity is used depends on the infrastructure layout and on the frequency and distribution of trafc.Given the dynamic short-term passenger demand, construct a feasible online or near real-time train scheduling with the guaranteed quality of service from both passenger and operation perspective, i.e., determine the frequency and distribution of train trafc under VC and the best number of trains to group together (adjust dynamically the number of train units in the virtually coupled train formation to match the passenger travel demand more accurately and fexibly) by connecting the timetables and operational trafc into one loop, by performing the near real-time trafc management of VC-enabledtraincentric railway operations, by merging timetable planning (dynamic preprogrammed train operation strategies), dispatching, and train operation [11], according to the new current trend [2].( 4) Te core problem is to determine dynamically the number of train units in a train convoy and the optimal train headway time, by considering the temporal-spatial correlation and cooperation between dynamic passenger travel demand and variable rail capacity supply.Tis is also a kind of near real-time dynamic scheduling, i.e., focus on shortterm and ad hoc passenger demand, combining train operation planning with scheduling/timetabling, merge timetable planning and trafc operating.
Service changes typically occur in stations.Take the passengers adapted travel behavior into account when scheduling/timetabling.And this consideration often results in a dynamically changed scheduling/timetabling, so as to meet the timedependent passenger demand better.( 5) Te simulation fow and algorithm adopt the ergodic strategy by traversing each O-D pair demand along each route on the rail transit network [33] with the multiagent technique on the NetLogo platform.
To develop the simulation fow and algorithms for schedule optimization for VC-enabled rail transit services with the multiagent technique, the following assumptions are made throughout this study.Assumption 1. Te passengers are frequent users.Te time slice-based transit demand OD matrix is generated in the many-origin-to-many-destination capacitated rail transit networks.Passengers are assumed to arrive at stations randomly according to a Poisson distribution.Te passenger OD demand matrix is assumed symmetric, and only the unidirectional track line (e.g., upstream or downstream) is considered in the network.Passengers can board and alight the trains at any junction or station.
Assumption 2. Te train can overtake any other trains at any station node and the vice versa.Any stations or junctions can be designated as skip-stop points.Junctions/stations have sufcient capacities to accommodate the inbound/outbound trains.Trains can couple/decouple at any station or on-the-run.Assumption 3. VC-enabled train units are homogeneous rather than with largely varying braking and acceleration capabilities.And each of them has the same volume of carrying capacity and number of seats.Trains can be located real-time and accurately on the network.Assumption 4. Te available feet size is sufcient.Te routes and frequencies of the train lines are predetermined and adjusted accordingly and iteratively.Te train running time on the rail track is deterministic.Te operation patterns of the trains adopt the same headway time in the same network [31], i.e., the headway times among all the trains within a certain study period in the same rail transit network keep invariant.
Te problem has some similarities with variable train formation of the operation planning problem [34,35], which, however, has two remarkable diferences with regard to our problem.First, unnecessarily originating from a depot, the follower trains can couple/combine with or split from its leader at any station, even on-the-run at track section, i.e., train compositions can be modifed anywhere if necessary, rather than only at certain stations.Second, it is rather than a pure train-unit assignment problem with a given train trip, and instead, it leads to a combination of train trafc organisation and timetabling.Compared with the fxed train formation, the virtually coupling train formation can meet the operational demands of a tidal passenger fow much better, in the form of variable-capacity provision, under the limited track and train resource conditions.

Representation of VC-Enabled Rail Transit Entity for Agent-Based Simulation
For the train trafc and passenger fow, diferent from those under conventional rail operation environment [36], i.e., the feature of them lies in between the weak-controllableautonomous trafc and strong-controllable-organised traffc, under the VC environment, both the automation and controllability of them have been improved greatly, and its self-organising feature is much stronger.
Besides the railway physical network (which is composed of links and nodes), the simulation entities of rail transit also include VC-enabled train unit, VC-enabled train convoy, and passengers.From the perspective of train operation and organisation, combined with GIS, GPS, and telecommunication technique, the operation process of the VC-enabled train convoy can be modularized and schematized.
In VCTS, the train units can recouple/decouple during operation according to transportation demands and plans [37]; thus, dynamic operation planning is necessary for train units coupling/decoupling under the VC system, and the number of train units in one virtually coupled train formation is variable.Te optimal number of train units in one virtually coupled train formation depends on the fexible match between the rail transit capacity and the passenger travel demand as accurate as possible.
According to Wu et al. and Li et al. [24,28], the desired distance (d desire ) between the trains in the platoon, i.e., the idea intradistance gap between trains, can be calculated as where k tc denotes the tracking time coefcient, v i denotes the following train speed in the platoon, and d 0 denotes the safe distance margin.

Representation of VC-Enabled Train Unit.
Under the condition of train-to-train communication, trains autonomously recognize each other, i.e., including those ahead of and behind them [14].Each autonomous train unit can be taken as an agent.By using the technique of the modern cyber network, automatic control, big data, train-train communication, artifcial intelligence, and sensor, the functions of the train unit agent include self-perception, self-recognition, self-adaptation, self-learning, selfdecision, and actively matching the passenger demand.
Te VC-enabled train unit agents have the options to move, couple, decouple, setback, split, platoon, combine, service, or wait, and each train unit agent acts individually.Cooperation mechanisms among agents should observe the operation rules of VC-enabled train units as well as the passenger travel demand pattern.According to the formal VC concept, the cross communication of intracoupled train units has to be negotiated locally, while the global behavior of the inter-coupled train formations has to follow the instruction authorized by the advanced automatic control system, e.g., ETCS.In this way, under the next generation signalling systems, i.e., VC, the intelligent train agents could negotiate and exchange individual scheduling decisions about position, velocity, accelerating, and braking to optimize global service levels and demand satisfaction and could impact the self-organising services on various performance indicators, e.g., fexibility, capacity, and resilience.Like in the conventional signalling system, the driving process of VC-enabled train unit still observe the principle of Davis equation.Not very likely in the conventional railway system, the train type in a station node can be classifed as originating, arriving, departing, passing by, destination, coupling, decoupling, and platooning.While, a train' routes can be characterized by the interdeparture time (headway time), arrival time, and by pass-through time at station nodes.A VC-enabled train unit on the railway transit route is represented by a 7-tuple topological component, namely, VC-enabled train unit � (time, position, train travel direction, activity, maximal carrying capacity, number of seats, and number of onboard passengers), where the item time includes two elements, i.e., time (arr/dep), where arr means the arrival time and dep means the departure time.Te item position includes two elements, i.e., position (h − i , h + i ), where h − i means the time gap with its preceding train and h + i means the time gap with its successive train.Te item activity includes six elements, i.e., depart, arrive, couple, decouple, dwell at station, and run in track section.
According to [31], the operation cost of each train agent l on route r can be calculated as follows: where N is the number of stations in the railway network, t lr i,i+1 means running time of train l on route r between station i and station i + 1, c + means the empty seat average cost per time unit, c − means the unserved passenger shortage cost per time unit, m r means the number of train unit in a virtually coupled train formation, decision variables, C max means the maximal carrying capacity of the train unit, and d lr i,i+1 means the passenger demand volume for train l on route r between station i and station i + 1.It can be obtained based on the passenger arrival rate of station i and the passenger assignment rate to other stations on the same route when simulation.
So, the total operation cost of train formation on route r can be calculated as follows: where ctsl is the operation cost of each train l on route r and ctsl � cts, l r is the number of train formation running on route r, and l r � T/h r , where T is the study period and h r is the interdeparture or headway time of trains on route r (decision variable).

Representation of VC-Enabled Train Convoy.
From the perspective of terminology, with regards to VCTS and train convoys, coupling and decoupling are used.For platooning, joining and splitting are used instead, i.e., platoon joining and splitting occur within a train convoy when applied to virtually coupled trains.VCTS is a kind of a connected and automated vehicle convoy, and the existing ATO (automatic train operation) algorithm based on single train behavior should be extended, so as to adapt to nature of the virtually coupled train convoy, i.e., the multitrain coordinated control with slim headway time.And it is a kind of self-organising rail trafc for evolution of decentralized mobility, and the VC-enabled train unit in the convoy can share position, velocity, and destination, with the convergence of speed and headway time.From the perspective of networked control, the train convoy can be described from following perspectives [38,39]: (i) Node dynamics (including tractive efort, braking force, and running resistance) (ii) Train convoy headway time for formation geometry (fxed headway time or nonlinear headway time relating to speed) (iii) Information fow topology of the train convoy (integration of information fow topology and distributed controller, describing the sender/receiver object of current train information) For communication topology of the train convoy, there are two typical solutions [12]: one is that the leading train is taken as the master and all other trains in the convoy communicate bidirectionally both with the master and their immediate predecessor.Te other one is that an intermediate train is taken as the role of the master, then the leading train has to provide ATP (automatic train protection) commands to the master for movement authorities with respect to train trafc outside the convoy.We prefer the former in this study.Te main function of the master train is to dictate the reference speed profle of the entire VCTS, e.g., determination of its own optimal train trajectory (relative dynamic distance, velocity, and acceleration), and then, the other trains in the convoy just follow their predecessor, leading to train-following behavior.In case of train platoons, possible topologies include fully connected mode and chain-like mode [40].Liu et al. [17] proposed the position, velocity, and operation status-space equation for the leading train and the following train under the virtually coupled condition.Te status of the VC-enabled train convoy can be described as follows: (i) Unstable state, which can be described with the mKdV equation (ii) Metastable state, which can be described with the Korteweg-de Vries (KdV) equation (iii) Stable state, which can be described with the Burgers' equation Whether the leading train coupled with the following trains depends on the following conditions: (i) Tere is larger volume of passengers waiting at the front station in the running direction of the leading train, and the passenger demand is greater than the available carrying capacity of the incoming leading train.(ii) Te running direction of the following train is similar to the leading train (iii) Te following train has enough available carrying capacity (iv) Coupling strategy of the VC-enabled train convoy [26]: dynamic priority and passenger driven (v) Te passingthrough capacity of the front station/ junction in the running direction of the incoming leading train is less than the sum of the following trains that need to pass by this bottleneck

Representation of Passenger Attributes and Behavior in
VC-Enabled Environment.In the rail transit physical network, the passenger fow type and its corresponding action sequence can be classifed as follows: (i) Departing passenger (action sequence: source, origin, ride, and destination) Journal of Advanced Transportation (ii) Passing through passenger(action sequence: ride, arrival, dwell, and departure) (iii) Arriving passenger (action sequence: ride and sink) Te travel cost of each passenger agent on route r can be calculated as follows: where cdlri means the onboard passenger riding comfort degree in track section i of route r on train l, t lr i,i+1 means the running time of train l on route r between station i and station i + 1, and N means the number of stations in the railway network.And in urban public transit, based on Assumption 4 (the operation patterns of the trains adopt the same headway time in the same network), similar to the majority of the previous studies, we approximate the mean waiting time of passengers at stops as half of the headway between the arrival of two successive trains on the same path [41,42].And the dwell time is designed as the headway time in the VCenabledself-organising railway system; thus, the travel cost of each passenger can be estimated as follows: where D i,i+1 is the total passenger travel demand between station i and i + 1, m rl i is the number of the train unit of train formation l on route r through station i, Z is the number of seat of each train unit, l ri is the number of trains' departure from station i on route r, and l ri � T/h r i , where T is the study period, h r i is the interdeparture or headway time of station i on route r, and h r i � h r , and C max is the maximal carrying capacity of the train unit.
Te average passenger-riding comfort degree of train l can be calculated as follows: where cdlravg means the average comfort degree of train l on route r and n means the number of track sections on route r.Te total passenger travel time in track section i of route r on train l can be computed as follows: i.e., ptcirl where pirl is the number of passengers in track section i of route r on onboard train l.
So, the total passenger travel cost on route r can be calculated as follows: Journal of Advanced Transportation ptcirl total �  n i�1 ptcirl. (9)

Defining Operational Principles for Flexible and Self-Organising Virtually Coupled Enabled Trains
Regarding the operational procedures, e.g., convoying on the run, platooning, cooperative merging, and cooperative departing, VC-enabled trains can provide fexible and selforganising intelligent railway operations.Quaglietta et al. [43] described the multistate fowchart of the train-following process in the rail track sections.According to the multistate train-following behavior, the complete process chain for VC-enabled train fow operation plan from coupling to decoupling can be summarized as follows: Merging into a convoy ⟶ coupling ⟶ maintaining the convoy ⟶ joining in a platoon ⟶ platooning ⟶ splitting from the platoon ⟶ maintaining the convoy ⟶ diverging from the convoy ⟶ decoupling.
According to the structure of the trafc fow under VC [12], in the VC environment (Figure 1) in junction areas for closer merging, assume train A (from direction 2) as the leading one and train B (from direction 1) as the following one in the later train convoys; the procedure for coupling train convoys on the run when passing through a junction (point area) can be summarized as follows: (i) Train A decelerates to point speed (ii) Switch the train unit to be coupled, i.e., train A and train B, from moving block to VC, after train A passing through the point (iii) Train B approaches train A, before train B passing through the junction.At this moment, the distance gap between train A and train B is greater than the safety distance.(iv) Train A accelerates while the distance gap between train A and train B is greater than safety distance (v) Train A and train B form a VC-enabled train convoy while their distance gap reaches the safety distance, and their velocities are equal when a platoon is formed.Platoon is one of the cooperative VC modes and diferent from the train convoy or VCTS.Also, a platoon is a set of trains that move cooperatively as close as possible to maximize track capacity by using cooperative adaptive control.
According to the structure of the trafc fow under VC [12], in the VC environment (Figure 2) in junction areas, the procedure for decoupling or diverging train convoys on the run when passing through a junction can be summarized as follows: (i) Train A (the leader, via direction 2 later) and train B (the follower, via direction 3 later) run in a VCenabled convoy from direction 1, while their distance gap equals the safety distance (ii) Train B slows down, and the distance gap between train A and train B become larger than safety distance (iii) Switch the train unit to be decoupled, i.e., train A and train B, from VC to moving block, after train A passing the point and running in direction 2 (iv) Train B approaches the point (v) Train B accelerates and passes through the point running in direction 3 Tese procedures can be extended in stations or hub areas, where the individual trains of a train convoy have to be decoupled/distributed to several station tracks and rejoined/ recoupled to a train convoy when leaving the station as necessary.For the frst time in the literature, Quaglietta [44] developed the operational principles and capacity occupation models under VC, which lay the foundation for planning techniques, e.g., timetable design, for train operations under VC, though they have not considered the passenger demand simultaneously.And they are defned in detail several cases of operational principles according to the velocity diference between the leader (V A ) and the follower (V B ), e.g., running/decoupling at points, diverging routes, and converging routes.In our study, we adopt these operational principles.

Journal of Advanced Transportation
Besides the layout of the track and/or junctions, the interactions among the trains running on the same track could determine the type of movement that the train will perform [29].Considering the train movement over an interlocking area or a track, the operational scenarios for VC-enabled train services include the trains running on a plain line (stopping cases or nonstopping cases), merging or diverging at a junction (stopping cases or nonstopping cases), which relate to trains following mutually in the same direction.For trains running under VC, Quaglietta [45] illustrated the state fow diagram of the VC-enabledtrainfollowing model, which identifed fve diferent operational states and corresponding transitions; moreover, they proposed a multistate train-following model for VC, aiming at the simulation of VC-enabled operations and assessment of capacity impacts.

Journal of Advanced Transportation
Similar to the conventional signalling environment, when scheduling, the potential conficts that need to be identifed [46] include conficts at track sections or routes, conficts at stops, connection/coupling conficts, and deadlock conficts.It is recommended to integrate timerelated dispatching (e.g., set recovery times to ensure the punctuality of trains) and location-related dispatching (e.g., designated reference points) methods together [46], i.e., temporal-spatial cooperation technique.In the physical rail transit network, the reference point can be a station route, a track or line section, and other infrastructure elements (e.g., point, track, and junction).Anyway, Robustness in Critical Points (RCP) should be put as the frst priority [47], so as to ensure the robustness of the whole VC-enabled rail trafc network.

VC-Enabled Train-Centric, Passenger Demand-Driven, and Agent-Based Simulation Flow and Algorithms
In order to develop simulation models to analyse dynamics and interactions of self-organising railway trafc under VCenabled systems, we connect the self-organisingdecisionmaking and passenger assignment methods together for VC-enabled intelligent rail trafc simulation.Te matching strategies for passengers-vehicles can be divided as instant matching and batch matching [48]; for the VC-enabled train service in this study, we adopt the near instant matching strategy, i.e., the additional and unnecessary waiting time can be neglected.Te simulation objective is to pursuit the optimal variation of the car unit number in train formation on route and headway time, to maximize passenger-riding comfort degree on route, and to minimize train operation cost as well as passenger travel cost.As mentioned before, the simulation fow adopts the ergodic strategy by traversing each O-D pair demand along each route section over the rail transit network.Te simulation fowchart for VC-enabled fexible train operation scheduling is illustrated as Figure 3.And the corresponding algorithms are shown as Algorithms 1 and 2.

Computational Experiments for Optimal Schedule Simulation with NetLogo
7.1.Experimental Design.Simulation of train operations under next generation signalling systems, such as virtual coupling, is pioneering in the public transport system it envisaged, and algorithms specifcation required making a series of assumptions about plausible characteristics of future VC-enabled rail transit systems as mentioned before.
NetLogo [49] can provide a programmable modelling environment and adapt to simulate the complex system that evolves with time, by which the modeler can instruct thousands of independent agents to run, so as to explore the diverse behaviors and interactions among the agents.Te  Journal of Advanced Transportation internal mechanism and principle of NetLogo are agent techniques, so NetLogo has the advantages in simulating multiagent systems.As this study is relatively pioneering in the public transport system it envisaged, our proposed ideas are tested on a mesoscopic hypothetical rail transit network built on the NetLogo platform (i.e., Y-type network of rail transit), which can lay the foundation for the applicability and generalizability of the study.Te transit network is assumed to be given as an 8-node rail network with 2-track lines, i.e., the trunk line (with the red color) and the branch line (with the blue color), as illustrated in Figure 4. Te link length of the network confguration is shown in Table 1.In the hypothetical Y-type network of rail transit, node 4 (with green color) is a pivotal station for two lines.And the capacity of each node is shown in Table 2. Te alighting proportion of each station node is set as a random number between 0 and 1.Consider one direction that trains run in the unidirection double track rail line, i.e., from upstream to downstream.For the train operation mode, trains can fully straight run through trunk-branch lines (Figure 5).In this mode, both the trunk route and the branch route originate from station node 1.On the trunk route, the train can run from station nodes 1 to 6 back and forth.While on the branch route, the train can also travel to and fro between station nodes 1 and 8, and in each single direction journey of the round-trip trajectory, it has to go through the intermediate pivotal station node 4. Tis kind of operation mode can reduce the transfer cost for passengers boarding and alighting trains on diferent lines.It is assumed that the trains can be overtaken and stop-skip for virtually coupling/ decoupling in all intermediate stations.Te alternative paths are given as follows: the trunk route is designated as route R1, i.e., route R1: 1-2-3-4-5-6; and the branch route is designated as route R2, i.e., route R2: 1-2-3-4-7-8.Te average train speed is set as 14.6 m/s.Te maximal carrying capacity of each train unit is set as 600 persons, and the number of its seat is set as 350.From the society-economy perspective, the empty seat average cost per time unit is estimated as 10 RMB, and the unserved passenger shortage cost per time unit 8 RMB.

Simulation Results
. By using the simulation platform NetLogo, the rail transit network (Figure 4) is setup as the simulation environment, and then, the passenger OD demand matrix is generated following the random Poisson arrival rates and demand distribution proportion.
According to simulation fowchart (Figure 3) and simulation fow Algorithms 1 and 2, after 500 ticks of simulation run within 15 min, the variation of VC-enabled car unit numbers in train formation on route R1 and R2 can be achieved, respectively (Figures 6 and 7), also the headway time for train formations operation in the Y-type rail transit network (Figure 8), the passenger riding comfort degree on routes R1 and R2, as well as the average comfort degree on both routes (Figure 9), the train operation cost (Figure 10), the passenger travel cost (Figure 11), and the passenger fow distribution profle on both routes (Figures 12 and 13).Correspondingly, in Figures 6 and 7, the meaning of the line legends in the fgure is explained in Tables 3 and 4.And in Figures 12 and 13, the meaning of the line legends in the fgure is explained in Tables 5 and 6.
Among these series of simulation results, the desirable average passenger-riding comfort degree on both routes of the Y-type rail transit network is achieved as 0.623627 (on route R1 0.57552 and on route R2 0.671733, respectively), at the total cost of 2968.695hours for passengers' travel on both      7.
7.3.Discussion.Usually, it is publicly recognized that the customers' preference should be the right paradigm in the market-oriented environment.From this point of view, given the stochastic passenger demand, the best number of train units can be obtained to group together and form train convoys fexibly on time by using the VC technique over 500 ticks of simulation runs (as illustrated in Figures 6 and 7), when the desired passenger-riding comfort degree is   14 Journal of Advanced Transportation achieved.Meanwhile, the headway time for train operation on the Y-type rail transit network is most adaptable, i.e., 300 seconds.On the other hand, when the minimum total passenger travel cost (2308.859hours) is taken into account, the corresponding desired headway time for the train formation is 194 seconds, and the average passenger-riding comfort degree is 0.36532.As far as the passenger travel time is concerned, due to the near instant matching strategy, passengers needless to transfer, so it can save the unnecessary transfer time.Also, it can ensure as less as possible the number of passengers left behind due to the variable-capacity supply.Meanwhile, in the VC-enabled service mode, train formations can be grouped together without stopping and run as a platoon or one train past/through certain bottleneck in the physical rail transit network, so as to reduce the number of train path.And furthermore, it can save the unnecessary additional waiting time or scheduling/rescheduling time before the bottleneck.
Tird, when the minimum total train operation cost (2926.208RMB) is concerned, the corresponding desired headway time for the train formation is 185 seconds, and the average passenger-riding comfort degree is 0.367213.What need to be stressed is that the train operation cost consists of two parts, i.e., the empty seat cost due to insufcient passenger demand and the unserved passenger shortage cost due to insufcient capacity supply.Moreover, the desirable average passenger-ridding comfort degree is not very high enough (only 0.623627 in most desirable scenarios).By combining these phenomena with the minimum total train operation cost (2926.208RMB) and its corresponding headway time (185 seconds), we can conclude that the total passenger demand is relatively large.
According to train-following behavior, there are two kinds of gaps of VC-enabled trains, i.e., the intra-platoon car-following gaps and the inter-platoon car-following gaps.In this study, we prefer the latter.In the current realization method for VC in this study, besides the actual passenger demand, the number of train units that can be virtually coupled depends on the initial number of trains operating on the route, which can be explained in an example as given Pseudocode 1. Due to the possibility of passengers left behind, this shortcoming in Algorithm 2   design is also a reason that decrease the passenger-riding comfort degree in general, which needs to be improved in the future study.

Platoon Operation
Oriented Future Study.Te leading or master train in the VC-enabled train convoy determines the reference speed profle or optimal train trajectory based on the timetable, guidelines, expertise, and ATO algorithms.Generation of train trajectory and tracking of multiple virtually connected trains in a convoy is a nontrivial issue [50].A platoon is a set of trains that move cooperatively as close as possible using cooperative adaptive control to maximize track capacity, which means that trains run synchronously with respect to operation control, and the platoon decision may afect the timetable and rolling stock allocation [12].Similarly, joining or splitting a platoon can occur at stations or on-the-run.
Platooning or platoon is recognized as a kind of ideal status, which all of the train operations should be oriented as possible as they can.In general, the normal relation between railway trafc control and train operation can be simplifed as shown in Figure 14 [51].In the future study, we could induce the optimal dynamic train operation plan by inversing this relation, i.e., starting from the known optimal railway trafc control status and taking platoon status as the reference scheme to seek the optimal timetable/schedule and train operation plan inversely (e.g., to determine the speed, time, and location where the virtual coupling/decoupling takes place) and shift from of-line planning to real-time trafc management solutions, which is shown in Figure 15.Tis is a kind of VC-enabled platoon-oriented train operation scheduling scheme.Meanwhile, it is necessary to set train operating rules for constraint generation, set the basic schedule structure (arrival time, departure time, through time, connection relationship, coupling, and decoupling),  6.

Line legends Explanation car126
Initial variation of car unit numbers in train formation in the track section between station node 1 and station node 2 on route R1 over 500 ticks of simulation runs car1261 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 1 and station node 2 on route R1 over 500 ticks of simulation runs car12623 Initial variation of car unit numbers in train formation in the track section between station node 2 and station node 3 on route R1 over 500 ticks of simulation runs car126231 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 2 and station node 3 on route R1 over 500 ticks of simulation runs car12634 Initial variation of car unit numbers in train formation in the track section between station node 3 and station node 4 on route R1 over 500 ticks of simulation runs car126341 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 3 and station node 4 on route R1 over 500 ticks of simulation runs car12645 Initial variation of car unit numbers in train formation in the track section between station node 4 and station node 5 on route R1 over 500 ticks of simulation runs car126451 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 4 and station node 5 on route R1 over 500 ticks of simulation runs car12656 Initial variation of car unit numbers in train formation in the track section between station node 5 and station node 6 on route R1 over 500 ticks of simulation runs car126561 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 5 and station node 6 on route R1 over 500 ticks of simulation runs 16 Journal of Advanced Transportation  7.

Line legends Explanation car128
Initial variation of car unit numbers in train formation in the track section between station node 1 and station node 2 on route R2 over 500 ticks of simulation runs car1281 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 1 and station node 2 on route R2 over 500 ticks of simulation runs car12823 Initial variation of car unit numbers in train formation in the track section between station node 2 and station node 3 on route R2 over 500 ticks of simulation runs car128231 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 2 and station node 3 on route R2 over 500 ticks of simulation runs car12834 Initial variation of car unit numbers in train formation in the track section between station node 3 and station node 4 on route R2 over 500 ticks of simulation runs car128341 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 3 and station node 4 on route R2 over 500 ticks of simulation runs car12847 Initial variation of car unit numbers in train formation in the track section between station node 4 and station node 7 on route R2 over 500 ticks of simulation runs car128471 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 4 and station node 7 on route R2 over 500 ticks of simulation runs car12878 Initial variation of car unit numbers in train formation in the track section between station node 7 and station node 8 on route R2 over 500 ticks of simulation runs car128781 Due to the possibility that the passenger demand maybe greater than the initial carrying capacity supply, by considering the virtually coupled situations, the partially updated variation of car unit numbers in train formation in the track section between station node 7 and station node 8 on route R2 over 500 ticks of simulation runs Journal of Advanced Transportation

Rail network traffic data
By observing closed-loop platoon dynamics [52] and relative braking distance [12], investigate the cooperative platoon operation as the reference scheme Regarding the cooperative platoon operation, decide the best trajectory and generate a series of target points, e.g., position, recommend speed Backstep to investigate the corresponding best schedule/timetable and train operation plan in traffic management Affect rail traffic network data Figure 15: VC-enabled platoon-oriented train operation scheduling scheme [52].
and fne-tune the related parameters for these rules when operating.

. Conclusions
Tis study investigated the simulation-based schedule optimization for VC-enabled rail transit services with the multiagent technique, by connecting the timetables and operational trafc into one loop, in line with the newly current trend.To a certain extent, such an equation can be held as timetabling + train operation planning � realtime dynamic scheduling.We use an agent to represent the VC-enabled rail transit entity, i.e., VC-enabled train unit, VC-enabled train convoy, and passengers.We defned operational principles for fexible and self-organisingVC-enabled trains.More importantly, we developed the VC-enabledtrain-centric, passenger demand-driven, and agent-based simulation fow and algorithms and then adopted the ergodic strategy for simulation by traversing each O-D pair demand along each route section over the rail transit network.We designed the computational experiment to test the proposed methodology on the NetLogo platform, and the simulation results series validated the efectiveness of the proposed methodology.Given the dynamic short-term passenger demand, using the proposed methodology, we can construct a feasible online or near real-timeVC-enabled train scheduling with the guaranteed quality of service from both passenger and operation perspective, i.e., optimize the interdeparture headway time, maximize the passenger-riding comfort degree, and minimize the passenger travel cost and train operation cost.On the other hand, the VC-enabled train services can provide variable capacity so as to meet the diverse passenger demand more accurately.For the attractiveness of rail transport, the train scheduling or operation plan represents the key elements.Trough shorter headway times and variable-capacity provision via the VC technique, railway infrastructure utilization and service level can be increased signifcantly.Passenger-riding comfort on board the vehicles is a constraint; it has to be guaranteed that none of the trains is ever overcrowded in the ideal status.Simulation results show that the desired headway time of the train trafc in the designed network can be achieved at 300 seconds, at the desirable average passenger-riding comfort degree point 0.623627, at the total cost of 2968.695hours passenger travel time, and 3070.717RMB for trains' operation costs.
Besides capacity, operational costs, running time, and waiting time, some additional objects could also be considered when deciding which trains should form VCenabled platoons [12], e.g., punctuality and energy efciency.More complete and enriched multiple-objective optimization for VC-enabled train services would be one of the themes for further study.Te simulation study lays the foundation for the further study incorporating the available real-time data into the simulation model in the future research, which just needs to replace the data in the experimental design sector with the data of the real case.
In terms of the estimated times for implementation of VC, according to scenario-based roadmaps for each market segment [12], e.g., high speed, mainline, regional, urban, and freight, both optimistic and pessimistic scenario supporting the urban market would be the frst one to fulfll the target of deploying VC, before the years 2035 (optimistic scenario) and 2045 (pessimistic scenario), respectively.For highly frequent train services or platoons, e.g., metro trains, the VC-enabled technique could be better of by using the dynamic operation strategy.Future research will focus on platoon operation oriented VC-enabled train service schedule as discussed in Section 7.4, so as to build a more robust and fexible schedule, with increased capacity, improved safety, better customer service, and more in line with the self-organising feature of the VC-enabled technique.

Figure 2 :
Figure 2: Decoupling train convoys on the run when passing through a junction (diverging).

1 2 3 Figure 1 :
Figure 1: Coupling train convoys on the run when passing through a junction (merging).

Figure 5 :
Figure 5: Trains fully straight run through trunk-branch lines back and forth.

Figure 6 :Figure 7 :
Figure 6: Variation of car unit numbers in VC-enabled train formation on route R1.

Figure 8 :
Figure 8: Headway time profle of VC-enabled train trafc in the Y-type rail transit network.

Figure 12 :
Figure 12: Passenger fow distribution profle on track section of route R1.

Figure 13 :
Figure 13: Passenger fow distribution profle on track section of route R2.

Figure 14 :
Figure 14: Conventional integrated relation between railway trafc control and train operations.
Input: time horizon T, x-coordinate and y-coordinate of nodes, node size, node label, alighting proportion of nodes, connected relationship among nodes, weight of links, number of OD passenger demand, arrival rate of node, and the matrix of OD demand distribution proportion Output: node set, mesoscopic network of rail transit, and OD demand matrix.Generation of simulation environment for the rail transit network.

Table 1 :
Link length of Y-type rail transit network confguration (unit: meter).

Table 2 :
Capacity of each node in the Y-type rail transit network.

Table 3 :
Explanation of line legends in Figure

Table 4 :
Explanation of line legends in Figure

Table 5 :
Explanation of line legends in Figure12.

Table 6 :
Explanation of line legends in Figure13.
Te volume of passenger demand between station O-D pair (4, 7) on route R2 Nump78 Te volume of passenger demand between station O-D pair (7, 8) on route R2

Table 7 :
Te details of the desired key simulation results.Initially set the number of trains (car_ini) operating on the route If initial carrying capacity (capa) < current passenger demand (nump) Compute the number of passengers left behind (numpleft): numpleft � capa − nump Compute the number of trains (ncar) needed to be virtually coupled: ncar � numpleft/capa if ncar < car_ini randomly choose the number of ncar train units to be virtually coupled elseTere would be still some passengers left behind Endif Endif PSEUDOCODE : Pseudocode for explanation of the possibility of passengers left behind.