Dynamics and Stochasticity in Transportation Systems: Tools for Transportation Network Modelling

345 Pages·2020·9.657 MB·English

by  Giulio Erberto Cantarella, David Paul Watling, Stefano de Luca, Roberta Di Pace

Dynamics and
Stochasticity in
Transportation
Systems
Dynamics and
Stochasticity in
Transportation
Systems
Tools for Transportation
Network Modelling
Giulio Erberto Cantarella
David Paul Watling
Stefano de Luca
Roberta Di Pace
Elsevier
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Contributors
Giulio Erberto Cantarella
University ofSalerno, Salerno, Italy
RobertaDi Pace
University ofSalerno, Salerno, Italy
Stefano de Luca
University ofSalerno, Salerno, Italy
David PaulWatling
Institute for TransportStudies, University ofLeeds, Leeds, United Kingdom
ix
Preface
Dissidenceandcontroversyarewhatbringscienceforward.
Agreementandacceptancerarelystimulateexperimentsandprogress.
ThorHeyerdahl.
Outline.Inthischapterthereadermayfindthecontentsandthepurposeofthisbook,
andaframeworkgeneralenoughtoencompassalmostallTTTtools.Besidethereader
mayfindaproposalofnomenclature.Mainemphasisinthisbookisonthemathemat-
icalfeaturesofmodelsandalgorithmsfortraveldemandassignmenttoatransportation
network.Implementationandapplicationissueswillbethetopicsofafuturecompanion
book(possiblybyotherauthors)aswellascontrolanddesigntools.
Sincehuntinggatheringerahumanbrainshaveevolvedtobemoresensitivetovar-
iations in space and/or time of the surrounding environment rather than regularity
and uniformity; (mostly unconscious) representations of location over space and
evolutionovertimeallowedhumanbeingstosurviveinchallengingconditions.This
is stillthe case: apedestrianwishingtocrossaurban street tries toanticipateevo-
lution over time ofthe locations ofthe surrounding vehicles.
Developing a (mathematical) model of real systems, as common in modern
applied sciences,is a more conscious way tofollow that ancestral attitude.
Even though future were perfectly determined by past, according to Beowulf’s
wellknownstatement“Fatewillunwindasitmust!”(butnottoauthors’opinion),
stillitmaynotbeperfectlyforecastedduetolackofenoughinformationaboutpast,
touncertaintyaffectingforecastingmethods,….Thus,howeverdesirable,inseveral
casesaprecisemodelprovidingdeterministicdescriptionandforecastingofsystem
state cannot be developed, and the most general modelling tools include both
dynamic andstochastic featurestogetherwithspace characterisation.
Itshouldberemarkedthatanykindofrepresentationormodelmentionedabove
is, as beauty, in the mind of the beholder; therefore dynamics or stochasticity are
features of (mathematical) models only, a sort of social constructions agreed by
themodellercommunity,notbeconfusedwiththeobjectoftheirapplications,such
variations in space and/or time in a real system. Along this line of reasoning
observations of real worldare facts, whilst models are opinions about them.
Thefocusofthisbookistheuseofmathematicalmodellingmethodstoassist
in the understanding, prediction, policy assessment and design of transportation
systems; but what is a “transportation system”, or most pertinently what do we
mean by it for the purposes of this book? Firstly, it contains the infrastructure,
the pavements to walk on, the roads on which we cycle, drive or may use a bus
xi
xii Preface
ortaxi,thetraintracks,aswellasthefleetsofbuses,airplanesandtrainsthatare
used to run services and transport goods. Secondly, it contains the users of the
transportation system, namely the people who choose where, when and how to
travel, as well as the goods operators and suppliers who decide how and where
totransporttheirgoods.Thirdly,itcontainsthevariouspublicandprivateorgani-
sationsresponsibleforplanning,operating,pricing andproviding informationon
the infrastructure.
Sucha“system”containsmanyinteractingelements.Atravellermaydecideto
driveto theirnormalplace of work during a morebusy(congested)periodofthe
day than they would normally, and by doing so contributes additionally to the
congestionforthatday.Thiscongestionmaydelayotherroaduserswhoareusing
someofthesameroads,butperhapstravellingbetweenanentirelydifferentorigin
anddestinationtothefirsttraveller.Theadditionaldelayexperiencedmay,onthe
other hand, hold back the second traveller so that traffic is in fact more freely
running that it might be on some downstream stretch of road on their intended
route. This may cause the responsive traffic signals at an intersection to trigger
at a different time, and so influence some other travellers. On the other hand,
our second traveller has such a bad experience of travelling that day that they
decidestotryadifferentroutewhentheymakethattripnexttime,whereasthefirst
travellerdecidesthatre-adjustingtheirdeparturetimewouldbewiseinthefuture.
As this happening, a private transport operator decides to introduce a new high-
speedtrainserviceinthearea,whichourfirsttravellerthendecidestouseonsome
subsequentday,thusalleviatingsomeofthepressureonroadcapacity.Atthesame
time as all these interactions are on-going, each minute of every day, a transport
plannerisdecidingonhowtomakeadjustmentstoachievesomepolicyobjective,
andasaresultintroducesonsomesubsequentdayanewhigh-occupancyvehicle
lane for certain hours of the day.
This is only one example. Making sense of such systems is no simple task.
Mathematical models are a tool for capturing at least some of this complexity,
assisting those who are responsible for planning and designing such systems for
the ‘public good’. They allow location-specific data to be systematically used to
calibrate a model to particular locale. Importantly, the models that will interest
usinthisbookhaveaclearforecastingcapability,allowingthemodellertostudy
“what-if” scenarios. These scenarios may range, for example, from studying the
impactofpotentialfuturechangestotraveldemandpatterns,theeffectofalterna-
tive controlmeasures, or the impact of policy measures on travellers’ experience
and network performance.
These models are, in some respect, always wrong, as always the case in all
applied sciences. They always omit or over-simplify or incorrectly capture some
phenomenon,andsowhenusingthemitisalwaysimportanttobeasclearaspossible
on the limitations of the model, what it is not able to capture as well as what it is
representing. The modeller has the responsibility to communicate this to the
decision-maker,howevermuchthedecision-makermaynotliketohearit.Todothis
effectively, we believe we need a clear, standard reference system’ for dynamic
Preface xiii
transportation analysis, in order that particular models and model assumptions fit
into such a unified framework. Developing such a consistent and systematic treat-
mentisamajorgoalofthisbook,andthereforewetakesometimeandcareindefin-
ingandexplainingourterminology,assumptionsandconcepts,andhowtheserelate
to both the real-worldand to common methods used for modelling dynamic trans-
portationsystems.
1 Purpose of this book
Travelandtransportationplayacentralroleinthelivesofmostoftheworld’spop-
ulation.Transportationprovidesbothameansoftradeinmovinggoods,andaway
ofmovingpeopletoengageinemployment,education,socialandotheractivities.
Ifwehad observedthe samegeographicalareaoveraperiodofpastdecades, we
wouldlikelyhaveseenthatthesizeandstructureofemployment,productionand
residentialareashadchangedovertime,andthesechangeshadinturnchangedthe
requirements and pressures on the transportation system. At the same time, these
changes will have made environmental, social and economic impacts, some
positiveandsomenegative,withsomewinnersandsomelosers.Itisnaturalthen
toaskwhetherwecanholdamirrortothepast,anduseittoseeintothefuture;at
least then we may be able to react in a better way to the inevitable changes the
mirror shows us, and thereby as a society expend resources more efficiently (in
the sense of less negative and more positive impacts). It is only one more step
tothenrealisethatthemirroranalogyislimited,thatunlesswebelievethefuture
is pre-determined we may influence it by our actions, both as individuals and as
organisations. Understanding such influences and their likely consequences then
provides a way of not only ‘managing’ a transportation system more effectively,
but also positively engineering it to improve the lives of the people using it.
The current book fits into this wide area of ‘transportation planning’, and partic-
ularlythefieldoftransportationmodellingwhichaimstopostulatemathematical
systems that broadly approximate the changes and processes underlying such
phenomena.
Space and time are two intrinsically important aspects to understanding travel-
lers’needsandwhattransportationsystemscansupply.Letusfirstlyconsiderspace.
Thetypeanddensityofactivitiesarenotdistributedevenlyacrossacityorregion,
andtherearefixedgeographicalfeatures(rivers,mountains,valleys,etc.)thatinflu-
encethefeasibilityofdifferenttransportationoptionsacrossanarea.Dense,‘verti-
cal’residentialareasprovideverydifferentchallengestomoresparselydistributed
ones.Therealsocomplexinteractionsthatplayoutinthetransportinfrastructure;a
congestedroadorovercrowdedbusmaybepartiallytheresultoftravellersavoiding
overloaded facilities, meaning that a good solution will not be understood without
considering system-level interactions between the various travel needs of people/
organisations and the services and facilities which are provided. Over the last
50 years the transportation community has developed rather sophisticated ways of
xiv Preface
representing these kinds of spatialinteractions, typically by representing the infra-
structure as a network (mathematical ‘graph’), and by considering various levels
of sophistication in representing the behavioural responses of travellers (e.g. from
the perfectly informed traveller to random utility approaches). At the same time,
however, it should be mentioned that while the individual fields have developed
toahighlevel,itisrelativelyraretofindaconsistentintegrationofdemandmodel-
lingand networkmodelling.
Thereareratherwelldeveloped(ifnotalwaysconsistent)methods,then,forcon-
sidering‘space’;sowhatabout‘time’?Whiletraveltime,asadisincentiveinmaking
travelchoices,isacentralaspectoftransportationplanning,bytheword‘time’we
areinsteadreferringheretochangesthatoccurovertime(“dynamics”).Asthereis
considerable potential for confusion, let us very early on make a clear distinction:
changesona‘within-day’time-scalearethekindofchangesthatwewouldexpect
toseeaswemadeajourneyonaparticularday,orifwecomparedourtravelexpe-
riencewithsomeonetravellingbythesameroute/servicebutatadifferenttimeon
thatday(therearemanyotherwaystocharacterisethiskindoftime,buttheseexam-
plessufficefornow).Ontheotherhand,changesona‘between-day’time-scalecon-
cern,forexample,thewayinwhichwemightadaptourtravelchoicenexttimewe
makeajourney,basedonourtravelexperiencestoday.Whileresearchershavebeen
awareofboth‘within-day’and‘between-day’effectsforseveraldecades,itisonly
relatively recently that a concerted effort has been made to develop tools and
methodstoexplicitlymodelthem.Onthewithin-dayscale,thishasbeenachieved
by introducing and adapting methods from traffic flow theory for use in network
models.Onthebetween-dayscale,ithasinvolvedbringinginnewtechniquesfrom
bothappliedmathematics(fordeterministicdynamicalsystems)andprobabilitythe-
ory (for stochasticprocesses).
Thenewstudenttothisfieldisfacedwithanextremelychallengingtasktodigest
andassimilatethesedevelopments,withtheirvariousassumptions,approachesand
needtodrawondifferentaspectsofmathematics.Infact,itisalsoachallengeforthe
experiencedresearchertokeepfullyabreastofdevelopmentsinthisfield,aswithout
detailedreadingitisoftenunclearwhereanewpaperfitswithintheliterature,and
howitcomplementsoradvancespreviousdevelopments.Theintentionofthisbook
istobringtogetherthetheoreticalworkinthisfieldinaninternallyconsistentway.
Thismeansunifyingtransportationnetworkmodellingtheory,travelchoicetheory
andtrafficflowtheory,whiledrawingonrelevantmathematicalconceptsfromoper-
ations research, matrix algebra, dynamical systems, statistics and simulation. Our
intention is that the book is self-contained, so does not require additional reading,
althoughwesuggestfurtherreadingforthoseinterested.Inordertoassistusinthis
goalofbeingself-contained,wesupplyamathematicalsupplementwhichoutlines
the main mathematical ideas that we will draw on.
Apart from the pedagogical aim, to assist newcomers to the field, it might be
asked:whydowewishtosetoutaconsistenttheoreticalapproachtosuchproblems?
Whatadvantagedoesitgive?Oneanswermightthatitisapurelyaestheticobjective,
thathavingasingleunifyingtheoreticalframeissatisfyingpurelyinitsownright.
Preface xv
Certainly we would admit that personally we do find satisfaction in this aesthetic
quality,howeverwefeelthatithasmuchgreatersignificancethanthis,forseveral
reasons.Firstly,asweshallshow,itprovidesawayofusingtheorytoassesswhatwe
mightexpectfromapplyingsuchamodellingapproachtoanycase-study,forexam-
pleintermsofuniqueness,stabilityorreproducibilityofitspredictions.Thesehave
importantimplicationsforprojectevaluation,andmaynotbeself-evidentfromcom-
putational application alone, especially given the complex nature and interactions
involved in such models. Secondly, our book is an attempt to integrate the state-
of-the-art in a way that we hope generates a kind of feedback effect with the aca-
demiccommunity,wherebyourworkprovokesareactioneitherintermsofdisagree-
ments with our method of integration, or the stimulus for new research directions,
which in turn will impact on the future state-of-the-art. Thirdly, we intend that
ourapproachleadstoakindoftaxonomyofmodelsthatfacilitateeasiercommuni-
cationofassumptions,byreferencetoacommonmodellingframe.Thisisimportant
inorderthatforecastingisnotseenasakindofsupernaturaldivination,akinto‘read-
ing’tarotcards,butsothatuncertaintyoverassumptionsmadeandtrendsassumed
can beproperly communicatedto decision-makers.
Giventhetasktobringtogetherseveraltheoreticalfields,ithasbeennecessaryto
keep the focus of the book firmly on the development of forecasting methods. In
orderthatthebookbeofamanageablesize,wethereforedonotconsidertwoactiv-
itiesthatmightbesaidto‘bookend’thetaskofforecasting,namelycalibrationand
design.Weshouldmention,however,thattheapproachesdescribedare,webelieve,
especially suited tothese two activities. Inthe case of calibration, aswe write this
book we are in a period of unprecedented data availability, ranging from various
kinds of‘tracking’data (from mobilephone activity,GPS orBluetooth,for exam-
ple),toarchiveddetectordataoverlongperiods,andothermeansofinferringactivity
patterns (e.g. shopping transaction data, video surveillance). Such data reveals a
complex,time-of-day-varying,daily-varying,heterogeneouspatternoftravelbehav-
iourthatisnotonlypoorlycapturedbysteady-stateapproaches,butisactuallyrather
difficultto‘project’ontotheconventionalideologies.Moreovertheapproachespre-
sented that are developed from probability theory provide a means of calibrating
such models using formal statistical inference. In terms of design, the process
approach we develop allows us to examine how likely it is that the system could
beinfluencedtoattainandoperateunderverydifferenttransportationsystemdesigns
to the present. The traditional, ‘comparative statics’ approach, on the other hand,
onlyallowsustoassessalternativedesignsonthepremisetheyareattainablefrom
the present.
Even givenourdecisiontofocus onthe theoreticaldevelopment offorecasting
methods, space limitations mean that it has still been necessary to be selective in
termsofthekinds ofproblemconsidered.Thismeans weexcludemanyimportant
areas,suchastheroutingoffreightvehicles,theuseoftaxis(ortaxi-likevehicles),
and the behaviour of pedestrians in continuous space, such as a square. Given its
ratherlongassociationwithdynamicprocesses,andthepracticaluseofdisequilib-
rium forecasts, it would have been interesting to have included a consideration of