12th International Conference on MOdeling, Optimization and SIMulation - MOSIM18 - June 27-29 2018Toulouse - France “The rise of connected systems in industry and services”

SIMULATION OF COMMUNICATION BASED TRAIN

CONTROL FOR ROBUSTNESS ASSESSMENT OF A MIXED

TRAFFIC MANAGEMENT SYSTEM

S. CORNET, P. BOUVAREL C. BUISSON

SNCF Reseau IFSTTAR - LICIT

34 rue du Commandant Mouchotte Rue Maurice Audin

75014 Paris - France 69518 Vaulx en Velin - France

selim.cornet2@reseau.sncf.fr, paul.bouvarel@reseau.sncf.fr christine.buisson@entpe.fr

F. RAMOND J. RODRIGUEZ

SNCF Innovation & Recherche IFSTTAR - ESTAS

40 avenue des Terroirs de France 20 rue Elisee Reclus

75012 Paris - France 59666 Villeneuve d’Ascq - France

francois.ramond@sncf.fr joaquin.rodriguez@ifsttar.fr

ABSTRACT: In order to achieve higher capacity on existing infrastructures with dense traffic, railwaycompanies are deploying Communication Based Train Control (CBTC) systems. These systems wouldconsiderably facilitate the implementation of new ways for managing traffic, such as headway-based control.However, for commercial reasons, traffic management systems using the timetable adherence principle have tobe maintained on low traffic areas; both traffic management systems should hence have to coexist on some lines.The aim of this paper is to present a simulation method for assessing the robustness of operations on such aline, located both in low and dense traffic area. More precisely, the capability of a headway-based control systemto resist to disturbances occurring out of its control perimeter is evaluated. The simulation tool reproduces traintraffic evolution, disturbances and dispatching decisions, allowing to estimate the quality of service for variousdisturbance scenarios. Numerical experiments are carried out on one of the most saturated lines in the Parissuburban area. The obtained results prove the practical feasibility of such a mixed traffic management up to acritical level of disturbances.

KEYWORDS: Communication-Based Train Control, headway-based control, railway operations, real-time traffic management

1 INTRODUCTION

1.1 Railway operations in dense urban areas

Most railway companies operating services in denselypopulated areas have been experiencing an increaseof demand for passenger transportation during lastyears. As a result, railway networks reach satura-tion, making it difficult to answer the demand. Inaddition, as the number of trains grows, operationsbecome more sensitive to disturbances, leading to apoor quality of service for passengers. The so-calledthree-aspects signaling system, used in many coun-tries for ensuring the operations safety, plays a partic-ular role in disturbances propagation in the network.This system allows to maintain a sufficient headway

between two consecutive trains. It works the follow-ing way. The track is divided into blocks, each ofthem protected by a signal. A green signal indicatesto the train driver that the next two blocks are free,and that he can proceed at the same speed. A yel-low signal means that the next block is free but thefollowing one is not, and the driver must thereforeprepare to stop before the limit of the current block.Finally, a red signal imposes the driver to stop as thenext block is occupied.

Figure 1 shows how this system may lead a delay topropagate as knock-on delays along a line. If a traindwells in a station for a longer time than the nominalone (due e.g. to a jammed door), the following trainsare likely to catch up and meet a yellow signal. This

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will force them to slow down and result in even higherdelays for these trains.

Figure 1 – Propagation of delays by a fixed signalingsystem

When designing timetables, railway companies usu-ally insert buffers between consecutive trains to pre-vent the propagation of delays. But this comes ata price, as it has the effect of reducing the capacityof an already saturated network while not guarantee-ing against delay propagation. Operating companiesseek therefore to improve the system capacity andreliability without resorting to heavy and costly in-frastructure modifications.

1.2 Communication-Based Train Control

Communication-Based Train Control (CBTC) sys-tems are intelligent signaling and vehicle control sys-tems that help to reduce the effect of the phenom-ena described in the previous section (IEEE Stan-dard 1474.1 (2004)). These kind of systems have beenwidely implemented on metro lines (such as line 14 inParis or line L in New York). Vehicles equipped withCBTC are precisely located on the network thanksto telecommunication systems, independently of thetrack detection devices. CBTC also integrates an Au-tomated Train Operation (ATO) system, that con-trols speed and acceleration of the train during itsdriving phases, and an Automated Train Supervi-sion (ATS) system that performs automatic trafficmanagement decisions. As a result, trains are ableto automatically adapt their speed depending on theposition on the preceding train. Train protection ishence ensured by a moving block signaling system.That allows much shorter headways than the fixedthree-aspects signaling system, and reduces the phe-nomenon of delay propagation described in the pre-vious subsection, resulting in higher capacity.

1.3 Headway-based traffic control

Most railway companies operate trains according toa timetable, even in dense and highly circulated ar-eas. When a disturbance occurs that results in delays,train drivers and traffic managers are required to be-

have in such a way that the trains arrival and depar-tures occur as close as possible to their planned times.However, this is not always the most efficient way tooperate commuter trains. Indeed, surveys show thatwhen the train frequency gets sufficiently high, pas-sengers do not pay attention to schedule and presentthemselves at the station with the purpose of board-ing the first train available (Luethi et al. (2007)). Inaddition, this operation mode does not guarantee agood quality of service to passengers. This is partic-ularly true at points where a good synchronization isrequired, such as junctions.

Figure 2 – A junction

Train 1 Train 2Station A 8:00Station A’ | 8:05Station B 8:05 8:10

Table 1 – Drawbacks of schedule-based traffic control

Consider two trains running on the network describedin Figure 2 according to the schedule given by Table1. Suppose that train 1 suffers a 5-minute delay andthat train 2 is on schedule. Then a conflict for infras-tructure utilization will occur at the junction, and oneof the trains will have to stop on the track, causinginconvenience to passengers and increasing delays. Itmight be better to allow train 2 to depart ahead ofschedule if possible, or to hold it at Station A’ for atime long enough to prevent the conflict.

In addition, Van Breusegem et al. (1991) proved thatuneven time intervals between train can damage thestability of operations if no dispatching decision ismade. Indeed, a train arriving at a station a longtime after the previous train will have to dwell alonger time, as more passengers will wish to board.The headway between trains will consequently grow,leading to an even higher dwell time at the next sta-tion and a higher delay, while the following train islikely to catch up with the delayed one. This phe-nomenon is well-known of bus passengers and oper-ators, where it is called “bus bunching” (Newell etal. (1964)). Finally, we can note that reducing theheadways variance leads to a smaller expected waitingtime for passengers (Ding et al. (2001)).

For those reasons, many bus and light rail opera-tors have given up schedule-based control to preferheadway-based traffic management. In this frame-work, vehicles do not have a pre-planned schedule,but are monitored in real-time in order to maintaineven headways between them. Up to our knowledge,

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this concept has been little applied to railway servicesso far ; the implementation of such a framework wouldbe considerably facilitated by the CBTC systems.However, it does not seem feasible to equip a wholesuburban line, due to the high cost of CBTC systems.Nor is it practicable to operate a line with brancheswith headway-based control in totality. Indeed, thecapacity limitations of the common section would re-sult in lower frequencies on the branches, where aschedule is needed for commercial reasons. As a re-sult, the option of operating a line with headway-based control coupled with a CBTC system on thedense common section, and schedule-based controlwith manual driving on the other parts of the line,is considered.

The aim of this paper is to assess the robustness ofsuch a traffic management scheme. For that purpose,we present a simulation method for reproducing rail-way traffic under headway-based traffic managementperformed by a CBTC system. We specifically studythe robustness of such an operations system, i.e. itscapability to resist to small disturbances occurringoutside the control area. The remainder of this pa-per is organized as follows. In section 2, we brieflyreview some related work. Section 3 is dedicated tothe description of the modeling framework and thesimulation method we developed. Numerical experi-ments are presented in section 4, where we apply themethod to a saturated line of Paris suburban network.Section 5 concludes the paper.

2 RELATED WORK

The real time railway traffic management problemhas been widely studied and many approaches havebeen proposed for solving it ; a review of these meth-ods is presented in Cacchiani et al. (2014). Amongthem, some consist in recovery algorithms after mi-nor disturbances. In that case, only reschedulingdecisions (such as re-timing arrival and departuresevents, re-ordering trains at junctions) need to betaken. Other consider the case of recovering a fea-sible schedule after a major disruption, for which therolling stock and crew have to be rescheduled as well,but this falls out of the scope of our study. Most of thedesigned algorithms rely on a mathematical program-ming formulation of the problem with a no-wait jobshop scheduling problem as studied by Mascis et al.(2002). D’Ariano et al. (2007) propose a branch-and-bound algorithm for computing a conflict-free sched-ule in real time after a perturbation. Pellegrini etal. (2015) consider the case where decisions can betaken in a fixed control area and describe a method forreacting to disturbances occurring outside this area.However, most of the works address the case wheretrain protection is ensured by a fixed block signalingsystem and trains are operated according to a sched-

ule. D’Ariano et al. (2008) investigate the concept offlexible timetables to improve real-time traffic man-agement, making thus a first step towards headway-based control in railway systems.

Headway-based traffic management, using in partic-ular holding strategies, have been studied for urbantransportation systems such as buses (see for exam-ple Sun et al. (2008), Daganzo (2009), Berrebi et al.(2017)). The aim is to provide methods for keepingheadways as even as possible so that approximatelythe same amount of passengers board each bus ata given stop. However, the constraints are not thesame as for railway systems ; the specific problem ofmanaging junctions is not considered. This issue isaddressed by Schanzenbacher et al. (2017), who pro-pose a model based on max-plus algebra to prove thatunder some hypothesis, the traffic evolves toward anequilibrium, and to compute its characteristics.

The development of CBTC systems has opened a newarea of research, concerning management and simu-lation of such systems. Ning et al. (2015) proposea control method for minimizing headway varianceand energy consumption by selecting adapted speedprofiles. Pochet et al. (2016) designed a genetic algo-rithm to reschedule trains when those are sharing in-frastructure with other vehicles that are not equippedwith a CBTC system. A tool for simulating traffic ona corridor is presented by Chen et al. (2010).

Finally, note that several railway traffic simulationtools already exist. They are used for various pur-poses, such as ensuring that a timetable is conflict-free, passenger information or robustness assessmentof a timetable. The commercial softwares OpenTrackand RailSys rely on a microscopic description of theinfrastructure and signaling system, and are notablyused for scheduling. However, these softwares requirea high computation time and are more adapted tolines operated with according to a schedule. Li et al.(2005) propose a simple cellular automaton model forsimulating railway traffic with a moving block signal-ing system.

3 MODELING RAILWAY OPERATIONSAND HEADWAY BASED CONTROL

3.1 Description of trains and infrastructure

In this preliminary work, we restricted ourselves tothe simulation of the area where trains are operatedaccording to a headway-based control scheme. Wemodel the infrastructure at a mesoscopic level, by anetwork (N,A). The set of arcs represents homoge-neous segments of tracks, linking nodes that are thesingular points (stopping points in stations, junctions,points where the speed limit changes). To each arca ∈ A, we associate a length `a, a speed limit sa

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and a capacity ca (meaning the highest number oftrains that can run on this segment simultaneously).In addition, following Pellegrini et al. (2015), we al-low some arcs to be reserved by a train before thistrain enters it, guaranteeing that no other train willenter the reserved infrastructure during the reserva-tion. This is used for determining train orders atjunctions.

The set of trains to be operated is denoted T . To eachtrain θ ∈ T we associate its physical characteristicsthat are its length `θ, its acceleration coefficient αθ

and its braking coefficient γθ. The service of train θis described by the following parameters: an itineraryIθ that is the ordered sequence of arcs taken by thetrain, a servicing Dθ that is the sequence of the sched-uled dwell times at each node of the network (thesetimes being null for the nodes that do not represent astation), and the time at which the train is scheduledto enter the network startθ. The train evolution is de-scribed by: the state of the train (running, dwelling,not operating), the arc aθ on which the head of thetrain is located, its position xθ on the arc, its speedsθ, its preceding train precθ and its current dwell timedwellθ.

3.2 Eulerian scheme

During the simulation, the trains evolution is com-puted using an Eulerian scheme, with a time horizonTf and a time step dt. The core algorithm can besynthetically described in the following way:

t=0 ;while t < Tf do

forall trains θ ∈ T doCompute safety distance ahead of train θ ;Update position and speed for train θ ;

endEnforce dispatching decisions ;t← t+ dt ;

endAlgorithm 1: Description of the core algorithm

We subsequently present each of the three functionsperformed by this algorithm. First, as train protec-tion is ensured by a moving block signaling system, itis necessary to compute the distance between a trainand the next point where it has to stop. We can thendeduce the maximal speed which allows the train tostop before that point. The computation of this safetydistance is performed by Algorithm 2. We assumedhere the arcs of Iθ to be ordered according to theitinerary of train θ.

The trains’ position is updated along the simulationusing an Eulerian scheme. At each time iteration t, anew speed instruction is computed for each running

if arc aθ contains another train ahead of θ thenθ′ ← closest train ahead of θ ;

dist← xθ′ − xθ − `θ′ ;

elsedist← `aθ − xθ ;

forall arc a ∈ Iθ not yet traveled by θ doif a contains a train θ′ then

dist← dist+ `a − xθ′ − `θ′ ;

break ;

elseif a is reserved by a train θ′ 6= θ or a is astation where θ is scheduled to stop then

break ;else

dist← dist+ `a ;end

end

end

endreturn dist ;Algorithm 2: Computation of safety distance oftrain θ

train: that is the speed the train will reach at timet + dt (assuming a constant acceleration between tand t + dt). The position is then updated accord-ingly. Algorithm 3 describes the performed opera-tions. Note that if a train cruises at speed s, ac-cording to the law of uniform deceleration, the min-imum distance for it to stop is s2/2γ. Therefore, ifa train has safety distance λ, the maximum speed itcan reach while still being able to stop before thatpoint is

√2γλ. However, as speed cannot be adapted

instantly, we compute a speed instruction for the nexttime step; the safety distance should be therefore re-duced to λ − sdt, and the maximum speed ensur-ing safety

√2γ(λ− sdt). We distinguish between two

cases:

• Either the train is able to speed up while stillsatisfying the safety constraints. Then it accel-erates to the highest possible speed according toits acceleration coefficient, maximum speed ofthe track segment and safety conditions. Notethat the maximum speed instruction satisfyingthe latter is the only solution of equation s =√

2γ(λ− sdt), that is√

2γλ+ γ2(dt)2 − γdt.

• Or the train has to slow down, and brakes withdeceleration coefficient γ.

3.3 Disturbances

Let us recall that our goal is to provide a simulationmethod for assessing the robustness of a traffic man-agement system where a transition between schedule-based and headway-based control is operated. Our

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method seeks therefore to reproduce the disturbancesthat are susceptible to occur in such a system. Weidentified two categories of disturbances:

• Disturbances occurring outside the headway-based control area. We do not delve into the de-tails of such disturbances, and model them by anarrival of trains at the entrance of this area withuneven time intervals. This is done by addingto the nominal arrival times the realizations ofindependent uniform random variables, with amagnitude to be chosen as a parameter.

• Prolonged dwell times at stations located in thedense area (due e.g. to passengers blocking doorsor driver waiting for passengers to board).

We introduced these disturbances as realizations ofindependent random variables following uniform dis-tributions. This choice is motivated by the lack ofavailable data for estimating the probabilistic distri-bution of such phenomena ; this is indeed a prospec-tive work and no railway system is currently oper-ated in such a paradigm. We therefore used ad hochypothesis coming from operators’ experience. How-ever, some refinements are possible: Yuan (2006) es-tablished that, under some hypothesis, arrival timesof trains follow a log-normal distribution.

3.4 Heuristics for railway traffic management

Last, the simulation method must be able to repro-duce traffic management decisions. For the sake ofsimplicity and performance in terms of computationtime, we implemented sub-optimal rule-based heuris-tics rather than more elaborated methods for solvingthe real-time traffic management problem. The pos-sible decisions are the following:

• All trains may depart stations as soon as pos-sible (No Holding policy), or some trains mightbe held longer in stations in order to re-adjustthe headways between trains in case of distur-bances (Holding policy). This policy might beparticularly efficient in stations located ahead ofjunctions, thus preventing trains to compete forthe use of infrastructure and to be forced to waitfor the junction to be free.

• When passenger data is unknown and traffic ishomogeneous (all trains stop in the same sta-tions), it seems reasonable to manage junctionsaccording to a First In First Out (FIFO) pol-icy. However, when direct and omnibus trainsshare the same infrastructure, our method pro-poses a Threshold policy : when a direct and anomnibus train are likely to compete for passingthe junction, the direct train is given priority if

sθ ← sθ ;λ← SafetyDistance(θ) ;if Train θ is running then

if sθ <√

2γ(λ− sθdt) then

sθ ← min(sθ + αθdt, saθ ,√2γλ+ γ2(dt)2 − γdt)

elsesθ ← max(0, sθ − γdt) ;

end

xθ ← xθ + (sθ + sθ)dt/2 ;

if xθ > `aθ thenxθ ← xθ − `aθ ;

aθ ← aθ + 1 ;

end

if sθ == 0 and aθ is a serviced station thenSet train θ’s state to “Dwelling” ;

dwellθ ← dtend

elseif Train θ is dwelling then

if dwellθ ≥ dwellT ime(aθ) thenSet θ’s state to “Running”

elsedwellθ ← dwellθ + dt

end

elseif t == startθ then

if λ > 0 thenSet θ’s state to “Running”

elsestartθ ← startθ + dt

end

end

end

endAlgorithm 3: Eulerian scheme for updating traindata

the resulting delay for the omnibus train remainsbelow a fixed threshold.

4 NUMERICAL EXPERIMENTS

4.1 Case study: line D of Paris suburban net-work

We applied our method to assess the feasibility of sucha mixed traffic control on one of the most saturatedlines in Paris suburban area, namely line D of theRER (Reseau Express Regional, the local express net-work). A map of the dense part of this line is given byFigure 3. We assumed this part to be equipped withCBTC and operated with headway-based control.

Line D crosses Paris for linking Orry-la-Ville (on thenorth) to Corbeil-Essonnes and Melun (on the south).This line presents several peculiarities. First, it shares

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D

B

Orry la Ville

CDG Airport Mitry

Corbeil Essonnes Melun

Saint-Rémy Robinson

Figure 3 – Line D of Paris RER

its infrastructure with line B of the RER network, an-other saturated line, between the stations Paris-Nordand Chatelet-les-Halles. For that reason, this com-mon segment is one of Europe’s busiest track sections,with a traffic reaching 32 trains per hour during thepeak period. Second, in order to increase the offeron the southern part of line D despite the satura-tion of the common section, some trains coming fromthe south end their journey at Paris-Lyon station andoperate from there a new service towards the south.Two tracks are dedicated for these turnaround ser-vices, while two other tracks are used for those run-ning through the station. Figures 4 and 5 presentrespectively a map of these track sections.

Paris-Nord Châtelet Les Halles

Figure 4 – Common section between Paris-Nord andChatelet

South North

Figure 5 – Paris-Lyon station

The transport offer is organized as follows in peakhours:

• 20 trains per hour on line B in each direction ;

• 12 trains per hour on line D from the north tothe south and from the south to the north ;

• 8 trains per hour on line D from the south toParis-Lyon and from Paris-Lyon to the south.

The nominal time interval between trains in the com-mon section is 90 seconds. Trains of line B are sched-uled every three minutes, while trains of line D followa 6 min/6 min/3 min pattern in the common sec-tion. South of Paris-Lyon, the nominal time intervalis three minutes. Figure 6 represents on a time-spacediagram the nominal trajectories of trains from Northto South ; the blue, green and red lines are associatedrespectively to the trains of line B, the trains of line

D from the north to the south and the trains of lineD from Paris-Lyon to the south. Trains of line D andline B are respectively 246 meters and 208 meterslong, and we assumed both acceleration and brakingcoefficients equal to 0.7 m/s2.

Figure 6 – Nominal trajectories from north to south

4.2 Results

Our aim is to assess the capability of the system toresist to disturbances that may occur upstream of theheadway-based control area. Figure 7 illustrates whatmay happen if trains enter this area without comply-ing by the nominal interval (because of disturbancesthat were not recovered by traffic management). Wecan observe on that figure some phenomena of con-gestion ahead of the junction between lines B andD at the station of Paris-Nord: indeed, some trainsare forced to stop ahead of the station. This resultsin an increase of travel time for passengers. We canalso note that some direct trains (red lines) get stuckbehind omnibus trains south of Paris-Lyon and aretherefore slowed down as well. For example, unlikeFigure 6, there is no spare time window for allowingthe first red train to insert on the south branch of theline. Consequently, this train has to follow the fifthgreen train that is a slower one, and gets delayed.

Figure 7 – Disturbed trajectories of trains

In order to quantify how the quality of service de-

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creases with the magnitude of upstream disturbances,we define the delay of a train in a given disturbancescenario as the difference between its total runningtime in this scenario and its running time in the nom-inal case (with no disturbances).

We ran several simulations with various magnitudesof uniform disturbances, and computed the averagedelay over all trains that completed their mission, ineach scenario. In all scenarios, we assumed the dwelltimes in stations to follow independent random vari-ables with uniform values in [40, 70] at stations insideParis and [20, 50] at stations outside Paris (the nomi-nal dwell times being respectively 50 and 30 seconds).The simulation horizon is 3 hours (the duration of thepeak period), and the time step is 5 seconds (chosenas a compromise between computation time and ac-curacy of the results).

For each level of disturbance and each policy, we per-formed 100 replications. The Holding policy is ap-plied in the stations located upstream of junctionsonly, and according to the following rule (we reuse thenotations of Figure 2). We denote by ∆AB (respec-tively ∆A′B) the nominal travel time between sta-tion A (respectively station A′) and station B, andI the nominal time interval between both trains. Iftrain 1 leaves station A at time depA, train 2 willnot be allowed to leave station A′ before the timedepA′ = depA+(∆AB−∆A′B)+I, thus ensuring thattrain 2 will not arrive at station B with a shorter in-terval than the nominal one. Results are plotted onFigure 8.

The junctions of Chatelet les Halles and Paris-Nordare managed according to a FIFO policy while thejunction of Paris-Lyon follows a Threshold policy(priority given to the fastest trains up to a 30s conse-quent delay for the other train). Indeed, both directand omnibus trains use the infrastructure south ofParis-Lyon while all trains are omnibus on the north-ern part of the line.

0 0 30 30 45 45 60 60 75 75 90 90 120120150150180180240240300300Disturbance magnitude (s)

−40

−20

0

20

40

60

80

100

120

Averag

e de

lay (s)

Figure 8 – Delays due to disturbances - No HoldingPolicy (white) and Holding Policy (yellow)

The distributions of delays using respectively theHolding and the No Holding policies are plotted on

figure 8. We note that for both policies, delays re-main limited both in average and extreme values forsmall levels of disturbances (up to approximately 45seconds), but grow and become more unpredictablefor higher levels. However, delays grow at a non-exponential rate: this is mostly due to the movingblock signaling system that is known to alleviate therisk of delay propagation from one train to the next,compared to a fixed signaling system.

In addition, up to a certain point the Holding Policyallows to reduce extreme values of delays, but in mostcases this comes at the price of a higher travel time inaverage. For greater levels of disturbances the Hold-ing Policy seems to become unable to cope even withthe extreme values. This work consequently does notappear conclusive on the relevancy of implementingsuch a policy and further studies seem to be needed.

This study also underscores the effects of stochastic-ity on the quality of operations in the dense area.A specific attention should therefore be paid to theschedule adherence in the upstream low traffic areas,where the system is less sensitive to disturbances, assmall delays in these parts of the network can lead toinstability in the common section. In case of delaysoccurring in the branches, traffic management deci-sions such as canceling a whole train or part of itsservice could be made to prevent propagation to thedense area, but this possibility was not investigatedin this work.

5 CONCLUSION

Our approach demonstrates the practical applicabil-ity of such a mixed traffic management for a railwayline crossing a dense area, the system being able to re-sist to disturbances of small magnitude. It also high-lights the benefits and drawbacks of a Holding policyto adjust headways.

Yet, some questions remain to be answered. First,the obtained results emphasize the need of an effi-cient traffic management ; improved control strate-gies should therefore be tested. In particular, thepossibility of adjusting headways by controlling thetrains speed between stations in addition to theirdwell times could be explored. Second, random dis-turbances upstream of the dense area were assumedto be independent and uniformly distributed, whichin practice is usually not the case: our results mightbenefit to be confirmed by a refined model. Last, nostudies have been made so far on how to build sched-ules and manage traffic in real time in the upstreamand downstream areas to facilitate the transition be-tween schedule-based and headway-based control. Allthose topics could be matters for further research.

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