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A framework for simulating large-scale complex urban traffic dynamics through hybrid agent-based modelling

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A framework for simulating large-scale complex urban traffic dynamics through hybrid agent-based modelling
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  A framework for simulating large-scale complex urban traffic dynamicsthrough hybrid agent-based modelling Ed Manley a,d, ⇑ , Tao Cheng a , Alan Penn b , Andy Emmonds c a Department of Civil, Environmental and Geomatic Engineering, University College London, London, UK  b Bartlett School of Graduate Studies, University College London, London, UK  c Network Performance, Traffic Directorate, Transport for London, London, UK  d Centre for Advanced Spatial Analysis, University College London, London, UK  a r t i c l e i n f o  Article history: Received 9 August 2012Receivedinrevisedform11November2013Accepted 12 November 2013 Keywords: Agent-based simulationUrban complexityHuman cognitionCollective phenomenaTraffic flowHybrid simulation a b s t r a c t Urban road traffic dynamics are the product of the behaviours and interactions of thousands, often mil-lions of individuals. Traditionally, models of these phenomena have incorporated simplistic representa-tions of individual behaviour, ensuring the maximisation of simulation scale under given computationalconstraints. Yet, by simplifying representations of behaviour, the overall predictive capability of themodel inevitably reduces. In this work a hybrid agent-based modelling framework is introduced thataims to balance the demands of behavioural realism and computational capacity, integrating a descrip-tive representation of driver behaviour with a simplified, collective model of traffic flow. The hybridisa-tion of these approaches within an agent-based modelling framework yields a representation of urbantraffic flow that is driven by individual behaviour, yet, in reducing the computational intensity of simu-latedphysical interaction, enables the scalable expansionto large numbers of agents. Areal-world proof-of-concept case study is presented, demonstrating the application of this approach, and showing thegains in computational efficiency made in utilising this approach against traditional agent-basedapproaches.Thepaperconcludesinaddressinghowthismodelmightbeextended,andexploringtherolehybrid agent-based modelling approaches may hold in the simulation of other complex urbanphenomena.   2013 Elsevier Ltd. All rights reserved. 1. Introduction It may be said that urban systems are a function of the behav-iour of its citizens. Whether one is concerned with short-term orlong-term dynamics, the actions and interactions of thousands,possibly millions of individuals shape the way in which urban sys-tems change and evolve. Throughthe decisions and activities of itscitizensacity’scomplexdynamicstructureis defined, transformedand disintegrated. While institutional interventions can play a rolein constraining and influencing behaviours, urban systems – interms of transportation, migration, economics, and a swathe of other phenomena – remain strongly influenced by the actions of the collective. Therefore, understanding this link between themicroscopic behaviour of individuals and complex macroscopicpatterns in the city is central to predicting how urban systemsmay shift and respond to new events and influences.Attempts to understand and predict urban transportationdynamics have been on-going for some considerable time, with agreat deal of research and development being carried out withinthe field of traffic simulation. However, representations of driverbehaviour have generally followed a consistent path. The vastmajority of conventional traffic simulation tools – be them micro-scopic, macroscopic or agent-based in focus – replicate the princi-ples of equilibrium in traffic distribution as described by Wardrop(1952). According to this principle, individuals will always seek toreduce their journey time, until no vehicle may reduce their own journey time unilaterally. This principle carries an underlyingassumption that all individuals maintain a complete knowledgeof the roadnetwork, and knowledgeof the prevailingtraffic condi-tions upon it. It furthermore assumes that the minimal journeytime route will always be selected by the individual regardless of alternative preferences or an inability to do so. This approach en-ables the distribution of traffic to be managed from a macroscopicperspective, assigning traffic according to an optimisation of jour-ney times and calculating traffic flows according to the level of traffic saturation of each link. As a result this approach is mathe-matically tractable and computationally efficient, meaning it canbeextendedtoawidespatialareaandlargenumberofindividuals.The approach remains popular and is widely used by city planners 0198-9715/$ - see front matter   2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.compenvurbsys.2013.11.003 ⇑ Corresponding author. E-mail addresses:  Ed.Manley@ucl.ac.uk (E. Manley), Tao.Cheng@ucl.ac.uk(T. Cheng), A.Penn@ucl.ac.uk (A. Penn), Andy.Emmonds@tfl.gov.uk (A. Emmonds). Computers, Environment and Urban Systems 44 (2014) 27–36 Contents lists available at ScienceDirect Computers, Environment and Urban Systems journal homepage: www.elsevier.com/locate/compenvurbsys  in the prediction of traffic flows across cities worldwide (Aimsun,2012; PTV, 2012).Yet the aforementioned underlying assumptions proffered bythese models do not fall in line with conventional thinking fromthe fields of spatial cognition and psychology in respect to humannavigation in urban areas. Rather, it has been demonstrated thatindividuals rarely do take a least journey time path from srcinto destination, as their ability to identify such a path is limited(Golledge, 1995; Wiener, Schnee, & Mallot, 2004; Zhu & Levinson,2010),andarehighlyunlikelytomaintainacomprehensiveknowl-edge of the road network structure, instead being bounded by anindividual’s prior experiences and their ability to remember theworld around them (McNamara, Hardy, & Hirtle, 1989). It is evi-dent,therefore,thatinordertomorecompletelyandcorrectlypre-dict the evolution of the traffic system, particularly in respect tothe formation of congestion, one must better represent the truenature of driver behaviour on the road network.With respect to this challenge, agent-based modelling (ABM)represents a highly promising platform for the representation of macroscopic phenomena as a product of individual behaviour. Bymodelling individually the most significant influencing elementsof a system, ABM enables one to examine how the behaviours of individual entities impact in influencing global patterns, movingbeyond any impositions of an assumed equilibrium state. Further-more, in enabling the representation of a populationof agents, onecan explore how inter-population heterogeneity can shape globaldynamics. This discretisation of the modelled scenario allows thericher representation of the behaviours impacting within a givenscenario,andthusenablespotentiallyamoredetailedexaminationof system-level outcomes. This approach has been used in the pre-diction of wide number of urban phenomena, notably land-usedynamics (Bretagnolle & Pumain, 2010), housing (Schelling, 1978), crowd movements (Torrens, 2012) and crime patterns (Malleson, See, Evans, & Heppenstall, 2012). In each of theseexamples, macroscopic patterns emerge through the interactionsof many autonomous constituent individuals. Within the contextoutlinedinthiswork,agent-basedmodellingrepresentsapotentialroute forward in the simulation of global traffic dynamics as aproduct of the behaviour of multiple individual drivers.Yet there exists an important challenge that must be consid-ered in the development of any agent-based simulation. This isthe challenge of managing limited computational resources. In-creased model complexity, with increased numbers of agentscan potentially lead to significantly rising memory usage and sub-sequent processing speeds. In many cases, particularly wherelarge-scale models are required, or results required at a nearreal-time basis, such performance levels may be prohibitive(Castle & Crooks, 2006). This challenge is particularly pertinentwhere considering the prediction of traffic flows within the urbanrealm. In these cases, the agents are complex, they are cognitivein their actions, and within the agent population there will be alarge degree of heterogeneity in individual preference, knowledgeand behaviour. Such representations will also require the simula-tion of thousands, possibly millions of cognitive individuals acrossa large spatial scale. Equally, a simulation must capture the roleof physical actions and interactions between agents on the road-way, as it is at this level where frictions occur and congestionultimately begins. Therefore, in coping with this level of complex-ity, one must carefully consider the deployment of computationalresources, specifically the relative importance of simulating infine detail (or otherwise) each aspect of the simulated scenario.Traditionally, modellers have been left with the decision of modelling many individuals in little detail or few individuals withhigh levels of detail.This paper presents a framework for an agent-based model of urban traffic flow that maintains a high degree of behaviouralcomplexity, acrossawidespatial scale, whilstremainingcomputa-tionally efficient. To achieve this agents are granted advanced cog-nitive abilities, but are constrained in their movement behavioursbya macroscopicmodel of trafficflow. Inincorporatingthe impor-tant capabilities of agent-based modelling in more fully represent-ing the behaviour of a population of individuals, this work aims tomove beyondexisting trafficsimulation models that model behav-iour in a simplistic fashion.Thepaper is presentedasfollows. Inthenext chapter, anexplo-rationoftherelevantliteraturethathasinformedthedevelopmentofthisframework–bothintermsofdriverbehaviourandroadwaydynamics – is laid out. Following this, the modelling framework ispresented in depth, detailing how both the behavioural and phys-ical models are implemented, before outlining how these modelsare integrated. Following this a real-world case study is presented,describing an application of the frameworks outlined here, withthe computational performance of the model assessed against atraditional agent-based modelling approach. The paper concludesin highlighting the ways in which this approach may hold widersignificance for existing agent-based modelling research, particu-larly research into complex urban systems, and identify ways inwhich this framework may be developed in the future. 2. Literature review As described above, much of the conventional thinking sur-rounding the simulation of urban traffic flow follows clear princi-ples of how a traffic system arranges itself. Agent-basedmodelling potentially offers a way forward in the more accuraterepresentation of the behaviours that contribute to the evolutionofsuchsystems. Thefollowingreviewfirsthighlightsrecentdevel-opments with respect to conventional transportation modelling,before addressing the application of agent-based modelling to-wards transportation simulation, and specifically the relative ben-efits it offers toward this domain.  2.1. Conventional road transportation simulation Conventional simulations of traffic flow have traditionally con-sisted of two core models of driver behaviour – one describing in-ter-vehicular dynamics on the roadway, the other describing thedistribution and route selection of vehicles across the entire net-work. The nature of traffic simulation is usually defined in termsof howthe former of these two processes is represented – broadly,from either a microscopic or macroscopic perspective – with thelatter process following principles common to both approaches.Themicroscopicrepresentationoftrafficflowdescribesvehicleson an individual level, modelling movements and speeds on theroadway and interactions with other vehicles in a broadly realisticfashion. These models are able to effectively replicate commonroadway phenomena such as traffic jam waves (Helbing,Hennecke, Shvetsov, & Treiber, 2003) and junction-level conges-tion. While conceptually similar to agent-based simulation, thesemodels represent individuals in a broadly homogenous fashion,withbehaviouralheterogeneityintroducedonlythroughstochasticvariation. Alternatively, macroscopic traffic models do not seek toreplicate the movement of the individual vehicle but rather thecollective movement of traffic flow across the road network. Inorder to achieve this, equations simulating the collective impactof inter-vehicular friction and interaction are implemented, vary-ing in their scale and complexity. These models, derived fromphysics-based models of inter-molecular dynamics, are capable,in their most advanced form, of replicating physical phenomenaand behaviours observable in real traffic systems (Daganzo,1993; Helbing et al., 2003). Macroscopic models generally enable, 28  E. Manley et al./Computers, Environment and Urban Systems 44 (2014) 27–36   with a reduced complexity with respect to modelling movement,larger-scale simulation, involving a higher number of travellers,than possible with microscopic models.Despite the converse approaches taken towards the physicalrepresentationoftrafficdynamicsontheroadway,bothsimulationperspectives followa single general approachtowards driver routechoice and traffic distribution. Whether the actual method em-ployed is macroscopic (such as Dynamic Traffic Assignment ( Jans-son, 1991)) or microscopic in perspective (such as Stochastic UserEquilibrium (Daganzo & Sheffi, 1977)), conventional traffic distri- bution models seek to achieve a network-wide equilibriumin traf-fic flow. In seeking to attainthis state, theseapproaches mayall bedescribed as theoretically macroscopic in perspective. Underlyingbehavioural assumptions intrinsic within these techniques are, asdescribedearlier,limitedandmaythusbeproblematicinfullypre-dicting network-wide traffic flow.Yet, issues with respect to the underlying description of driverbehaviour do not fully exclude these models from being of someimportant benefit. Models of physical traffic interaction along theroadway can effectively describe the link between vehicle densityandlocalcongestionformation.Usingestablishedrelationshipsbe-tween traffic flow, density and speed (Lighthill & Whitham, 1955;Richards, 1956), one is able to derive a volume–delay function,describing how delay increases with rising traffic volume. Thisrelationship represents a mathematically simple method for link-ing between on-route demand and subsequent traffic flowthroughput on the roadway.Thesemodels of traffic dynamics, althoughusedpredominantlywithin the process of traffic assignment, have also previously beenappliedinthemodellingoftrafficflowonindividualroads.Intheseinstances, microscopically-driven models of traffic distributionhave been combined with these macroscopic representations of traffic flow dynamics to form an alternative ‘mesoscopic’ trafficsimulation approach ( Jayakrishnan, Mahmassani, & Hu, 1994;Mahmassani, 2001). These models, however, in continuing toincorporate relatively simplistic representations of individualbehaviour, exhibit many of the limitations observed in all micro-scopictrafficsimulationmodels.Theassumptionofequilibriumre-mains central to these approaches. The model presented in thispaper represents a step forward on from these representations.  2.2. Agent-based modelling for road transportation There has been a considerable growth in interest in the use of agent-basedmodellingfortransportationapplicationsoverthelast10 years. This has in part been brought about by an increasing rec-ognitionthat thegreater discretisationandpopulation-level heter-ogeneity presented by agent-based modelling leads to a morerealistic representation of on-the-ground activities. Agent-basedmodelling holds the potential to move beyond traditional assump-tionsoftrafficequilibrium,buildingtrafficpatternsfromindividualbehaviours upwards. In spite of the potential within these ap-proaches, developments within this field have been broadly con-strained within the dichotomy described earlier, concerning theplay-off between high behavioural complexity and wide areaapplicability.With respect to agent-based models with high scalability –thosecapableofsimulatingdynamicsacrossawidearea–themostsignificant developments consist of models to represent whole,multi-modal transport systems, such as the TRANSIMS (Smith,Beckman, Baggerly, Anson, & Williams, 1995) project and morenotably MATSim (Balmer et al., 2009). These models representmanyaspectsoftransport-relatedbehavioursthroughagent-basedrepresentation across a large spatial area. This approach enables amore intuitive relationship between trip generation and transportmode selection behaviours, linking choices at the individual-levelratherthanaggregatingintospatialzones,asdoneusingtraditionaltransport modelling approaches. At the other end of the scale – attheroadnetworklevel–acellularautomata-basedqueuingsystemis implemented(Nagel & Schreckenberg, 1992), allowinga replica- tion of queuing phenomena on the roadway. However, given thesemodels’ objectives to represent transport flows across a wide spa-tial area – something successfully achievedby MATSimin the sim-ulation of traffic across the whole of Switzerland, some 7.3 millionagents (Waraich, Charypar, Balmer, & Axhausen, 2009) – there hasultimately been some necessary simplification of individual-levelchoice behaviours. This is noticeable with respect to the individualrouteselectionprocess,wheremodelsbasedontrafficequilibrium,describedearlier,areimplemented.Heterogeneityamongtheagentpopulation is introduced through random error functions ratherthan any consideration for actual population variation (Zheng,Waraich, Axhausen, & Geroliminis, 2012). These representationsofbehaviour,whilecomputationallyefficient,areinadequatelyrep-resentative of observed behaviours, a point noted by lead develop-ers of MATSim (Nagel & Flötteröd, 2009). As was highlighted earlier, one of the key advantages of agent-based modelling is that it enables the representation of a highlybehaviourally complex and heterogeneous population of agents.Alternative efforts to employ agent-based modelling within thetransportation domain have therefore sought to capitalise on thesebenefits, developing sophisticated representations of behaviour.With respect to the representation of driver behaviour, many suchmodels have sought to incorporate cognitive architectures – suchas BDI (Beliefs–Desires–Intentions) and ACT-R (Adaptive Control of Throught-Rational) – within a representation of individual behav-iour (Rossetti et al., 2002; Wahle, Bazzan, Klugl, & Schreckenberg,2000;Salvucci,2006).Yetsuchimplementationshavegenerallycon-sidered only low-level vehicular interactions and behaviours, withlittle detailed consideration for strategic, choice-oriented behav-iours.Othermodelshavegenerallyalsoconcentratedonthedetailedrepresentation of low-level inter-agent dynamics, such as anticipa-tory behaviour and norm violation at junctions (Doniec, Mandiau,Piechowiak, & Espie, 2008), car following (Dai & Li, 2010) and lane changing behaviours (Hidas, 2002). While these developments are significantinthattheyapproachtherepresentationofagentbehav-iourfromamorecognitively-realisticperspective,theyagaindonotconsider the important strategic and choice behaviours that influ-ence wider network dynamics. Of greatest importance with respectto these models, however, is that the representation of all feasibledriver behaviour in such detail is computationally very expensive.This means that these approaches are effectively prohibited fromrepresenting many agents within one simulation, and thus limitedtosmall area representation of transport dynamics.Recent developments in agent-based modelling for transporta-tion have demonstrated that modellers face the familiar challengeof dividing computational resources between simulation volumeand behavioural complexity. The effective simulation of wide areatransport dynamics, however, requires the implementation of both. Agent-based modelling clearly has a great deal of promisewith respect to the representation of individuals on transport net-works, however it is important that computational load is effec-tively managed in order to maximise scalability. In this respect,conventional models of traffic flow offer some promise, while lim-itedincertainaforementionedrespects,suchmodelsarecapableof simulating wide spatial areas incorporating many individuals. 3. A hybrid agent-based modelling framework for traffic flowsimulation From the literature review, two important findings are appar-ent. Firstly, despite the proliferation of the usage of agent-based E. Manley et al./Computers, Environment and Urban Systems 44 (2014) 27–36   29  modelling within the transportation domain, there exists no cur-rent model that is able to simulate driver behaviour in a detailedfashion at a highly scalable level. Furthermore, while conventionaltrafficsimulationsfallshortinadequatelydescribingdriverbehav-iours, they have been proven to be highly capable of simulatingtransport dynamics across wide spatial areas involving manyindividuals.The next section combines the findings from both parts of thisreview,describinganewframeworkforthedevelopmentofamorebehaviourallydescriptiveyetcomputationallyefficientrepresenta-tionoftrafficphenomena. Inlinewiththeaforementioneddivisionbetween behavioural and physical models of traffic dynamics, ourmodel maintains the same structure. In our representation, how-ever, agent-based modelling is employed to more completely de-scribe the behaviour of a population of cognitive agents, withmacroscopic-level traffic dynamic models utilised in constrainingthe movement of agents around the road network. The combina-tionofbothofthesecomponents–theformerofferingbehaviouralcomplexity, the latter reducing the load inherent in computingmovement and interactions – represents a novel development.  3.1. Agent-based driver behaviour framework The wayinwhichindividualsbehaveontheroadnetwork–theroute they select, the time they depart, their planneddestination–are fundamental in establishing the nature of network-wide trafficdynamics.Inmanyways,thesebehavioursarepredictable.Onecanidentify the end result of these interactions on a day-to-day basis,simply by observing where road congestion commonly arises. Yet,under certain circumstances, when the network changes in re-sponse to an incident or shock, when individuals are forced intonon-habitual behaviour, the influence of these actions is all themore important. It is therefore vital that, within a model of trafficdynamics, one fully embraces the full extent of behaviours thatmay influence these systems.In this section, we firstly examine some recent research intoindividual routing behaviour within the urban realm, and identifyhow these elements may contribute in better explaining collectivemovement patterns. Through this process a framework of driverrouting behaviour, better aligned with conventional theory in cog-nitive and neuroscience, is established.Over the past 50 years, a great deal of researchhas beencarriedout within the fields of spatial cognition and psychology to morecompletely identify the methods by which individuals movethrough the urban realm. This research can be divided into twointertwined strands – the nature and existence of an individual’scognitivemapofalocation,andthemethodbywhichanindividualselects aroutethroughagivenspace. The existenceof the first ele-ment in this equation – the cognitive map – was raised by Tolmanin 1948 (Tolman, 1948). The cognitive map is a personal, incom-pleteandsubjectivementalrepresentationoftheworld,influencedstrongly by experience and non-Euclidean in construction. It hasbeenidentifiedtoresidewithinthehippocampus(O’Keefe&Nadel,1978), and has been proven vital in the task of human orientationand navigation. Further developments by Lynch (1970) and others(Kuipers, 1978; Tomko, Winter, &Claramunt, 2008) havesought toidentify a relationship between architectural and urban structuresand the nature of spatial knowledge. This research has led to thebroadly held view that spatial knowledge may be deconstructedintothreefacets–routes(pathandroadfeatures),landmarks(sali-ent features) and a survey knowledge (an image of the environ-ment) (Montello, 1998). Due to the subjective nature of  knowledge, a hierarchy naturally develops over time, meaningmore personal, salient features appear more prominently withinan individual’s cognitive map (McNamara et al., 1989; Pailhous,1970; Passini, 1981). It is clear that, in seeking to understand therelationship between driver behaviour and the distribution of traf-ficflow,particularlyinresponsetoroadcongestion,onemustmorefully incorporate heterogeneity in spatial knowledge within thepopulation of modelled individuals.An individual’s knowledge of space is highly influential in theselectionofaroutethroughanurbanarea,yetitishowthisknowl-edge is used that determines the exact path used. A significantamount of additional research has also been carried out in identi-fyingthe techniques bywhichindividuals select routes throughanarea. Findings vary with respect to the exact method, but there isapparent agreement within the literature that individuals employa heuristic approach to route selection, minimising cognitive loadin their planning (Passini, 1981). While the shortest distance path – widely employed within conventional transport models – isnoted as an important factor in route selection (Golledge, 1995), anindividual’sabilitytoidentifythisexactpathishighlyquestion-able. Instead, alternative route choice heuristic representationshave noted that individuals may select routes according to a re-gion-by-regiontypeapproach(Wiener&Mallot,2003),areduction in number of decision points on route (Wiener et al., 2004), or selectionofthestraightestpathtowardsthetarget(Conroy-Dalton,2001; Hochmair & Frank, 2002). This latter process of maintainingminimal angular deviation has been highlighted elsewhere as animportant facet in route selection (Hillier & Iida, 2005). In line with the definitions identified within the literature, arealistic representation of the driver decision process must incor-porate three key elements – the presence of a distinct and con-strained spatial knowledge, a preference mechanism for routeselection and consideration of any additional, non-cognitive ele-mentsthatinfluenceroutingbehaviour(e.g.avoidanceoftolls,ten-dencytochangeroute,usageofnavigationdevices).Inthisrespect,these three elements may be encapsulated according to the con-ceptual representation of behaviour described in Fig. 1.Thisrepresentationdescribesonlytherelationshipbetweenthekey elements of behaviour, not necessarily ascribing how thesebehaviours may be exactly specified. Defined in this way, an agentcreates a route plan according to an innate preference mechanism(definedaccordingtomethodsdescribedabove), basedonapartialandsubjectiverepresentationofspatialknowledge.Thisrouteplanis selected at the start of a journey but may be revised en-route inresponse to changing network conditions or priorities. The agentmay, furthermore, be influenced by additional factors. These as-pects may include route restrictions, information utilisation andnavigation advice.The inclusion of this level of behavioural detail within anagent-basedmodel,withalargenumberofautonomousandheter-ogeneous individuals, represents an important computationalchallenge. A complex route selection process combined withindependent spatial knowledge and supplementary behaviour atthe level of the individual potentially requires a large amount of computation. The following section describes how elements of  Fig. 1.  Conceptual representation of driver behaviour.30  E. Manley et al./Computers, Environment and Urban Systems 44 (2014) 27–36   oursimulationplatformaresimplifiedtoallowustomaintainhighbehavioural complexity with acceptable levels of computation.  3.2. Macroscopic model of roadway traffic dynamics As was described earlier, within many conventional agent-based models, the movement of individual agents is modelledexplicitly. Simulating agent interactions and movement behav-iours can become, over a large number of individuals, costly. Mac-roscopic models of traffic flow have been shown to significantlyreduce the computational load of this process. In the case of ourhybridsimulationplatform,trafficdynamicsoccurringoneachlink(alink, or segment, ofroadconsistsof thesingledirectedstretchof road between two junctions) of the road are instead governed bymacroscopic principles of traffic flow describing the relationshipbetween traffic volume and delay. Rather than calculating themovements and dependencies between multiple agents, a simplecalculationis made at the roadwaylevel andapplied to all affectedagents.The approach employed here represents the relationshipbetween traffic saturation and resulting journey time. Simplyput, individual travel time along a link is reduced when othersare also trying to do the same. The most widely used of thesefunctions is the BPR (Bureau of Public Roads) volume–delay func-tion. According to this formulation, travel time is calculated asfollows: t  a  ¼  t  0 a  1 þ a  q a C  a  b !  ð 1 Þ where  t  a  is the calculated travel time on link  a ,  t  0 a  is free flowtraveltimeonlinka(length a /speed limit 0 a ),  q a  is trafficflowonlink a ,  C  a  ismaximum inflow capacity on link  a  and  a ; b  is parameters cali-brated for network.In effect, travel time becomes a function of present traffic satu-ration,theproportionofcurrenttrafficflow( q a )inrelationtomax-imum allowable inflow ( C  a ). So travel time increases above freeflow as saturation approaches unity. Where saturation exceeds 1,the formula is modified to include an additional element, increas-ing the influence of oversaturated traffic flow: t  a  ¼  t  0 a  1 þ a  q a C  a  b ! þ ð q a    C  a Þ   d  ð 2 Þ where  d  is the parameter calibrated for network.These calculations are applied for an individual road segment,andtheassociatedparameterscalculatedaccordinglytothenatureof the road network (e.g. urban, suburban, rural, motorway etc.).Traffic can continue to be added to a road segment until the abso-lute road capacity ( Q  ) is reached. This figure represents the maxi-mum number of vehicles, assumed to be of an average 4m inlength, which may feasibly fit on the road segment (e.g. bumper-to-bumper).  3.3. Hybrid agent-based traffic simulation The two models – describing drivers’ behaviour and trafficdynamics – are integrated within an encompassing agent-basedmodelling framework. The model is essentially driven by thebehaviour of driver agents, with their intentions to move acrossthe road network and to complete their journey driving the simu-lation. Driver agents select a route between their srcin and desti-nation, and attempt to complete this journey. Driver movement iscontrolled by the characteristics of the road network. With respectto the constraint of movement, roadsegments are modelledas vir-tual agents – independent in controlling local dynamics, yetconnected within a network of other road segment agents. Duringthe simulation, the segment agent will accept a driver (providingthere is available capacity) and prevent its progression to its nextdestination segment based on ensuing local dynamics. In thissense, road segments constrain the progression of driver agentsacross that stretch of road, according to the traffic rules governingtravel time and saturation.Thenatureoftheinteractionsbetweendriverandroadsegmentagents is outlined below. During the course of a journey, driversmake numerous autonomous decisions, yet their progression iseffectively dependent upon a number of road agents. Agents aregenerated initially in accordance with an external srcin to desti-nation trip matrix, with trip departure time spread linearly acrossthe time period specified by the trip matrix. The processes in-volved, describedbelow, are checked for executionat eachsimula-tion time step.1. Drivercreation:Driveragentcreatedandassignedanoriginand destination, a departure time, a level of spatial knowl-edge, route preference mechanism and any additionalparameters that are being incorporated at the level of theindividual driver.2. Route selection: At the departure time, a driver agent isactivated at its srcin location. A route is selected from ori-gintodestinationandstoredbythatagent.Therouteselec-tion process may take any form(i.e. shortest distance, leastturns, or least time path) and is discussed in more detail inthe next section.3. Joininga road: Driver requests tojointhe initial road. If theroad is not at absolute capacity (e.g. maximum number of vehicles that may be contained on that road) then driver joins road and is added to end of road segment agent’s dri-ver list. Road traffic inflow(calculated as traffic inflowdur-ing the previous minute) is incremented, saturationrecalculated based on newconditions, and the arriving dri-ver is provided with a travel time calculated according tocurrent conditions using formulae (1) and (2). This timespecifies the expected time of departure, based on the cur-rent conditions on the road segment ahead of them, fromthe current road segment. The individual driver will thenremain on this segment until their departure time isreached. No further calculations pertaining to the agent’smovementacrossthelinkaremadeuntiltheagent’sdepar-ture time.4. Road handover: When the driver’s road travel time hasexpired (i.e. it has reached the next junction), the driverseeks to move between its current and next road (asdefined within its route plan). These requests to movebetween roads are handled in the order that the driver ini-tially arrived on the segment, maintaining a queuing struc-ture. If agent’s next road segment is uncongested andavailable then they will join it at the next simulation timestep, following the procedure detailed in step 3 for thatroad segment.In congested environments, when a driver at the front of the queue is unable to make the transition to the next roadduetoitbeingatabsolutecapacity(e.g.theroadsegmentisfully congested and may accept no further vehicles), thenthey must wait on the current road. This causes all otheragentsbehindtheminthequeuetobedelayed,asnotrafficmay leave the roadway until the vehicle at the front of thequeue leaves first. In these situations, a queue will thenbuild on this roadway until the absolute road capacity ( Q  )is reached at which point no further vehicles will beallowedto jointhe trafficqueue. It is throughthis principlethat road congestion propagates across the road network. E. Manley et al./Computers, Environment and Urban Systems 44 (2014) 27–36   31
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