An investigation of the environmental impact of urban road capacity reductions

POSTER  P13-­‐5973  

INTRODUCTION  

ABSTRACT   OBJECTIVES  

ROADWORKS  

MECHANISM  OF  IMPACT  The  road  network  is  a  vital  medium  for  surface  movements  of  goods  and  people,  but  also  a  conduit  for  the  distribuRon  of  essenRal  services  such  as  gas  and  electricity  below  ground.  CongesRon  of  the  road  network  is  caused  by  demand  exceeding  capacity.  Various  forms  of  traffic  management,  for  example  changes  in  speed  limit,  traffic  calming  measures  or  network  design,  can  lead  to  a  capacity  reducRon  on  the  network.  Accidents,  roadworks  or  vehicles  infringing  on  parking  restricRons  can  have  a  similar  effect.      CongesRon  has  an  impact  on  vehicle  emissions  and  the  environment,  both  of  which  are  becoming  increasingly  important  to  decision  makers   and   road  users   due   to   their   influence  on   air   quality   and  human  health.   These   issues   are   especially   significant   in   densely  populated  urban  areas.  While  methods  exist  to  represent  the  relaRonships  between  capacity  reducRon  and  vehicle  delay,  these  are  less   well   developed   for   urban   networks,   and   the   influence   of   capacity   reducRon   on   vehicle   emissions   and   how   the   locaRon   or  intensity  of  pollutant  emission  hotspots  may  change  has  not  previously  been  considered.        This  poster  proposes  and  demonstrates  a  methodology  for  assessing  how  localised  capacity  reducRons,  focusing  on  roadworks,  can  affect   vehicle   dynamics   and   thus   vehicle   emissions   and   network   performance   indicators.   Simple   relaRonships   between   the  characterisRcs   of   the   roadworks   and   key   traffic   engineering   parameters   are   proposed.   The   methodology   is   tested   using   a  microsimulaRon  model  and  a  range  of  roadwork  scenarios.  Analysis  focuses  on  an  urban  road  network  segment  and  suggests  that  a  typical  roadwork  may  increase  emissions  by  100%,  101%  and  80%  for  CO2,  NOX  and  PM10  emissions  respecRvely,  with  an  associated  34%   increase   in  delay.  The   importance  of   local   vehicle  acceleraRon  paaerns   in   influencing   the  distribuRon  of  emissions   is   clearly  seen.  Further  work  to  invesRgate  the  fidelity  of  acceleraRon  simulaRon  in  traffic  microsimulaRon  is  required  to  enable  idenRficaRon  of  efficient  traffic  management  intervenRons  for  management  of  temporary  capacity  reducRons.  

Road  Network  Required  for  the  movement  of  good  and  people    

Required  for  the  distribuRon  of  essenRal  services  

The  road  network  is  primarily  used  for  the  movement  of  goods  and  people  on  both  the  carriageway  and  footway  (sidewalk),  which  form  the   highway.   However,   the   road   network   is   also   used   for   the  distribuRon  of  essenRal  services    such  as  gas,  electricity,  water  and  communicaRon  networks.  The  diagram  on  the  right  shows  a  typical  cross  secRon  of  a  road.  

Image  available  from:  hap://www.infovisual.info/05/025_en.html  

CongesRon  When  demand  >  capacity  

Impact  on  environment  and  network  performance    

The   demand   is   the   number   of   vehicles   desiring   to   travel   along   a  parRcular   link   per   unit   Rme,   and   the   capacity   is   the   maximum  number   of   vehicles   that   can   pass   through   a   link   using   all   available  road   space   per   unit   Rme   (TransportaRon   Research   Board,   2010).  When   demand   exceeds   capacity,   we   expect   congesRon.   The   stop-­‐start   driving   behaviour   in   a   congested   network   will   result   in  increased   vehicle   emissions   compared   to   a   smoother   driving  behaviour  as  would  be  expected  in  free  flow  condiRons.  CongesRon  will   also   have   a   negaRve   impact   on   network   performance   by  increasing  travel  Rme  and  reducing  average  speeds.  

Image  available  from:  hap://society6.com/IkuannaStudios/CongesRon-­‐Ahead-­‐Expect-­‐Delays-­‐Highway-­‐Sign_Print  

Capacity  reducRon  Physical  reducRon  in  available  road  space  

Can  be  planned  or  unplanned  

A   capacity   reducRon   is   an   event,   acRvity   or   process   that   results   in  the   physical   loss   of   road   space.   A   capacity   reducRon   can   be  temporary,   for   example   a   broken   down   vehicle   blocking   a   lane   or  permanent,  for  example  a  reduced  speed  limit.  A  capacity  reducRon  can   also   be   termed   planned   or   unplanned.   A   planned   capacity  reducRon   could   be   the   closing   of   a   lane   to   carry   out   rouRne  maintenance,   where   as   an   unplanned   capacity   reducRon   could   be  emergency  roadworks.  

Image  available  from:  hap://news.bbcimg.co.uk/media/images/55503000/jpg/_55503555_55503554.jpg  

Significant  economic  costs  

The   Department   for   Transport   (2011)   esRmates   that   the   1.2   million  roadworks   in  England  each  year  result   in  a  cost   to  the  economy  of  over  £4  billion   due   to   the   delay   caused.   This   figure   fails   to   consider   the   addiRonal  costs   of   congested   traffic   as   highlighted   by   the   Greater   London   Authority  (2012),  for  example  frustraRon  to  road  users  and  the  environmental  impact.    

1.2M  roadworks  in  England  each  year  cost  economy  £4B  

The  World  Health  OrganisaRon   (2011)   states   that   40  million   people   in   the  115   largest   ciRes   in   the   European   Union   are   exposed   to   air   that   exceeds  WHO   air   quality   guideline   values   for   at   least   one   pollutant.   Roadworks,   a  typical  capacity  reducRon,  can  cause  congesRon  in  a  saturated  network  and  this  is  expect  to  increase  vehicle  emissions.  

40M  people  in  115  largest  EU  ciRes  at  risk  due  to  poor  air  quality  

Roadworks,   also   commonly   referred   to   as   workzones,   are   becoming  increasingly   important,  and  are   the   focus  of  many  pieces  of   legislaRon  and  guidance   documentaRon.   In   London,   UK,   there   is   now   a   formal   procedure  that  contractors  have  to  follow  to  gain  access  to  the  highway,  known  as  the  London  Permit  Scheme  (LoPS  2009).  Other  schemes  such  as  the  Lane  Rental  Scheme  (TLRS  2012)  force  contractors  to   ‘rent’  secRons  of  the  carriageway.  Other   key   documents   include   the   Design   Manual   for   Roads   and   Bridges  (DMRB   2012),   New   Roads   and   Street   Works   Act   (NRSWA   1991),   Traffic  Management  Act  (TMA  2004)  and  the  Mayor’s  Code  of  Conduct  (2009).  

New  legislaRon  and  guidance  documentaRon  in  London  

Health  impacts  

Policy  implicaRons  

Roadworks   are   an   example   of   a   capacity   reducRon   and   can   have   a  significant  impact  on  network  performance  in  a  saturated  network.  If  there  is   insufficient   pracRcal   reserve   capacity,   the   introducRon   of   a   set   of  roadworks  will   result   in   congesRon.  Roadworks,  which   can  be  planned  or  unplanned,   are   a   form   of   non-­‐recurrent   congesRon.   Non-­‐recurrent  congesRon   is  the  build  up  of  traffic  due  to  an   incident  and   is  unexpected,  the   opposite   of   recurrent   congesRon   which   is   predictable,   for   example  during  the  AM  peak.  

The  management   of   roadworks   varies   greatly   depending   on  whether   the  roadworks  are  planned  or  unplanned,  but  also  based  on  the  severity  of  the  roadworks.   With   planned   roadworks,   the   contractor   needs   to   noRfy   the  relevant  highway  authority  between  3  days  and  3  months  in  advance  of  the  works.   The   contractor   and   highway   authority   will   then  work   together   to  put   in   the   necessary   traffic  management   and   ensure   the   duraRon   of   the  works  and  the  space  required  is  appropriate  for  the  works  to  be  conducted.  With  unplanned  roadworks,   the  contractor   informs  the  highway  authority  of  the  works  up  to  5  hours  aper  the  works  have  commenced.  The  highway  authority   may   then   ask   the   contractor   to   stop   and   put   in   the   necessary  traffic  management  or  conRnue.  Unplanned  roadworks  have  the  potenRal  to  be  more  disrupRve  as  road  users  will  not  have  been  noRfied  in  advance  and  a  traffic  management  plan  will  not  be  in  effect.  

Planned  v  unplanned  roadworks    

Are  unplanned  roadworks  more  disrupRve?  

CongesRon  

Management  

Stakeholders  

There  are  numerous  stakeholders  involved  with  roadworks,  including  local  residents,   road   users,   roadwork   promoters,   local   authoriRes   and   central  government   each   of   whom   may   have   different   agendas   and   prioriRes.  There   is  a  clear  need  to   invesRgate  all  of  the  cost  components  associated  with   roadworks,   including   the   environmental   impact,   in   order   to   support  decisions  about  future  roadwork  management.  

Image  available  from:  hap://27gen.files.wordpress.com/2011/09/sixthinkinghats1.jpg  

CongesRon  

Non-­‐recurrent  congesRon    (incident  based)  Recurrent  congesRon  

Traffic  calming  measures  

Lack  of  capacity   Roadworks   Parked  

vehicles  

Pothole  filling  

Many  others  

Many  others  Accidents  

Repair  gas  leak  

Minor  works  

Planned   Unplanned  

Standard  works   Major  works   Immediate  emergency  works    

Immediate  urgent  works    

RouRne  resurfacing  

Streetscape  redevelopment   Repair  burst  

water  main  

A   localised   reducRon   in   lane   capacity  will   affect   the  dynamics  of   individual  vehicle   operaRon   and   therefore   emissions   and   network   performance  indicators   such   as   delay.   Accurate   assessment   of   emissions   depends   on  analysis  at  this  level  (Smit  et  al.,  2010).  Above  a  certain  degree  of  saturaRon,  this   capacity   reducRon   and   the   characterisRcs   of   the   associated   traffic  management   may   lead   to   measurable   changes   in   link   performance.   In  principle,  a  change  in  link  performance  characterisRcs  will  have  an  impact  on  the  route  choice  and  behaviour  across  the  network    (Sheu  (2006)).      Furthermore,   driver   behaviour   such   as   sensiRvity   to   informaRon   and  familiarity  with   the   network  will   affect   the   level   of   rerouRng   and   thus   the  extent  of  the  network  that  is  affected  by  the  capacity  reducRon  (e.g.  Hu  et  al.  (2007)).  A   key  output,   therefore,   of   a  microscopic,   link-­‐based  analysis   is   to  determine   the   extent   to   which   a   localised   capacity   reducRon   affects   the  generalised  cost  of  using  different  links  and  nodes  in  the  network.    

Capacity Reduction

Link Effect

Network Effect

E.g.  –  lower  average  speeds,  increased  delay,  higher  fuel  usage,  increased  local  

polluRon  

E.g.  –  changes  in  demand  and  mode,  reassignment  of  vehicles,  re-­‐distribuRon  of  emissions  

If  degree  of  saturaRon  is  sufficiently  high  

If  effects  cause  changes  in  assignment  

•  In  this  study  we  focus  on  the  simple  link  component  of  a  roadwork  in  an  urban  network  

•  In  the  scenarios  explored,  the  presence  of  traffic  management  in  the  form  of  temporary  traffic  signals  is  required  

•  The  condiRons  under  which  link-­‐level  capacity  reducRons  influence  adjacent  links  and  nodes  is  idenRfied    •  A  series  of  models  built  to  simulate  different  roadwork  scenarios  

•  Underlying  theoreRcal  framework  is  based  on  basic  traffic  engineering  concepts    

SCOPE  

THEORETICAL  FRAMEWORK  

Key  equaRons  

Blocking-­‐back  

The   capacity   is   defined   to   be   the   maximum   throughput   of   a   parRcular  segment  of  the  network.  The  capacity  can  be  calculated  as  a  funcRon  of  the  green   raRo   and   saturaRon   flow.   The   green   raRo   is   the   raRo   of   effecRve  green  Rme  g   to   the   traffic  signal   cycle   length  c.   The   saturaRon  flow,  also  commonly  referred  to  as  the  queue  discharge  rate,  is  denoted  by  s.

! = !! ∗ !

By  manipulaRng   the   equaRon   above,   an   expression   for   the   criRcal   green  Rme  gcrit    can  be  formed.  q   is  the  number  of  vehicles  aaempRng  to  enter  the  capacity  restrained  link  and  the  other  variables  are  as  defined  above.

!!"#$ = ! ∗ !!

Using   the  diagram  below,   it   is  possible   to  define  an  equaRon   to  esRmate  the   criRcal   length   of   the   platoon   of   the   vehicles   aaempRng   to   enter   the  capacity   restrained   link   that  will   result   in   blocking-­‐back   into   the   adjacent  nodes   and   juncRons.   As   shown   in   the   diagram   below,   d   is   the   distance  between   the   juncRon   and   the   stop   line   of   the   temporary   traffic  management.  z  is  the  length  of  the  queue  that  forms  due  to  the  temporary  traffic  signals  and  x   is   the   length  of   the  platoon  of  vehicles  aaempRng   to  enter  the  capacity  restrained  link.

!"!! → ! − ! !!"#$%&'(!!"#$!!"#$!!ℎ!!!"#$%&'(!!"#$%&'#!!""#$%

!!"#$ ≈ ! − !

d

x1 z

Stop line

Back of queue

x2

x3

x  =  x1+x2+x3  = Length of platoon of vehicles entering capacity reduced link during analysis timeframe

Aravinth Thiyagarajah (a.thiyagarajah@imperial.ac.uk) Dr Robin North (robin.north@imperial.ac.uk)

This poster describes doctoral work supported by the RJRF and supervised by Dr Robin North, Professor Michael Bell and

Professor John Polak at the Centre for Transport Studies, Imperial College London

Centre  for  Transport  Studies  www.imperial.ac.uk/cts  

An investigation of the environmental impact of urban road capacity reductions

Aravinth Thiyagarajah (a.thiyagarajah@imperial.ac.uk) Dr Robin North (robin.north@imperial.ac.uk)

POSTER  P13-­‐5973  

This poster describes doctoral work supported by the RJRF and supervised by Dr Robin North, Professor Michael Bell and

Professor John Polak at the Centre for Transport Studies, Imperial College London

Centre  for  Transport  Studies  www.imperial.ac.uk/cts  

MODELLING  

MODELLING  FRAMEWORK   RESULTS   CONCLUSION  

FURTHER  WORK  

REFERENCES  

In   order   to   assess   the   impact   of   urban   capacity   reducRons,   VISSIM   (Verkehr   In   Stadten   –   SIMulaRonsmodell),   a   mulR-­‐modal  microscopic  traffic  simulaRon  sopware  was  used  (PTV  AG,  2012).  VISSIM  has  its  limitaRons  as  highlighted  by  Treiber  et  al.  (2006)  and  Jie  et  al.  (2012),  however  it  is  the  microsimulaRon  tool  recommended  for  use  in  several  modelling  guidelines,  for  example  Transport  for  London  (2010).        To   esRmate   the   vehicle   emissions,   the   individual   vehicle   records   from   VISSIM   were   exported   into   EnViVer,   an   instantaneous  emissions  modelling  tool  created  by  TNO  (The  Netherlands  OrganisaRon  for  Applied  ScienRfic  Research)  (TNO,  2012).  The  emissions  are   calculated   by   assigning   each   VISSIM   vehicle   type   to   an   emissions   class   in   EnViVer   and   applying   a   polynomial   based   on  acceleraRon  behaviour.    

Traffic model

Emission model

Traffic  data  

Network  data  

Roadwork  data  

Vehicle  fleet  data  

VISSIM  

EnViVer  

The  modelling  process,  adapted  from  North  et  al.  (2009)  is  shown  to  the  right.  Traffic,  network  and  roadwork   data   support   the   building   and  configuraRon   of   the   traffic   model,   and   then   the  outputs   of   the   traffic   model   are   combined   with  the   vehicle   fleet   data   for   emissions   predicRon   in  the  emission  model.  

Model  structure  

A   simple  model  has  been  created  where  a  parRal   closure  of   a   link   is   required   and   the   introducRon   of   a   signalised  contra-­‐flow   to   maintain   the   flow   of   traffic.   The   model,  denoted  ‘A’  is  composed  of  a  300m  link,  typical  of  an  urban  city  centre,  and  100m  entry  links  to  control  the  behaviour  of  the  vehicles  as  they  enter  the  network.      The  image  denoted  ‘B’  shows  how  the  contraflow  has  been  implemented   with   a   10m   buffer   zone   on   either   side   to  allow   for   vehicles   to   manoeuvre   around   the   works.   The  temporary  traffic  signals  that  are  present  on  the  entrances  to   the   contraflow   have   been   programmed   with   a   cycle  Rme   of   90   seconds,   typical   of   urban   environments.   The  green   Rme   has   been   set   to   minimise   the   queuing   of  vehicles   but   ensure   sufficient   inter-­‐green   Rme   to   allow  vehicles  to  safely  leave  the  contraflow.  

A

B

100m Entry link 100m Entry link 300m Link (50kph)

600 veh/hr 600 veh/hr

100m Entry link 100m Entry link

600 veh/hr 600 veh/hr

115m (50kph)

50m contraflow (30kph)

10m buffer zone (20kph)

115m (50kph)

Temporary traffic signal Temporary traffic signal

Scenarios  

100m Entry link

600 veh/hr (as on all entry links)

Traffic signals on each arm of junction

50m link “Yellow box” junction

115m (50kph)

50m contraflow (30kph)

10m buffer zone (20kph)

115m (50kph)

Temporary traffic signal Temporary traffic signal

C  In  order  to   invesRgate  a  range  of   levels  of  degradaRon  of  network   performance,   the   length   of   the   roadwork   was  varied   between   30m-­‐120m,   represenRng   a   10-­‐40%  reducRon  in  eastbound  lane  area.  As  links  do  not  appear  in  isolaRon,   addiRonal   models   were   created   with   the  presence   of   juncRons   adjacent   to   the   capacity   restrained  link.   The   signalised   crossroads   were   programmed   with   a  two-­‐stage  signal  plan  that  allows  for  the  same  vehicle  flow  of  600   veh/hr.  As  with   the   link  models,   the   length  of   the  roadwork  was  varied  between  30m-­‐120m.  

SimulaRon  

In   total  5   link  models  and  5   juncRon  models  were  built   in  VISSIM.   Over   100   simulaRons   were   carried   out,   with  mulRple   runs   for   each   scenario.   Various   parameters   in  VISSIM  such  as  delay,  average  speed  and  journey  Rme  were  output.  Other  vehicle  specific  characterisRcs  such  as  speed,  posiRon  and  Rme  in  network  were  output  from  VISSIM  and  used   as   an   input   into   EnViVer   to   esRmate   the   vehicle  emissions.   The   outputs   from   EnViVer   and   VISSIM   were  post-­‐processed   in  MATLAB   and   Excel   in   order   to   average  across   mulRple   seeds   and   to   calculate   the   total   mass   of  pollutant  emiaed  from  the  capacity  restrained  link  only.  

From  the  research  presented  in  this  poster,  the  following  conclusions  can  be  drawn:    •  Link  level  capacity  reducRons  can  have  a  significant  impact  on  vehicle  emissions  and  Rme-­‐related  network  performance  variables  

•  The  length  of  the  capacity  reducRon  and  its  proximity  to  adjacent  juncRons  is  criRcal  for  determining  whether  just  the  capacity  restrained  link  or  the  wider  network  needs  to  be  taken  into  consideraRon  when  assessing  the  impact  of  a  capacity  reducRon  

•  The  posiRon  of  the  stop  line  for  temporary  traffic  management  and  the  effecRve  green  Rme  on  the  temporary  traffic  signals  are  important,  especially  when  the  queue  that  forms  during  the  inter-­‐green  Rme  extends  beyond  the  link  

•  The   highest   emissions   are   observed   with   zones   of   high   acceleraRon   and   this   is   something   pracRRoners   should   avoid   when  configuring  roadworks  and  workzones  

The  research  presented  in  this  poster  forms  part  of  a  wider  invesRgaRon  that  will  feed  into  Mr.  Thiyagarajah’s  PhD  thesis.  Further  work  to  address  the  following  will  be  conducted  in  due  course:    •   Assessment  of  the  suitability  of  exisRng  modelling  tools  

•  Improving  the  realism  of  the  modelling  procedure  by  increasing  the  complexity  and  including  re-­‐rouRng  of  traffic    •  CalibraRon  and  validaRon  of  the  modelling  procedure  using  real-­‐world  data  

•  TranslaRng  the  impact  of  capacity  reducRons  on  the  environment  and  network  performance  into  a  generalised  cost  which  can  be  used  to  support  decision  making    and  feed  into  future  policy  

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Trends  

Intensity  maps  

Blocking-­‐back  

•  149%,   180%   and   112%   increase   in   CO2,   NOX   and   PM10  emissions   respecRvely   between   the   no   roadwork   case  and  shortest  (30m)  roadwork  case  

 •  Comparing  the  no  roadwork  case  for  the   link  model  and  

juncRon   model,   we   observe   a   69%,   36%   and   34%  increase   in   CO2,   NOX   and   PM10   emissions   aaributed   to  increased  queuing  

•  Comparing  the   juncRon  model  with  no  roadworks  and  a  30m   roadwork,   100%,   101%   and   80%   increases   in   CO2,  NOX  and  PM10  emissions  respecRvely  are  observed  

•  A  25%  reducRon  in  average  speed  was  observed  when  a  30m  roadwork  was  introduced  into  the  link  model  and  a  34%  reducRon  in  average  speed  for  the  juncRon  model.  A  similar   effect   on   average   vehicle   delay  was   observed   in  each  case  

JuncRon  model  results  

Link  model  results  

EnViVer  is  able  to  esRmate  and  output  the  mass  of  pollutant  emiaed   for   CO2,   NOX   and   PM10   for   each   5m   grid   square.  Using  a  combinaRon  of  MATLAB  and  Excel,  the  outputs  have  been   averaged   across   mulRple   seeds   and   normalised  between   the   different   scenarios   invesRgated.   Emissions  intensity   maps   have   then   been   produced   by   plo{ng   the  total  emissions  for  each  grid  square  using  a  linear  grey  scale,  where  black  represents  the  maximum  emissions.  

Length of disruption (m) 0 30 50 70 120 CO2 (kg) 57.70 143.50 151.10 157.70 171.00 NOX (g) 154.00 430.50 454.50 475.10 536.60 PM10 (g) 13.99 29.70 31.21 32.53 34.41 Average vehicle delay (s) 0.29 26.01 31.92 36.18 78.56 Average speed (kph) 52.60 25.73 23.10 21.36 12.83

Length of disruption (m) 0 30 40 70 120 CO2 (kg) 97.29 194.70 202.40 208.80 201.4 NOX (g) 299.00 602.70 661.80 674.40 641.90 PM10 (g) 21.17 38.18 39.06 40.29 39.01 Average vehicle delay (s) 25.42 38.45 39.90 49.46 82.25 Average speed (kph) 21.78 16.46 15.90 13.71 9.28

Intensity  maps  for  CO2  (link  model)  

Increasing  emissions  

No  roadwork  

30m  roadwork  

50m  roadwork  

Intensity  maps  for  CO2  (juncRon  model)  

No  roadwork  

30m  roadwork  

50m  roadwork  

The   intensity   map   for   the   no   roadwork   case   link   model  shows  a  conRnuous  grey  scale,  unlike  the  maps  for  the  30m  and  50m  roadwork  case  where  there  is  a  peak  in  emissions  around  the  roadwork.    The  emissions  intensity  maps  for  the  juncRon  model  show  a  similar   trend,   however   there   are   addiRonal   zones   of  increased   emissions   on   the   exits   from   the   capacity  restrained   link.   Comparing   the   30m   and   50m   roadwork  cases,  we  see  a  more  dispersed  map  for  the  50m  case,  this  is  likely   to   be   due   to   vehicles   travelling   in   a   constant   queue  rather  than  acceleraRng  between  queues.  

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Focusing  on   the   juncRon  model,  we  observe  a   reducRon   in  emissions  across  all   three  pollutants  between  the  70m  and  120m  roadwork  cases.  A  possible  explanaRon  is  that  vehicles  are  blocking-­‐back   into  the  adjacent   juncRons,   resulRng   in  a  flow  reducRon  through  the  network.  This  can  be  confirmed  by   calculaRng   the   criRcal   green   Rme,   gcrit   for   this   network.  For  the  70m  roadwork,  the  temporary  traffic  signals  have  a  green  Rme  of  30s,  which  is  higher  than  gcrit,  however  for  the  120m  roadwork,  the  green  Rme  is  25s,  less  than  the  criRcal  green  Rme.    For   the   120m   roadwork,   the   queue   that   forms   at   the  temporary   traffic   signals   during   the   inter-­‐green   is   not   fully  served   and   the   queue   becomes   a   funcRon   of   Rme.  Eventually   z=d   and  no  new  vehicles   can   enter   the   capacity  restrained  link.