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Performance Assessment of an Urbain Collective Cars System
1st IFAC Conference on Cyber-Physical & Human-Systems 1st IFAC Conference on Cyber-Physical Human-Systems December 7-9, 2016. Florianopolis, Brazil& 1st IFAC IFAC Conference Conference on Cyber-Physical Cyber-Physical & Human-Systems Human-Systems 1st on & December 7-9, 2016. Florianopolis, Brazil Available online at www.sciencedirect.com December December 7-9, 7-9, 2016. 2016. Florianopolis, Florianopolis, Brazil Brazil
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Performance Assessment of an Performance Assessment of an Performance Assessment of Performance Assessment of an an Collective Cars System Collective Cars System Collective Cars System Collective Cars System
Urbain Urbain Urbain Urbain
∗∗∗ Regine Seidowsky ∗∗ ∗∗ Habib Haj-Salem ∗∗∗ and Regine Seidowsky ∗∗ Habib ∗∗∗ and ∗∗∗∗Haj-Salem ∗∗ Regine Seidowsky Habib Haj-Salem Jean-Patricl Lebacque ∗∗∗∗Haj-Salem ∗∗∗ and Regine Seidowsky Habib and Jean-Patricl Lebacque ∗∗∗∗ Jean-Patricl Jean-Patricl Lebacque Lebacque ∗∗∗∗ ∗ ∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗ ∗ ∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗ IFSTTAR, IFSTTAR,GRETTIA, GRETTIA,Paris Paris(e-mail: (e-mail:[email protected]) [email protected]) ∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗∗ ∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) IFSTTAR,GRETTIA, GRETTIA,Paris Paris(e-mail: (e-mail:[email protected]) [email protected]) ∗∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗∗ IFSTTAR,∗∗∗∗ ∗∗∗ IFSTTAR,∗∗∗∗ GRETTIA, (e-mail: [email protected]) IFSTTAR,Paris GRETTIA, (e-mail: IFSTTAR,∗∗∗∗ GRETTIA, (e-mail: Paris [email protected]) IFSTTAR,Paris GRETTIA, Paris (e-mail: ∗∗∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) [email protected]) [email protected]) Abstract: A constrained optimization framework of an autonomous urban transport system, Abstract: A constrained optimization framework of an autonomous urban transport system, Abstract: A optimization framework of urban associated with reduced rates, is presented. A decentralized management is transport consideredsystem, where Abstract: A constrained constrained optimization framework of an an autonomous autonomous urbanis transport system, associated with reduced rates, is presented. A decentralized management considered where associated with reduced rates, is presented. A decentralized management is considered where prior seat reservation is rates, not a isprerequisite for the system functioning. Well-adapted vehicle associated with reduced presented. A decentralized management is considered where prior seat reservation is not a prerequisite for the system functioning. Well-adapted vehicle prior seat reservation is not the functioning. Well-adapted vehicle itineraries on the demand andfor state are constructed. The event-driven prior seat based reservation is current not a a prerequisite prerequisite forvehicle the system system functioning. Well-adapted vehicle itineraries based on the current demand and vehicle state are constructed. The event-driven itineraries based on the current demand and vehicle state are constructed. The event-driven system dynamics characterizing the non-deterministic features of the corresponding complex itineraries based on the current demand and vehicle state are constructed. The event-driven system dynamics characterizing the non-deterministic features of the corresponding complex system dynamics characterizing features of complex mathematical problem, encouragethe fornon-deterministic a discrete event system The implied stressing system dynamics characterizing the non-deterministic featuresapproach. of the the corresponding corresponding complex mathematical problem, encourage for aa discrete event system approach. The implied stressing mathematical problem, encourage for discrete event system approach. The implied stressing needs of a comprehensive study, will bediscrete achieved by system intense approach. simulations. Various strategies, mathematical problem, encourage for a event The implied stressing needs of a comprehensive study, will be achieved by intense simulations. Various strategies, needs of a comprehensive study, be by simulations. Various strategies, related time controls and will system dimensioning as well, are studied. A methodology needs ofto a real comprehensive study, will be achieved achieved by intense intense simulations. Various strategies, related to real time controls and system dimensioning as well, are studied. A methodology related to real time controls and system dimensioning as well, are studied. A methodology appraising the system performance is introduced where the resulting system behaviour is related to real time controls and system dimensioning as well, are studied. A methodology appraising the system performance is introduced where the resulting system behaviour is appraising the system performance is introduced where the resulting system behaviour is evaluated in terms of client waiting time, detours, vehicle occupancy, travel times etc. Moreover, appraising the system performance is introduced where the resulting behaviour is evaluated in terms of client waiting time, detours, vehicle occupancy, travelsystem times etc. Moreover, evaluated in client waiting time, detours, occupancy, times Moreover, optimal parameter tuning is discussed underlying the importance oftravel reasonable trade-offs for evaluated in terms terms of oftuning client is waiting time,underlying detours, vehicle vehicle occupancy,of travel times etc. etc. Moreover, optimal parameter discussed the importance reasonable trade-offs for optimal parameter tuning is underlying importance of trade-offs for achieving the desired performance. Thus, involving the optimisation, operational research methods optimal parameter tuning is discussed discussed underlying the importance of reasonable reasonable trade-offs for achieving the desired performance. Thus, involving optimisation, operational research methods achieving the desired performance. Thus, involving optimisation, operational research methods and simulation techniques a significantly efficacious well-operating system can be achieved, achieving the desired performance. Thus, involving optimisation, operational research methods and techniques a efficacious well-operating system can achieved, and simulation simulation techniques a significantly significantly efficacious well-operating systemUtilising can be bepreviously achieved, providing the best suited configuration for any demandwell-operating level and geometry. and simulation techniques a significantly efficacious system can be achieved, providing the best suited configuration for any demand level and geometry. Utilising previously providing the best suited configuration for any demand level and geometry. Utilising previously wasted vehicle capacity may reduce costs for both vehicles and clients whileUtilising forms an ongoing providing the best suited configuration for any demand level and geometry. previously wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing attempt to control extended traffic congestion, air pollution, energy consumption etc. wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing attempt to control extended traffic congestion, air pollution, energy consumption etc. attempt to control extended traffic congestion, air pollution, energy consumption etc. attempt to control extended traffic congestion, air pollution, energy consumption etc. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Demand responsive transportation; discrete event systems; asynchronous Keywords: Demand responsive responsive transportation; transportation; discrete discrete event event systems; systems; asynchronous asynchronous Keywords: Demand behaviour; Monte Carlo simulation; performance evaluation; optimisation Keywords: Demand responsive transportation; discrete event parameter systems; asynchronous behaviour; Monte Carlo simulation; performance evaluation; parameter optimisation behaviour; Monte Carlo simulation; performance evaluation; parameter behaviour; Monte Carlo simulation; performance evaluation; parameter optimisation optimisation 1. INTRODUCTION often at the disposal of elderly or persons with restricted 1. INTRODUCTION INTRODUCTION often at at the the disposal of of elderly or or persons with with restricted 1. often mobility. 1. INTRODUCTION often at the disposal disposal of elderly elderly or persons persons with restricted restricted mobility. An operational transportation structure can only improve mobility. mobility. An operational transportation structure can only improve work presents an optimised DRT system, imposing An operational transportation structure only all challenges when considering competent city This This work work presents presents an an optimised optimised DRT DRT system, system, imposing imposing An operationalfaced transportation structure aacan can only improve improve all challenges challenges faced when considering considering competent city This the minimum number constraints customers. It is This work presents an of optimised DRTto system, imposing all faced when a competent city activities and improved quality of life. Public transit often the minimum number of constraints to customers. It is is all challenges faced when considering a competent city activities and improved quality of life. Public transit often the minimum number of constraints to customers. It destined to all commuter types, providing independent minimum number of constraints to customers. It is activities and quality of Public transit often the appears to satisfy encouraging destined to all commuter types, providing independent activitiesinadequate and improved improved qualityurban of life. life.mobility Public transit often appears inadequate to satisfy urban mobility encouraging to commuter types, providing mobility and travel conditions similar to theindependent ones of the destined to all all commuter types, providing appears to satisfy urban mobility encouraging the use ofinadequate private cars and resulting in constantly growing destined mobility and and travel conditions similar to the theindependent ones of of the the appears to and satisfy urban in mobility encouraging the use use of ofinadequate private cars cars resulting constantly growing mobility conditions similar to ones private car at travel a low cost for both vehicles and passengers. mobility and travel conditions similar to the ones of the the private and resulting in constantly growing traffic density. Alternative structures associating public private car at a low cost for both vehicles and passengers. the use of private cars and resulting in constantly growing traffic density. density. Alternative Alternative structures structures associating associating public public private car low cost both and a model by Fargier and Cohen private car at at aawas lowinitially cost for forstudied both vehicles vehicles and passengers. passengers. traffic and private transportation, prohibitionassociating or imposingpublic tolls Such Such aa model model was initially studied by Fargier Fargier and Cohen Cohen traffic density. Alternative structures and private transportation, prohibition or imposing tolls Such was initially studied by and (1971) and this research is an advancement of their work. model initially studied by Fargier and Cohen and private for the city centre,prohibition have been or putimposing forward,tolls re- Such (1971)a and and thiswas research is an an advancement of their their work. and entering private transportation, transportation, prohibition or imposing tolls for entering the city centre, have been put forward, re(1971) this research is advancement of work. The related transportation problem is characterised by (1971) and this research is an advancement of their work. for entering the city centre, have been put forward, remaining partial solutions requiring the driver willingness The related transportation problem is characterised by for entering the city centre, have been put forward, remaining partial partial solutions solutions requiring requiring the the driver driver willingness The related transportation is characterised by complex dynamics, belongingproblem to the class of discrete event The related transportation problem is characterised by maining willingness to bear additional costs to ensure contort and convenience. complex dynamics, belonging to the class of discrete event maining partial solutions requiring the driver willingness to bear bear additional additional costs costs to to ensure ensure contort contort and and convenience. convenience. complex dynamics, to the class of discrete event system, (DES). Thebelonging system evolution is ruled by the occomplex dynamics, belonging to the class of discrete event to Systems like car sharing do not necessarily diminish the system, (DES). (DES). The The system system evolution evolution is is ruled ruled by by the the ococto bear additional costs todo ensure and diminish convenience. Systems like car car sharing sharing not contort necessarily the system, currence of asynchronous events over time, solely system, The system evolution is ruled by responthe ocSystems not necessarily the passenger to vehicle ratio do often by adiminish poor spatial currence(DES). of asynchronous asynchronous events over time, time, solely responSystems like like car sharing do notfollowed necessarily diminish the currence passenger to vehicle ratio often followed by a poor spatial of events over solely responfor generating state transitions. Explicit modelling of currence of asynchronous events overExplicit time, solely responpassenger to vehicle often by distribution concentration on high-demand desti- sible sible for for generating generating state transitions. transitions. modelling of passenger to (greater vehicle ratio ratio often followed followed by aa poor poor spatial spatial distribution (greater concentration on high-demand high-demand desti- sible state Explicit modelling of the nondeterministic behaviour is required often through sible for generating state transitions. Explicit modelling of distribution (greater concentration on destinations) unless additional constraints are imposed obliging the nondeterministic behaviour is required often through distribution (greater concentration on high-demand destinations) unless unless additional additional constraints constraints are are imposed imposed obliging obliging the nondeterministic behaviour is required through inclusion of appropriate stochastic modeloften components. the nondeterministic behaviour is required often through nations) users to return them to specific stations. For a very long the inclusion inclusion of of appropriate appropriate stochastic stochastic model model components. components. nations) constraints are imposed obliging users to to unless return additional them to to specific specific stations. For aa very very long the theofinvolved complexity requires combination the inclusion appropriate stochastic modelaa components. users return stations. time, carpooling has been presented as a For prestigious eco- Moreover, Moreover, the involved involved complexity requires combination users to return them them to specific stations. For a very long long time, carpooling has been presented as a prestigious ecoMoreover, the complexity requires a combination of mathematical techniques and effective processing of exMoreover, the involved complexity requires a combination time, carpooling has been presented as a prestigious economical transit mode but it presented still holds as many disadvantages. of mathematical techniques and effective processing of exextime, carpooling has been a prestigious economical transit transit mode mode but but it it still still holds holds many many disadvantages. disadvantages. of mathematical techniques and effective processing of perimental data for efficacious system performance. Thus, of mathematical techniques and effective processing of exnomical Passengers have to administer their own arrangements for perimental data for efficacious system performance. Thus, nomical transit mode but it still holds many disadvantages. Passengers have have to to administer administer their their own own arrangements arrangements for for perimental data for system performance. Thus, discrete event simulations allowing a deep understanding perimental data for efficacious efficacious system performance. Thus, Passengers defining mutually up points and discrete event event simulations allowing a deep deep understanding Passengers have toacceptable administerpredefined their ownpick arrangements for discrete defining mutually acceptable predefined pick up points and simulations allowing a understanding of the system behaviour together with appropriate mathediscrete event simulations allowing a deep understanding defining mutually acceptable predefined pick up points and and of the system behaviour together with appropriate mathetimetables, inevitably time consuming tasks. defining mutually acceptable predefined pick up points timetables, inevitably inevitably time time consuming consuming tasks. tasks. of the together with appropriate matical theorybehaviour will lead to an optimal of the mathesystem of the system system together withcontrol appropriate timetables, matical theorybehaviour will lead lead to to an optimal optimal control of the the mathesystem timetables, inevitablyTransport time consuming Demand Responsive (DRT) tasks. is getting increas- matical theory will an control of system evolution. matical theory will lead to an optimal control of the system Demand Responsive Transport (DRT) is getting increasevolution. Demand Responsive (DRT) is increasingly popular. So far, Transport in many existing various re- evolution. Demand Responsive Transport (DRT)schemes is getting getting increasevolution. ingly popular. So far, in many existing schemes various reThe next of the paper is organised as follows: §2 formalises ingly popular. So many schemes restrictions are presented routes, advanced booking), The next next of of the paper paper is is organised organised as as follows: follows: §2 §2 formalises formalises ingly popular. So far, far, in in (fixed many existing existing schemes various various re- The strictions are presented presented (fixed routes, advanced booking), the decision problem and discusses the utilised controls. The next of the the paper is organised as the follows: §2 formalises strictions are (fixed routes, advanced booking), Tao (2007), Fu (2002), London Dial a Ride, Kunaka (1996) the decision problem and discusses utilised controls. strictions are presented (fixed routes, advanced booking), Tao (2007), Fu (2002), London Dial a Ride, Kunaka (1996) the decision problem and discusses the utilised controls. Tao Tao (2007), (2007), Fu Fu (2002), (2002), London London Dial Dial aa Ride, Ride, Kunaka Kunaka (1996) (1996) the decision problem and discusses the utilised controls.
Jennie Jennie Jennie Jennie
Lioris ∗∗ Lioris ∗ Lioris Lioris ∗
Copyright@ 2016 IFAC 83 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright@ 2016 IFAC 83 Copyright@ 2016 IFAC 83 Peer review under of International Federation of Automatic Copyright@ 2016 responsibility IFAC 83 Control. 10.1016/j.ifacol.2016.12.194
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max tpj , min toi + s × δ(noi , ndi ) i∈d−1 (j) lim if nj ∈ L, t (j) = d t + s × δ(n , n ) 0 c 0 if nj = ndc and if ndc ∈ L.
§3 and §4 illustrate the system performance under the simulated scenario. §5 presents a methodology for adjusting parameter values. Finally, §6 summarises the main conclusions of this study. ACKNOWLEDGEMENTS The authors are indebted to Professor Guy Cohen for expert advise, support and all interesting and mostly stimulating discussions concerning this work.
The underlying idea is that for each passenger the diversion threshold must not be exceeded proportionally to his direct travel. But at the same time it may be impossible to satisfy that constraint due to delays for doing various operations at nodes, past stochastic arrival times etc.
2. CONTROLLING THE SYSTEM
We are seeking to minimise the sum of the predicted arrival times by taking into consideration the number of disembarking passengers at each node.
A system comprised of a network, clients wishing to join particular destinations and a related set of vehicles in service is considered. At any time, a prospective customer appearing at a network node searches for a potential vehicle able to serve a specific destination. Whenever that is not possible, the client according to his/her preferences either decides to join a queue for a limited period or quits the system. Similarly, cars bring passengers to their destinations while they are also interested in new passengers. Non-served clients, idle cars or an increased number of detours penalise the system performance. No advanced seat arrangement is required while an optimised passenger assignment to a particular vehicle accompanied by well adapted itineraries will reduce all related costs for both vehicles and clients.
Inactive Vehicle Management A station node should be chosen for an empty vehicle and an associated maximal parking period. If no client is found within this time, the vehicle makes a new request for updating the previously taken decision. The choice of the parking node is provided by a probability law involving the distance of present vehicle position and the station node while considering the client arrival intensity of the candidate node. 3. SYSTEM ASSESSMENT 3.1 Data Within this section the utilised reformulated data are presented since the real information can not be easily provided for publication. Nevertheless, the study is not going to be influenced and the intended proposed methodology remains valid, since under different data different numerical values will be resulted.
Client Acceptance Algorithm to a given vehicle Problem Definition: A vehicle with a given number of passengers aboard having an itinerary (destinations sorted according to the visiting order) encounters a new client. A decision should be taken whether the new client should be accepted in which case the new car itinerary must be provided.
3.2 Operating area
Hereafter, a client decision algorithm is presented, however different versions of controls can be developed and evaluated. One of the strong simulation points is that it reproduces precisely the system behaviour without the risk consequences of a poor decision making.
The employed network is inspired by the Paris plan comprised of 288 nodes and 674 edges as shown in Figure 1. Travel times may vary during an implementation representing varying traffic conditions. Approximatively 15, 400 clients are generated per hour according to a centripetal demand geometry (movements from the periphery towards the city centre). The maximal client waiting time at the origin node is of 10 minutes. The acceptable client detour threshold w.r.t. direct travel is taken equal to s = 1.9. Each vehicle has 5 available passenger seats and 3, 744 vehicles are employed. The maximal stationary time of each idle vehicle is of 15 minutes. The employed scheme (demand intensity and the number of vehicles in service) reflects the actual situation in Paris. The involved centripetal demand geometry corresponds to the early morning hours, when population moves from the suburbs towards the city center.
Notations n0 : present vehicle position; t0 : meeting time; ndc : the destination of the candidate client; δ(a, b) : the duration of the direct travel from node a to node b; L = {n1 , n2 , . . . , nm } : vehicle itinerary at t0 ; 1 = {x(1), . . . , x(||)} : a possible tour of visiting all nodes in = L ∪ {ndc }; t(k) : is the predicted arrival time at node x(k), element of 1 ; p x(k) : the number of disembarking passengers at node x(k); s : the diversion threshold accepted by each passenger proportionally to the direct travel; toi , noi , ndi : the entry time, the origin and destination node of passenger i respectively; tpj : the predicted arrival time at destination nj ∈ L : the deadline for arrival at node nj ∈ where tlim j
4. SINGLE DETAILED SIMULATION ANALYSIS 4.1 Checking Client Arrival Rates Statistics drawn for the simulation run with theoretical values are compared. Figure 2 illustrates verification the 84
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99 seconds. Figure 3 represents the histogram of the client waiting times. The distribution is roughly exponential. %
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waiting time (sec.) 0
100
200
300
400
500
600
700
Fig. 3. Waiting Time Histogram 4.4 Queue Lengths
Fig. 1. Paris plan
• The overall average client queue length is 1.54 and the per-node analysis shows a strong correlation with waiting times. • The analysis can be focussed on particular nodes on demand (e.g. analysing critical nodes).
employed demand. For every node i, the total number of clients appeared during the simulation divided by the simulation length is the y-coordinate whereas λi is the x-coordinate (288 points) corresponding to the client intensity at node i.
4.5 Measuring System Reliability • The histogram of the diversion ratio, depicted in Figure 4, is evaluated as the ratio of the client effective trip duration over the direct trip duration (evaluated by the average distance from the client origin to client destination node by the shortest path — matrix δ). The average diversion ratio is equal to 1.54 with standard deviation of 0.39. • For the total diversion ratio, illustrated in Fig. 5, the initial waiting time is included at the numerator of the ratio. The average total diversion ratio is equal to 1.64 with standard deviation of 0.40. %
Fig. 2. Demand Verification: parameter λi 4.2 Abandonment Customers quit their origin node after 10 mins from their arrival time, if no suitable vehicle is found during this period. The average abandonment rate for this simulation is 1.33%. This rate can be examined per node, revealing some critical nodes which can then be further and more carefully analysed.
ratio 0.5
1.0
1.5
2.0
2.5
trip duration (average) direct trip duration 3.0
3.5
4.0
Fig. 4. Histogram Trajectory Detour
4.3 Waiting Times and Queue Lengths 4.6 Car Activity
Global Statistics The average waiting time of clients (who finally embarked in a vehicle) for the whole network is of 97 seconds (including the dialog duration) with a standard deviation of
Number of clients served. For the 8 hour performed simulation, vehicles carried from 2.63 to 5.13 clients per hour with an average of 3.77 clients per hour. 85
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%
travels – 88%
parking – 3%
ratio 0.5
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2.0
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stops – 9%
trip duration + initial waiting time (average) direct trip duration
3.0
3.5
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Fig. 5. Histogram Total Trajectory Detour Average number of vehicle passengers In average, vehicles carry 2.16 passengers (individual values range from 1.29 to 3.15). Figure 6 resumes the number of vehicle passengers and the percentage of time during which vehicles were occupied by the related customer number. As one can see, within the current the total available vehicle capacity was utilised only during 5% of the total time. What allows for a high service quality.
Fig. 7. Vehicle Activity • the number n of vehicles in service.
These two parameters have an impact on almost all statistical indicators we may observe through simulations. 5.1 Service Quality Indicators (SQI) Three classes of statistical indicators, characrerising the system behaviour, can be defined: (1) SQI strongly positively correlated with each other. For this category, it suffices to retain only one statistical measure. This is the case of the customer waiting time and the client queue length at a node. (2) SQI which are independent and can only be directly observed. Thus, clients who have not found an appropriate vehicle during their maximal waiting period are only reflected by the abandonment rate since they left the system prematurely. (3) In addition, some indicators are conflicting and therefore they must be monitored simultaneously in order to achieve a reasonable trade-off: for example, increasing n will obviously improve all service quality indicators from the client point of view. At the same time, the average taxi activity will be reduced, which in return will increase all related costs and consequently fares.
1 passenger – 32%
0 passenger – 2%
2 passengers – 33%
5 passengers – 4%
4 passengers – 9%
3 passengers – 20%
Fig. 6. Taxi Occupancy Vehicle Activity
Choice of SQI
As Figure 7 illustrates cars
During this study, the following three indicators are retained:
• circulate on network links for the 88% of the time, • are stopped at nodes for interacting with passengers during 9% of the time, • are parked at an empty state for the 3% of the time.
x : the average abandonment rate over the whole network y : minus the average number of clients transported per taxi during a 8 hour simulation z : the average total diversion ratio.
5. PARAMETER TUNING
• Indicator z is related to clients who effectively reached their desired destination. It incorporates two service quality indicators: the initial client waiting time and the amount of diversion of their effective journey compared to the direct trip. • x accounts for the clients who finally gave up the system.
Two important parameters are integrated into the study of “collective cars” performance: • the threshold s which limits diversion in the decision algorithm related to the client acceptance or rejection by a given vehicle 86
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• Both previous measures certainly improve (i.e. decrease) as the number of taxis in service n, increases; therefore, −y should be monitored to relativize this improvement. The minus sign has been included in order that, for all three indicators x, y, z, “better” is equivalent to “smaller”.
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2D representation of the surfaces in the (x, y) plane while the z coordinate is represented by its level curves. The level curves are indicated in square boxes in Figure 9. The points chosen on each surface are located on the level curve 1.7 (that is, both achieve an average total detour ratio of 1.7) and they also both achieve a global abandonment rate (x coordinate) of 1%. However, the corresponding average number of transported clients per vehicle y is greater with the centripetal geometry (about 30 clients for simulations corresponding to 8 hours of real time) than with the centrifugal (only about 28.5). This is consistent with the fact that more vehicles are needed with the centrifugal demand to achieve those performances (3, 910 versus 3, 744). Finally, a different value of s is also needed: 1.98 versus 2.1.
5.2 Methodology Adjusting Parameter Values As previously discussed, three SQI measures x, y, z are chosen depending on two parameters s and n. We seek values of these parameters inducing values of x, y, z as small as possible. Hence, all reachable values of x, y, z lie on a 2D-surface in a 3D-space. A point has to be chosen lying on the lower left-hand border of this surface. This choice is not unique (Pareto optimality) and reflects the relative importance assigned to each indicator. Nevertheless, when two surfaces corresponding to two different situations (e.g. two geometries of demand) can be compared with respect to the positions of their lower left-hand borders, one can ascertain which one is the most favourable for the performance of the system.
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29
In what follows, a methodology of analysis comparing two demand geometries is illustrated.
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5.3 Comparison between Centripetal and Centrifugal Demands 31
A series of simulations is implemented for two demand geometries, a centripetal and a centrifugal demand, when varying values of s and n. In Figure 8 the red (lower) surface corresponds to the centripetal demand while the green surface is associated with the centrifugal demand. Both demands are of the same intensity and amount of imbalance (they correspond to reversed travels of clients from origins to destinations).
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Average number of clients transported per taxi (8 hour sim.)
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1.7
s = 1.98 n = 3910 1.8 1.7
s = 2.1 n = 3744 1.8
0.5
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Abandonment rate (%) 1.5
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Fig. 9. Centripetal-Centrifugal 2D demands
2.0
tio ersion ra Total div
.) ents f cli our sim h ber o num r taxi (8 e rage Ave orted p sp tran
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6. CONCLUSION-FUTURE WORK
1.4
An efficient transportation mode is often perceived as an important support contributing to the numerous requirements of urban productivity. Public transport often is inadequate for daily metropolitan mobility and private car remains consumer’s first choice preserving confort and convenience. Therefore, cogestion is implied accompanied by difficult driving conditions and consequently raised accidents rates. Classical taxis could be a successful solution if only they were more affordable. Exploitation of the vehicle capacity within an accessible flexible system could be a promising idea to be explored, reducing transportation costs, limiting congestion and energy consumption. Systems like car sharing do not necessarily diminish the
(%) t rate nmen 2 bando
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One can conclude that the centripetal geometry of demand in a network having a topology inspired by the Paris metro plan, tending to accumulate vehicles towards the city center, is more favorable than the centrifugal one, which tends to disperse taxis toward the suburbs. Obviously, other topologies may lead to different conclusions (work not included in this paper).
A
1
Fig. 8. Centripetal-Centrifugal 3D demands For each of the two scenarios, a particular point on the corresponding surface is chosen in such a way that two of the three coordinates of those points are equal. We search for a difference over the third one. In order to facilitate the study, Figure 9 will be utilized illustrating a 87
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passenger to vehicle ratio often followed by a poor spatial distribution. Carpooling schemes require passengers to administer the related arrangements (inevitably time consuming tasks) while vehicle itineraries are not necessarily optimised.
Dessouky, M., Rahimi, M., and Weidner, M. (2003). Jointly optimizing cost, service, and environmental performance in demand-responsive transit scheduling. Transportation Research Part D, 8, 433465. Fargier, P. and Cohen, G. (1971). Study of a collective taxi system. In G. Newell (ed.), Proceedings of the Fifth International Symposium on the Theory of Traffic Flow and Transportation, 361–376. American Elsevier, University of California, Berkeley. Fu, L. (2002). A simulation model for evaluating advanced dial-a-ride paratransit systems. Transportation Research Part A, 36, 291–307. John S. Niles and Paul A. Toliver (1992). IVHS technology for improving ridesharing. In Annual Meeting of ITS America. Newport Beach, California. Kunaka, C. (1996). Simulation modelling of paratransit services using GIS. In The Association for European Transport Conference. London Dial a Ride (2016). London dial a ride. http://www.tfl.gov.uk/gettingaround/3222.aspx. Report-UK (2015). The pathway to driverless cars, department for transport. U.K Summary report and action plan. Tao, C. (2007). Dynamic taxi-sharing service using intelligent transportation system technologies. In International Conference on Wireless Communications, Networking and Mobile Computing (WiCom 2007), 3209– 3212. Shanghai, China. Tesla Motors (2016) (2016). Tesla completely driverless cars. http://www.dezeen.com/2015/09/30/teslaelectric-model-x-car-safest-suv-ever-bioweapon-defence-mode-elon-musk/. Tsitsiklis, J. (1992). Special cases of travelling salesman and repairman problems with time windows. Networks, 22, 263–282. Xu, J. and Huang, Z. (2009). Autonomous dial-a-ride transit introductory overview. Journal of Software, 4(7), 766–776.
This paper suggests an autonomous DRT system, reducing commuter fares while assuring a quick delivery to destinations. A decentralised approach is studied, requiring only local information where each vehicle management is optimised independently of the others. Some other principal differences from the existing structures consist in an autonomous system operation, no requirement for prior seat reservation is any more necessary while the entire network is served and not only some specific areas. The related transit problem is studied from a DES approach. Thus, association of Optimisation and Operational Research methods combined with advanced simulation techniques will lead to an optimal system functioning and desired tradeoffs. Specific control designs allocate customers to vehicles while the vehicle itinerary is dynamically optimised every time its state changes. Moreover, management of empty vehicles improves the system productivity while additional car costs are diminished. Since a whole category of decision algorithms can be conceived (in addition to the ones proposed in this study) a methodology evaluating the system performance according to the currently utilised scenario is discussed. Hence, client and vehicle metrics are presented such as client waiting times, abandon rates and detours, vehicle occupancy and activity etc. At present, more sophisticated control policies related to client acceptance are about to be developed taking into consideration the stochastic demand model. Aiming at an optimised system performance, all vehicle decisions are provided by associated algorithms taking into consideration the current system state. A transportation mode involving fully autonomous electric cars, where information technologies will be incorporated coordinating vehicle control and decisions, tuning and timing trips, can increase operational efficiency. Such a vehicle structure would also contribute to a successful management when recurring and non-recurring congestion, safety (human error constitutes a major factor to accidents) while it controls additional energy consumption. Many successful demonstrations and studies, on fully autonomous electric cars, are conducted in the USA and Europe, Tesla Motors (2016), Report-UK (2015) while current research investigates the problem of efficient risk resolution. Since present traffic regulation still prohibits entry of fully autonomous vehicles in traffic, specific road infrastructure and geometry design could be envisaged amongst other eventual possibilities as a first step towards an efficacious, innovative and accessible future transport mode. REFERENCES Baccelli, F., Cohen, G., and Gaujal, B. (1992). Recursive equations and basic properties of timed petri nets. Journal of Discrete Event Dynamic Systems, 2, 415–439. Ciari, F., Balmer, M., and Axhausen, K. (2009). Large scale use of collective taxis: a multi-agent approach. In 12th International Conference on Travel Behaviour Research. Jaipur, India. 88
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Performance Assessment of an Performance Assessment of an Performance Assessment of Performance Assessment of an an Collective Cars System Collective Cars System Collective Cars System Collective Cars System
Urbain Urbain Urbain Urbain
∗∗∗ Regine Seidowsky ∗∗ ∗∗ Habib Haj-Salem ∗∗∗ and Regine Seidowsky ∗∗ Habib ∗∗∗ and ∗∗∗∗Haj-Salem ∗∗ Regine Seidowsky Habib Haj-Salem Jean-Patricl Lebacque ∗∗∗∗Haj-Salem ∗∗∗ and Regine Seidowsky Habib and Jean-Patricl Lebacque ∗∗∗∗ Jean-Patricl Jean-Patricl Lebacque Lebacque ∗∗∗∗ ∗ ∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗ ∗ ∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗ IFSTTAR, IFSTTAR,GRETTIA, GRETTIA,Paris Paris(e-mail: (e-mail:[email protected]) [email protected]) ∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗∗ ∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) IFSTTAR,GRETTIA, GRETTIA,Paris Paris(e-mail: (e-mail:[email protected]) [email protected]) ∗∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) ∗∗∗ IFSTTAR,∗∗∗∗ ∗∗∗ IFSTTAR,∗∗∗∗ GRETTIA, (e-mail: [email protected]) IFSTTAR,Paris GRETTIA, (e-mail: IFSTTAR,∗∗∗∗ GRETTIA, (e-mail: Paris [email protected]) IFSTTAR,Paris GRETTIA, Paris (e-mail: ∗∗∗∗ IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) IFSTTAR, GRETTIA, Paris (e-mail: [email protected]) [email protected]) [email protected]) Abstract: A constrained optimization framework of an autonomous urban transport system, Abstract: A constrained optimization framework of an autonomous urban transport system, Abstract: A optimization framework of urban associated with reduced rates, is presented. A decentralized management is transport consideredsystem, where Abstract: A constrained constrained optimization framework of an an autonomous autonomous urbanis transport system, associated with reduced rates, is presented. A decentralized management considered where associated with reduced rates, is presented. A decentralized management is considered where prior seat reservation is rates, not a isprerequisite for the system functioning. Well-adapted vehicle associated with reduced presented. A decentralized management is considered where prior seat reservation is not a prerequisite for the system functioning. Well-adapted vehicle prior seat reservation is not the functioning. Well-adapted vehicle itineraries on the demand andfor state are constructed. The event-driven prior seat based reservation is current not a a prerequisite prerequisite forvehicle the system system functioning. Well-adapted vehicle itineraries based on the current demand and vehicle state are constructed. The event-driven itineraries based on the current demand and vehicle state are constructed. The event-driven system dynamics characterizing the non-deterministic features of the corresponding complex itineraries based on the current demand and vehicle state are constructed. The event-driven system dynamics characterizing the non-deterministic features of the corresponding complex system dynamics characterizing features of complex mathematical problem, encouragethe fornon-deterministic a discrete event system The implied stressing system dynamics characterizing the non-deterministic featuresapproach. of the the corresponding corresponding complex mathematical problem, encourage for aa discrete event system approach. The implied stressing mathematical problem, encourage for discrete event system approach. The implied stressing needs of a comprehensive study, will bediscrete achieved by system intense approach. simulations. Various strategies, mathematical problem, encourage for a event The implied stressing needs of a comprehensive study, will be achieved by intense simulations. Various strategies, needs of a comprehensive study, be by simulations. Various strategies, related time controls and will system dimensioning as well, are studied. A methodology needs ofto a real comprehensive study, will be achieved achieved by intense intense simulations. Various strategies, related to real time controls and system dimensioning as well, are studied. A methodology related to real time controls and system dimensioning as well, are studied. A methodology appraising the system performance is introduced where the resulting system behaviour is related to real time controls and system dimensioning as well, are studied. A methodology appraising the system performance is introduced where the resulting system behaviour is appraising the system performance is introduced where the resulting system behaviour is evaluated in terms of client waiting time, detours, vehicle occupancy, travel times etc. Moreover, appraising the system performance is introduced where the resulting behaviour is evaluated in terms of client waiting time, detours, vehicle occupancy, travelsystem times etc. Moreover, evaluated in client waiting time, detours, occupancy, times Moreover, optimal parameter tuning is discussed underlying the importance oftravel reasonable trade-offs for evaluated in terms terms of oftuning client is waiting time,underlying detours, vehicle vehicle occupancy,of travel times etc. etc. Moreover, optimal parameter discussed the importance reasonable trade-offs for optimal parameter tuning is underlying importance of trade-offs for achieving the desired performance. Thus, involving the optimisation, operational research methods optimal parameter tuning is discussed discussed underlying the importance of reasonable reasonable trade-offs for achieving the desired performance. Thus, involving optimisation, operational research methods achieving the desired performance. Thus, involving optimisation, operational research methods and simulation techniques a significantly efficacious well-operating system can be achieved, achieving the desired performance. Thus, involving optimisation, operational research methods and techniques a efficacious well-operating system can achieved, and simulation simulation techniques a significantly significantly efficacious well-operating systemUtilising can be bepreviously achieved, providing the best suited configuration for any demandwell-operating level and geometry. and simulation techniques a significantly efficacious system can be achieved, providing the best suited configuration for any demand level and geometry. Utilising previously providing the best suited configuration for any demand level and geometry. Utilising previously wasted vehicle capacity may reduce costs for both vehicles and clients whileUtilising forms an ongoing providing the best suited configuration for any demand level and geometry. previously wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing attempt to control extended traffic congestion, air pollution, energy consumption etc. wasted vehicle capacity may reduce costs for both vehicles and clients while forms an ongoing attempt to control extended traffic congestion, air pollution, energy consumption etc. attempt to control extended traffic congestion, air pollution, energy consumption etc. attempt to control extended traffic congestion, air pollution, energy consumption etc. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Demand responsive transportation; discrete event systems; asynchronous Keywords: Demand responsive responsive transportation; transportation; discrete discrete event event systems; systems; asynchronous asynchronous Keywords: Demand behaviour; Monte Carlo simulation; performance evaluation; optimisation Keywords: Demand responsive transportation; discrete event parameter systems; asynchronous behaviour; Monte Carlo simulation; performance evaluation; parameter optimisation behaviour; Monte Carlo simulation; performance evaluation; parameter behaviour; Monte Carlo simulation; performance evaluation; parameter optimisation optimisation 1. INTRODUCTION often at the disposal of elderly or persons with restricted 1. INTRODUCTION INTRODUCTION often at at the the disposal of of elderly or or persons with with restricted 1. often mobility. 1. INTRODUCTION often at the disposal disposal of elderly elderly or persons persons with restricted restricted mobility. An operational transportation structure can only improve mobility. mobility. An operational transportation structure can only improve work presents an optimised DRT system, imposing An operational transportation structure only all challenges when considering competent city This This work work presents presents an an optimised optimised DRT DRT system, system, imposing imposing An operationalfaced transportation structure aacan can only improve improve all challenges challenges faced when considering considering competent city This the minimum number constraints customers. It is This work presents an of optimised DRTto system, imposing all faced when a competent city activities and improved quality of life. Public transit often the minimum number of constraints to customers. It is is all challenges faced when considering a competent city activities and improved quality of life. Public transit often the minimum number of constraints to customers. It destined to all commuter types, providing independent minimum number of constraints to customers. It is activities and quality of Public transit often the appears to satisfy encouraging destined to all commuter types, providing independent activitiesinadequate and improved improved qualityurban of life. life.mobility Public transit often appears inadequate to satisfy urban mobility encouraging to commuter types, providing mobility and travel conditions similar to theindependent ones of the destined to all all commuter types, providing appears to satisfy urban mobility encouraging the use ofinadequate private cars and resulting in constantly growing destined mobility and and travel conditions similar to the theindependent ones of of the the appears to and satisfy urban in mobility encouraging the use use of ofinadequate private cars cars resulting constantly growing mobility conditions similar to ones private car at travel a low cost for both vehicles and passengers. mobility and travel conditions similar to the ones of the the private and resulting in constantly growing traffic density. Alternative structures associating public private car at a low cost for both vehicles and passengers. the use of private cars and resulting in constantly growing traffic density. density. Alternative Alternative structures structures associating associating public public private car low cost both and a model by Fargier and Cohen private car at at aawas lowinitially cost for forstudied both vehicles vehicles and passengers. passengers. traffic and private transportation, prohibitionassociating or imposingpublic tolls Such Such aa model model was initially studied by Fargier Fargier and Cohen Cohen traffic density. Alternative structures and private transportation, prohibition or imposing tolls Such was initially studied by and (1971) and this research is an advancement of their work. model initially studied by Fargier and Cohen and private for the city centre,prohibition have been or putimposing forward,tolls re- Such (1971)a and and thiswas research is an an advancement of their their work. and entering private transportation, transportation, prohibition or imposing tolls for entering the city centre, have been put forward, re(1971) this research is advancement of work. The related transportation problem is characterised by (1971) and this research is an advancement of their work. for entering the city centre, have been put forward, remaining partial solutions requiring the driver willingness The related transportation problem is characterised by for entering the city centre, have been put forward, remaining partial partial solutions solutions requiring requiring the the driver driver willingness The related transportation is characterised by complex dynamics, belongingproblem to the class of discrete event The related transportation problem is characterised by maining willingness to bear additional costs to ensure contort and convenience. complex dynamics, belonging to the class of discrete event maining partial solutions requiring the driver willingness to bear bear additional additional costs costs to to ensure ensure contort contort and and convenience. convenience. complex dynamics, to the class of discrete event system, (DES). Thebelonging system evolution is ruled by the occomplex dynamics, belonging to the class of discrete event to Systems like car sharing do not necessarily diminish the system, (DES). (DES). The The system system evolution evolution is is ruled ruled by by the the ococto bear additional costs todo ensure and diminish convenience. Systems like car car sharing sharing not contort necessarily the system, currence of asynchronous events over time, solely system, The system evolution is ruled by responthe ocSystems not necessarily the passenger to vehicle ratio do often by adiminish poor spatial currence(DES). of asynchronous asynchronous events over time, time, solely responSystems like like car sharing do notfollowed necessarily diminish the currence passenger to vehicle ratio often followed by a poor spatial of events over solely responfor generating state transitions. Explicit modelling of currence of asynchronous events overExplicit time, solely responpassenger to vehicle often by distribution concentration on high-demand desti- sible sible for for generating generating state transitions. transitions. modelling of passenger to (greater vehicle ratio ratio often followed followed by aa poor poor spatial spatial distribution (greater concentration on high-demand high-demand desti- sible state Explicit modelling of the nondeterministic behaviour is required often through sible for generating state transitions. Explicit modelling of distribution (greater concentration on destinations) unless additional constraints are imposed obliging the nondeterministic behaviour is required often through distribution (greater concentration on high-demand destinations) unless unless additional additional constraints constraints are are imposed imposed obliging obliging the nondeterministic behaviour is required through inclusion of appropriate stochastic modeloften components. the nondeterministic behaviour is required often through nations) users to return them to specific stations. For a very long the inclusion inclusion of of appropriate appropriate stochastic stochastic model model components. components. nations) constraints are imposed obliging users to to unless return additional them to to specific specific stations. For aa very very long the theofinvolved complexity requires combination the inclusion appropriate stochastic modelaa components. users return stations. time, carpooling has been presented as a For prestigious eco- Moreover, Moreover, the involved involved complexity requires combination users to return them them to specific stations. For a very long long time, carpooling has been presented as a prestigious ecoMoreover, the complexity requires a combination of mathematical techniques and effective processing of exMoreover, the involved complexity requires a combination time, carpooling has been presented as a prestigious economical transit mode but it presented still holds as many disadvantages. of mathematical techniques and effective processing of exextime, carpooling has been a prestigious economical transit transit mode mode but but it it still still holds holds many many disadvantages. disadvantages. of mathematical techniques and effective processing of perimental data for efficacious system performance. Thus, of mathematical techniques and effective processing of exnomical Passengers have to administer their own arrangements for perimental data for efficacious system performance. Thus, nomical transit mode but it still holds many disadvantages. Passengers have have to to administer administer their their own own arrangements arrangements for for perimental data for system performance. Thus, discrete event simulations allowing a deep understanding perimental data for efficacious efficacious system performance. Thus, Passengers defining mutually up points and discrete event event simulations allowing a deep deep understanding Passengers have toacceptable administerpredefined their ownpick arrangements for discrete defining mutually acceptable predefined pick up points and simulations allowing a understanding of the system behaviour together with appropriate mathediscrete event simulations allowing a deep understanding defining mutually acceptable predefined pick up points and and of the system behaviour together with appropriate mathetimetables, inevitably time consuming tasks. defining mutually acceptable predefined pick up points timetables, inevitably inevitably time time consuming consuming tasks. tasks. of the together with appropriate matical theorybehaviour will lead to an optimal of the mathesystem of the system system together withcontrol appropriate timetables, matical theorybehaviour will lead lead to to an optimal optimal control of the the mathesystem timetables, inevitablyTransport time consuming Demand Responsive (DRT) tasks. is getting increas- matical theory will an control of system evolution. matical theory will lead to an optimal control of the system Demand Responsive Transport (DRT) is getting increasevolution. Demand Responsive (DRT) is increasingly popular. So far, Transport in many existing various re- evolution. Demand Responsive Transport (DRT)schemes is getting getting increasevolution. ingly popular. So far, in many existing schemes various reThe next of the paper is organised as follows: §2 formalises ingly popular. So many schemes restrictions are presented routes, advanced booking), The next next of of the paper paper is is organised organised as as follows: follows: §2 §2 formalises formalises ingly popular. So far, far, in in (fixed many existing existing schemes various various re- The strictions are presented presented (fixed routes, advanced booking), the decision problem and discusses the utilised controls. The next of the the paper is organised as the follows: §2 formalises strictions are (fixed routes, advanced booking), Tao (2007), Fu (2002), London Dial a Ride, Kunaka (1996) the decision problem and discusses utilised controls. strictions are presented (fixed routes, advanced booking), Tao (2007), Fu (2002), London Dial a Ride, Kunaka (1996) the decision problem and discusses the utilised controls. Tao Tao (2007), (2007), Fu Fu (2002), (2002), London London Dial Dial aa Ride, Ride, Kunaka Kunaka (1996) (1996) the decision problem and discusses the utilised controls.
Jennie Jennie Jennie Jennie
Lioris ∗∗ Lioris ∗ Lioris Lioris ∗
Copyright@ 2016 IFAC 83 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2016, IFAC (International Federation of Automatic Control) Copyright@ 2016 IFAC 83 Copyright@ 2016 IFAC 83 Peer review under of International Federation of Automatic Copyright@ 2016 responsibility IFAC 83 Control. 10.1016/j.ifacol.2016.12.194
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max tpj , min toi + s × δ(noi , ndi ) i∈d−1 (j) lim if nj ∈ L, t (j) = d t + s × δ(n , n ) 0 c 0 if nj = ndc and if ndc ∈ L.
§3 and §4 illustrate the system performance under the simulated scenario. §5 presents a methodology for adjusting parameter values. Finally, §6 summarises the main conclusions of this study. ACKNOWLEDGEMENTS The authors are indebted to Professor Guy Cohen for expert advise, support and all interesting and mostly stimulating discussions concerning this work.
The underlying idea is that for each passenger the diversion threshold must not be exceeded proportionally to his direct travel. But at the same time it may be impossible to satisfy that constraint due to delays for doing various operations at nodes, past stochastic arrival times etc.
2. CONTROLLING THE SYSTEM
We are seeking to minimise the sum of the predicted arrival times by taking into consideration the number of disembarking passengers at each node.
A system comprised of a network, clients wishing to join particular destinations and a related set of vehicles in service is considered. At any time, a prospective customer appearing at a network node searches for a potential vehicle able to serve a specific destination. Whenever that is not possible, the client according to his/her preferences either decides to join a queue for a limited period or quits the system. Similarly, cars bring passengers to their destinations while they are also interested in new passengers. Non-served clients, idle cars or an increased number of detours penalise the system performance. No advanced seat arrangement is required while an optimised passenger assignment to a particular vehicle accompanied by well adapted itineraries will reduce all related costs for both vehicles and clients.
Inactive Vehicle Management A station node should be chosen for an empty vehicle and an associated maximal parking period. If no client is found within this time, the vehicle makes a new request for updating the previously taken decision. The choice of the parking node is provided by a probability law involving the distance of present vehicle position and the station node while considering the client arrival intensity of the candidate node. 3. SYSTEM ASSESSMENT 3.1 Data Within this section the utilised reformulated data are presented since the real information can not be easily provided for publication. Nevertheless, the study is not going to be influenced and the intended proposed methodology remains valid, since under different data different numerical values will be resulted.
Client Acceptance Algorithm to a given vehicle Problem Definition: A vehicle with a given number of passengers aboard having an itinerary (destinations sorted according to the visiting order) encounters a new client. A decision should be taken whether the new client should be accepted in which case the new car itinerary must be provided.
3.2 Operating area
Hereafter, a client decision algorithm is presented, however different versions of controls can be developed and evaluated. One of the strong simulation points is that it reproduces precisely the system behaviour without the risk consequences of a poor decision making.
The employed network is inspired by the Paris plan comprised of 288 nodes and 674 edges as shown in Figure 1. Travel times may vary during an implementation representing varying traffic conditions. Approximatively 15, 400 clients are generated per hour according to a centripetal demand geometry (movements from the periphery towards the city centre). The maximal client waiting time at the origin node is of 10 minutes. The acceptable client detour threshold w.r.t. direct travel is taken equal to s = 1.9. Each vehicle has 5 available passenger seats and 3, 744 vehicles are employed. The maximal stationary time of each idle vehicle is of 15 minutes. The employed scheme (demand intensity and the number of vehicles in service) reflects the actual situation in Paris. The involved centripetal demand geometry corresponds to the early morning hours, when population moves from the suburbs towards the city center.
Notations n0 : present vehicle position; t0 : meeting time; ndc : the destination of the candidate client; δ(a, b) : the duration of the direct travel from node a to node b; L = {n1 , n2 , . . . , nm } : vehicle itinerary at t0 ; 1 = {x(1), . . . , x(||)} : a possible tour of visiting all nodes in = L ∪ {ndc }; t(k) : is the predicted arrival time at node x(k), element of 1 ; p x(k) : the number of disembarking passengers at node x(k); s : the diversion threshold accepted by each passenger proportionally to the direct travel; toi , noi , ndi : the entry time, the origin and destination node of passenger i respectively; tpj : the predicted arrival time at destination nj ∈ L : the deadline for arrival at node nj ∈ where tlim j
4. SINGLE DETAILED SIMULATION ANALYSIS 4.1 Checking Client Arrival Rates Statistics drawn for the simulation run with theoretical values are compared. Figure 2 illustrates verification the 84
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99 seconds. Figure 3 represents the histogram of the client waiting times. The distribution is roughly exponential. %
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Fig. 3. Waiting Time Histogram 4.4 Queue Lengths
Fig. 1. Paris plan
• The overall average client queue length is 1.54 and the per-node analysis shows a strong correlation with waiting times. • The analysis can be focussed on particular nodes on demand (e.g. analysing critical nodes).
employed demand. For every node i, the total number of clients appeared during the simulation divided by the simulation length is the y-coordinate whereas λi is the x-coordinate (288 points) corresponding to the client intensity at node i.
4.5 Measuring System Reliability • The histogram of the diversion ratio, depicted in Figure 4, is evaluated as the ratio of the client effective trip duration over the direct trip duration (evaluated by the average distance from the client origin to client destination node by the shortest path — matrix δ). The average diversion ratio is equal to 1.54 with standard deviation of 0.39. • For the total diversion ratio, illustrated in Fig. 5, the initial waiting time is included at the numerator of the ratio. The average total diversion ratio is equal to 1.64 with standard deviation of 0.40. %
Fig. 2. Demand Verification: parameter λi 4.2 Abandonment Customers quit their origin node after 10 mins from their arrival time, if no suitable vehicle is found during this period. The average abandonment rate for this simulation is 1.33%. This rate can be examined per node, revealing some critical nodes which can then be further and more carefully analysed.
ratio 0.5
1.0
1.5
2.0
2.5
trip duration (average) direct trip duration 3.0
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Fig. 4. Histogram Trajectory Detour
4.3 Waiting Times and Queue Lengths 4.6 Car Activity
Global Statistics The average waiting time of clients (who finally embarked in a vehicle) for the whole network is of 97 seconds (including the dialog duration) with a standard deviation of
Number of clients served. For the 8 hour performed simulation, vehicles carried from 2.63 to 5.13 clients per hour with an average of 3.77 clients per hour. 85
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travels – 88%
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Fig. 5. Histogram Total Trajectory Detour Average number of vehicle passengers In average, vehicles carry 2.16 passengers (individual values range from 1.29 to 3.15). Figure 6 resumes the number of vehicle passengers and the percentage of time during which vehicles were occupied by the related customer number. As one can see, within the current the total available vehicle capacity was utilised only during 5% of the total time. What allows for a high service quality.
Fig. 7. Vehicle Activity • the number n of vehicles in service.
These two parameters have an impact on almost all statistical indicators we may observe through simulations. 5.1 Service Quality Indicators (SQI) Three classes of statistical indicators, characrerising the system behaviour, can be defined: (1) SQI strongly positively correlated with each other. For this category, it suffices to retain only one statistical measure. This is the case of the customer waiting time and the client queue length at a node. (2) SQI which are independent and can only be directly observed. Thus, clients who have not found an appropriate vehicle during their maximal waiting period are only reflected by the abandonment rate since they left the system prematurely. (3) In addition, some indicators are conflicting and therefore they must be monitored simultaneously in order to achieve a reasonable trade-off: for example, increasing n will obviously improve all service quality indicators from the client point of view. At the same time, the average taxi activity will be reduced, which in return will increase all related costs and consequently fares.
1 passenger – 32%
0 passenger – 2%
2 passengers – 33%
5 passengers – 4%
4 passengers – 9%
3 passengers – 20%
Fig. 6. Taxi Occupancy Vehicle Activity
Choice of SQI
As Figure 7 illustrates cars
During this study, the following three indicators are retained:
• circulate on network links for the 88% of the time, • are stopped at nodes for interacting with passengers during 9% of the time, • are parked at an empty state for the 3% of the time.
x : the average abandonment rate over the whole network y : minus the average number of clients transported per taxi during a 8 hour simulation z : the average total diversion ratio.
5. PARAMETER TUNING
• Indicator z is related to clients who effectively reached their desired destination. It incorporates two service quality indicators: the initial client waiting time and the amount of diversion of their effective journey compared to the direct trip. • x accounts for the clients who finally gave up the system.
Two important parameters are integrated into the study of “collective cars” performance: • the threshold s which limits diversion in the decision algorithm related to the client acceptance or rejection by a given vehicle 86
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• Both previous measures certainly improve (i.e. decrease) as the number of taxis in service n, increases; therefore, −y should be monitored to relativize this improvement. The minus sign has been included in order that, for all three indicators x, y, z, “better” is equivalent to “smaller”.
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2D representation of the surfaces in the (x, y) plane while the z coordinate is represented by its level curves. The level curves are indicated in square boxes in Figure 9. The points chosen on each surface are located on the level curve 1.7 (that is, both achieve an average total detour ratio of 1.7) and they also both achieve a global abandonment rate (x coordinate) of 1%. However, the corresponding average number of transported clients per vehicle y is greater with the centripetal geometry (about 30 clients for simulations corresponding to 8 hours of real time) than with the centrifugal (only about 28.5). This is consistent with the fact that more vehicles are needed with the centrifugal demand to achieve those performances (3, 910 versus 3, 744). Finally, a different value of s is also needed: 1.98 versus 2.1.
5.2 Methodology Adjusting Parameter Values As previously discussed, three SQI measures x, y, z are chosen depending on two parameters s and n. We seek values of these parameters inducing values of x, y, z as small as possible. Hence, all reachable values of x, y, z lie on a 2D-surface in a 3D-space. A point has to be chosen lying on the lower left-hand border of this surface. This choice is not unique (Pareto optimality) and reflects the relative importance assigned to each indicator. Nevertheless, when two surfaces corresponding to two different situations (e.g. two geometries of demand) can be compared with respect to the positions of their lower left-hand borders, one can ascertain which one is the most favourable for the performance of the system.
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29
In what follows, a methodology of analysis comparing two demand geometries is illustrated.
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5.3 Comparison between Centripetal and Centrifugal Demands 31
A series of simulations is implemented for two demand geometries, a centripetal and a centrifugal demand, when varying values of s and n. In Figure 8 the red (lower) surface corresponds to the centripetal demand while the green surface is associated with the centrifugal demand. Both demands are of the same intensity and amount of imbalance (they correspond to reversed travels of clients from origins to destinations).
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Average number of clients transported per taxi (8 hour sim.)
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1.7
s = 1.98 n = 3910 1.8 1.7
s = 2.1 n = 3744 1.8
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Fig. 9. Centripetal-Centrifugal 2D demands
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tio ersion ra Total div
.) ents f cli our sim h ber o num r taxi (8 e rage Ave orted p sp tran
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6. CONCLUSION-FUTURE WORK
1.4
An efficient transportation mode is often perceived as an important support contributing to the numerous requirements of urban productivity. Public transport often is inadequate for daily metropolitan mobility and private car remains consumer’s first choice preserving confort and convenience. Therefore, cogestion is implied accompanied by difficult driving conditions and consequently raised accidents rates. Classical taxis could be a successful solution if only they were more affordable. Exploitation of the vehicle capacity within an accessible flexible system could be a promising idea to be explored, reducing transportation costs, limiting congestion and energy consumption. Systems like car sharing do not necessarily diminish the
(%) t rate nmen 2 bando
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One can conclude that the centripetal geometry of demand in a network having a topology inspired by the Paris metro plan, tending to accumulate vehicles towards the city center, is more favorable than the centrifugal one, which tends to disperse taxis toward the suburbs. Obviously, other topologies may lead to different conclusions (work not included in this paper).
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Fig. 8. Centripetal-Centrifugal 3D demands For each of the two scenarios, a particular point on the corresponding surface is chosen in such a way that two of the three coordinates of those points are equal. We search for a difference over the third one. In order to facilitate the study, Figure 9 will be utilized illustrating a 87
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passenger to vehicle ratio often followed by a poor spatial distribution. Carpooling schemes require passengers to administer the related arrangements (inevitably time consuming tasks) while vehicle itineraries are not necessarily optimised.
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This paper suggests an autonomous DRT system, reducing commuter fares while assuring a quick delivery to destinations. A decentralised approach is studied, requiring only local information where each vehicle management is optimised independently of the others. Some other principal differences from the existing structures consist in an autonomous system operation, no requirement for prior seat reservation is any more necessary while the entire network is served and not only some specific areas. The related transit problem is studied from a DES approach. Thus, association of Optimisation and Operational Research methods combined with advanced simulation techniques will lead to an optimal system functioning and desired tradeoffs. Specific control designs allocate customers to vehicles while the vehicle itinerary is dynamically optimised every time its state changes. Moreover, management of empty vehicles improves the system productivity while additional car costs are diminished. Since a whole category of decision algorithms can be conceived (in addition to the ones proposed in this study) a methodology evaluating the system performance according to the currently utilised scenario is discussed. Hence, client and vehicle metrics are presented such as client waiting times, abandon rates and detours, vehicle occupancy and activity etc. At present, more sophisticated control policies related to client acceptance are about to be developed taking into consideration the stochastic demand model. Aiming at an optimised system performance, all vehicle decisions are provided by associated algorithms taking into consideration the current system state. A transportation mode involving fully autonomous electric cars, where information technologies will be incorporated coordinating vehicle control and decisions, tuning and timing trips, can increase operational efficiency. Such a vehicle structure would also contribute to a successful management when recurring and non-recurring congestion, safety (human error constitutes a major factor to accidents) while it controls additional energy consumption. Many successful demonstrations and studies, on fully autonomous electric cars, are conducted in the USA and Europe, Tesla Motors (2016), Report-UK (2015) while current research investigates the problem of efficient risk resolution. Since present traffic regulation still prohibits entry of fully autonomous vehicles in traffic, specific road infrastructure and geometry design could be envisaged amongst other eventual possibilities as a first step towards an efficacious, innovative and accessible future transport mode. REFERENCES Baccelli, F., Cohen, G., and Gaujal, B. (1992). Recursive equations and basic properties of timed petri nets. Journal of Discrete Event Dynamic Systems, 2, 415–439. Ciari, F., Balmer, M., and Axhausen, K. (2009). Large scale use of collective taxis: a multi-agent approach. In 12th International Conference on Travel Behaviour Research. Jaipur, India. 88