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Y         2     Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?   '      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good and usable estimates from the off-line estimation of the model. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. 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RB 1d s *D8cH d 0޽h ? ___ff3ffy___PPT10Y+D=' = @B +m { 0  |$(  |r | S X _^  X r | S X _^ X H | 0޽h ? ___ff3ffy___PPT10Y+D=' = @B +M{ 0 tlP(    B0f qThank you for your attention!,   6 *X  tY {] Jitka Homolov jkratoch@utia.cas.cz 6^0FPB~        0BVH  0޽h ? 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K2 Z -Academy of Sciences of Czech Republic, Prague.-@Tahoma-. 2 cGCzech Republic.-@Tahoma-. 2 iAjkratoch.-@Tahoma-. 2 iS@utia..-@Tahoma-.  2 iccas.-@Tahoma-.  2 ij..-@Tahoma-.  2 ilcz.-JJIIHGGFFEDDCCBAA@@?>>==;::99  !!!""####$$$$%%&&&'())))*****++++,-..../////000001111122222UUTSSRRQPONNMLLKKJIIHHGFFEEDCCBBA@@??>==;;:<9  !!"""####$$$%%%&&''())))*****+++,,-..../////0000011111222223UTSSRRQOONNMLLKKJIIHHGFFEEDCCBBA@@??>==;;:99  !!!""###LRovnice Equation.30"Editor rovnic 3.0ORovnice Equation.30"Editor rovnic 3.0PRovnice Equation.30"Editor rovnic 3.0QRovnice Equation.30"Editor rovnic 3.0RRovnice Equation.30"Editor rovnic 3.0/ 0DArialrdeBk BTTTyܖ 0ܖDTimes New RomanTTyܖ 0ܖ DAvantGarde Bk BTTyܖ 0ܖ"0DWingdings Bk BTTyܖ 0ܖ@DSymbolgs Bk BTTyܖ 0ܖPDAvantGardeBk BTTyܖ 0ܖt "`DTahomardeBk BTTyܖ 0ܖ A . @n?" dd@  @@`` 80H" ..,,   () .. 5  HH  21 21    21    5     )   2    !"#$%&'()*+ /012 78`2$q"p]ij2$棼smn!d2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ2$m*%7a>aB2$)Wg/832$w焅T /     e               <Traffic variables  xData = detector measuring Intensity = amount of passing vehTahomaSmsiceEditor rovnic 3.0%Multi-level control of traffic flowsUrban Transportation Traffic SystemsTraffic variablesOur Approach Model of a microregionEstimation on the local levelControl on the local levelControl of the macroregionTestingModel in picturesQueue estimationControl Conclusions Snmek 15 Pouit psmaablona nvrhuVloen servery OLENadpisy DTimes New Romanhhy 0 DAvantGarde Bk BThy 0"0DWingdings Bk BThy 0@DSymbolgs Bk BThy 0PDAvantGardeBk BThy 0t " A . @n?" dd@  z[ 0DTimes New Roman0z[ 0 DAvantGarde Bk BT0z[ 0"0DWingdings Bk BT0z[ 0@DSymbolgs Bk BT0z[ 0PDAvantGardeBk BT0z[ 0t " A . @n?" dd@  @@`` XQ ..,,   () .. 5  HH  21 21    21    5     )   2   4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$2$w焅TZiZ,ZTZ H   8T  @m         Our Approach   tMultilevel control system Local level  con   z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialarde-0z[ 0DTimes New Roman0z[ 0 DAvantGarde Bk BT0z[ 0"0DWingdings Bk BT0z[ 0@DSymbolgs Bk BT0z[ 0PDAvantGardeBk BT0z[ 0t " A . @n?" dd@  @@`` XQ ..,,   () .. 5  HH  21 21    21    5     )   2   4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$2$w焅T?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~2Problems: Increasing traffic demand urban street networks become deficient Restricted possibilities of reconstructing the deficient street network within cities Solution: Efficient signal traffic control ITS on-line control, real-time optimization  O )V  %  '  Traffic Systems  Microregion = streets and junctions One junction with signal control at least Detectors equip main streets. Macroregion = several microregions Data = detectoPowerPoint Document(5DocumentSummaryInformation8@@``  ..,,   () .. 5  HH  21 21    21    5     )   2    !"#$%&'toch@utia.cas.cz6mailto:jkratoch@utia.cas.czz(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialardeBk BTTTX,ܖ 0ܖDTimes New RomanTTX,ܖ 0ܖ DAvantGarde Bk BTTX,ܖ 0ܖ"0DWingdingr measuring Intensity = amount of passing vehicles Occupancy = proportion of time when a detector is being activated Control variable = Splits (relative greens) impacting the capacities of all junction approaches, i.e. the amount of passed cars%ZHZ>ZiZ,ZTZ H   8T  @m         Our Approach   Multilevel control system Local level  control of a microregion Coordination level  global control Estimation of non-detected traffic flows and non-measurable quantities Parking, non-detected or non-controlled flows Restricted possibilities of measuring in practice Optimal signal traffic control as LP task Linearity of local relations and restrictions LG`*/KG-2*.    &5   & &Local traffic control of a microregion'' &     Linear model of a microregion for queues Basic relations between traffic quantities Correction equation (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities Formulation of the linear control task Optimization by LP)@ X' )@ X'      +      83Coordination level - control of a whole macroregion44 p        Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the linear task Optimization by LP Several strategies  the easiest one is the analogy of the local level!Z ! Y         2     Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good and usable estimates from the off-line estimation of the model. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)( :D _  B 7|K0 00(  x  c $̾ $m]   x  c $ $]   b  <d޽h ?"  CCC___PPT10i..F+D=' = @B +rmٗ? m8)(   z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialarde-0trol of a microregion Coordination level  global control Explicit state for an actual traffic situation Other variables are not explicit Queue length  intuitively understandable Optimal signal traffic control as LP task Linearity of local relations and restrictions K/M*/K/L  *  .    :5   $  &Local traffic control of a microregion'' &     Linear model of a microregion for queues Basic relations between traffic quantities Correction equation (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities Formulation of the linear control task Optimization by LP)@ X' )@ X'      +      83Coordination level - control of a whole macroregion44 p        Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the linear task Optimization by LP Several strategies  the easiest one is the analogy of the local level!Z ! Y         2     Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good and usable estimates from the off-line estimation of the model. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)( :D _  B 7m { ,$(  ,r , S   _^   r , S ! GH>  H , 0޽h ? ___ff3ffy___PPT10Y+D=' = @B +rؚ? 8 *(   z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.czz(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialarde-<$0<z[ 04DTimes New Roman<$0<z[ 04 DAvantGarde Bk BT$0<z[ 04"0DWingdings Bk BT$0<z[ 04@DSymbolgs Bk BT$0<z[ 04PDAvantGardeBk BT$0<z[ 04t " A . @n?" dd@  @@`` XS ..,,   () .. 5  HH  21 21    21    5     )   2   4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$2$w焅TZiZ,ZTZ H   8T  @m         Our Approach   tMultilevel control system Local level  control of a microregion Coordination level  global control Explicit state for an actual traffic situation Other variables are not explicit Queue length  intuitively understandable Optimal signal traffic control as LP task Linearity of local relations and restrictions K/M*/K/L  *  .    :5   $  &Local traffic control of a microregion'' &     Linear model of a microregion for queues Basic relations between traffic quantities Correction equation (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities Formulation of the linear control task Optimization by LP)@ X' )@ X'      +      83Coordination level - control of a whole macroregion44 p        Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the optimization task Optimization by LP Several strategies  the easiest one is the analogy of the local level!%Z !% Y                Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)}( ~:D   B 7 {K0 0(  x  c $Xb _^   x  c $,c _^  f  Nb޽h ? ___ff3ffy___PPT10Y+D=' = @B +A { h` |(  |r | S  _^   r | S ؕ _^    | B V i6 qThank you for your attention!,  | 6> G {] Jitka Homolov jkratoch@utia.cas.cz 6^0FPB~       U 0BVH | 0޽h ? ___ff3ffy___PPT10Y+D=' = @B +r;08L? L8.(   z(jkras Bk BTTX,ܖ 0ܖ@DSymbolgs Bk BTTX,ܖ 0ܖPDAvantGardeBk BTTX,ܖ 0ܖt " A . @n?" dd@  @@`` ( hV ..,,   () .. 5  HH  21 21    21    5     )   2   4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$()*+4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$2$w焅TZrZ,ZTZ H  & 8T  ^m       B   Our Approach   Multi-level control system Local level  control of a microregion Coordination level  global control State space approach to the actual traffic situation Individual traffic variables do not bring full information Queue length as a state  intuitively understandable Optimal signal traffic control as LP task Linearity of local relations and restrictions ZKZ5ZrZZ*Z/ZK5q  *  .     e  &Local traffic control of a microregion''  '  Linear model of a microregion for queues Basic equation  hydrodynamic analogy Supplementary equation for occupancy (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities)&% X )M   X    (     p :&Local traffic control of a microregion''  '  Formulation of the linear control task Optimization by LP Criterion  weighted sum of queues Restrictions  traffic nature of all variables and relations between them State space model Non-negativity Total sum of splits Restricted increments of splits z'6JV '7J  V*  85Coordination level - control of the whole macroregion66 p       Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the optimization task Optimization by LP Several strategies  the easiest one is the analogy of the local level!%Z !% Y                Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)}( ~:D   B 7| 0L0 00(  x  c $$m]  x  c $0$]  b  <d޽h ?"  CCC___PPT10i..F+D=' R= @B +m { 0 4$(  4r 4 S GN _^  N r 4 S pHN /G N H 4 0޽h ? ___ff3ffy___PPT10Y+D=' R= @B +m { 0 ,$(  ,r , S WN _^  N r , S D\N GH N H , 0޽h ? ___ff3ffy___PPT10Y+D=' R= @B + { 0L0 0*(  0r 0 S dN _^  N x 0 c $eN _, N f 0 Nb޽h ? ___ff3ffy___PPT10Y+D=' R= @B + { 0L0 0(  x  c $h _^  h x  c $h _^ h f  Nb޽h ? ___ff3ffy___PPT10Y+D=' R= @B + { 0L0 0(  x  c $nN _^  N x  c $toN _^ N f  Nb޽h ? ___ff3ffy___PPT10Y+D=' R= @B +r0(0O-/*8,5:u2l7:1T2( ;  z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.czz(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialardeBk BThhy 0icles per time [veh/h] Occupancy = proportion of sample time when a detector is being activated [%] Velocity, density = not always measured Control variable = Splits (relative greens) Signal scheme = course of light signals Impact on the capacities of all junction approaches, i.e. the amount of passed carsX0w,| 6 D  lD@    !  Our Approach   Multi-level control system Local level  control of a microregion Coordination level  global control State space approach Queue length as a state intuitively understandable, fully expresses an actual traffic situation non-measurable Optimal signal traffic control as LP task Linearity of local relations and restrictions ZKZZZXZ*Z.ZZKX  *. e  Model of a microregion   Linear model of a microregion for queues Basic equation  hydrodynamic analogy Supplementary equation for occupancy State space model )'' )         x  )   # :Estimation on the local level.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialardeBk BThhy 0DTimes New Romanhhy 0 DAvantGarde Bk BThy 0"0DWingdings Bk BThy 0@DSymbolgs Bk BThy 0PDAvantGardeBk BThy 0t " A . @n?" dd@  @@``  ..,,   (Root EntrydO)p[@Pictures\Current UserYSummaryInformation(h:&t>%      !"#$?()*+,-./01P3456789<=C@AxtDEFGHIJKLMNO'QRSTUVWXYZ[\]^_`abcdefghijklmnopqrsBuvwy|z{}~ +_4Jitka KratochvlovJitka K՜.+,D՜.+,    Pedvdn na obrazovceVUT5 ArialTimes New RomanAvantGarde Bk BT WingdingsSymbol AvantGardesnmk 8@ _PID_HLINKSApmailto:jkratoch@utia.cas.czkratoch@utia.cas.czratochvlov@"AvantGarde Bk BT-.  2 9clov.-@"AvantGarde Bk BT-.  2 9k~j0___PPT10 pp*___PPT9 z? %"$Multi-level control of traffic flows%%,p Jitka Homolov Adaptive Systems Department, Institute of Information Theory and Automation, Academy of Sciences of Czech Republic, Prague Czech Republic jkratoch@utia.cas.czZ }   $ n  Urban Transportation   Problems: Increasing traffic demand urban street networks become deficient Restricted possibilities of reconstructing the deficient street network within cities Solution: Efficient signal traffic control ITS on-line control, real-time optimization  O )V  %  '  Traffic Systems  Microregion = streets and junctions Connected junctions One junction with signal control at least Precondition: strategic detectors on borders of microregion Macroregion = several microregions Connected microregions%{$ > 0 $  e               <Traffic Systems  <Data = detector measuring Intensity = amount of passing vehicles per time [veh/h] Occupancy = proportion of sample time when a detector is being activated [%] Velocity, density = Control variable = Splits (relative greens) impacting the capacities of all junction approaches, i.e. the amount of passed cars0c,T 6 DT^@    b    Our Approach   Multi-level control system Local level  control of a microregion Coordination level  global control State space approach to the actual traffic situation Individual traffic variables do not bring full information Queue length as a state  intuitively understandable Optimal signal traffic control as LP task Linearity of local relations and restrictions ZKZ5ZrZZ*Z/ZK5q  *  .     e  &Local traffic control of a microregion''  '  Linear model of a microregion for queues Basic equation  hydrodynamic analogy Supplementary equation for occupancy (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities)&% X )M   X    (     p :&Local traffic control of a microregion''  '  Formulation of the linear control task Optimization by LP Criterion  weighted sum of queues Restrictions  traffic nature of all variables and relations between them State space model Non-negativity Total sum of splits Restricted increments of splits z'6JV '7J  V*  85Coordination level - control of the whole macroregion66 p       Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the optimization task Optimization by LP Several strategies  the easiest one is the analogy of the local level!%Z !% Y                Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)}( ~:D   B 7/l=>?@ABCDEF G H I *  0` ___ff3ff` ___33f̙ffff` CCC` d___a%qw` *(Z___fFQt` 6CCCff3` CCCff` CCCf3f` f333ff` f333f3̙>?" dd@$?Fd@l A@lF`< n?" dd@   @@``PP   @ ` `(p>>     (   \T ``    "`` B   C H8@AB}C}EvFGxGH`I{QUNVWX}} }}}} `$ }} }}  G H I }} }} }}           `  `` "(`  D0  B   C H@AB}C}EvFGFH`I}QUNVWX}} }}}} `$ }} }}  G H I }} }} }}           `  `` "   hB   s *D1"``   < "_^  XKlepnutm lze upravit styl pYedlohy nadpiso.- -   6 "_^  Klepnutm lze upravit styly pYedlohy textu. Druh roveH TYet roveH tvrt roveH Pt roveH,    `   6 #" `` `  F*0    64; #" ``  ; H*0    6T ; #" `` ` ; H*0    Zbd޽h ?"` CCC80___PPT10. 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Druh roveH TYet roveH tvrt roveH Pt roveH,   `   6= _P  = T*    6= _  = V*  H  0޽h ? 3380___PPT10.u`d| 0L0 00(  x  c $HA$m] A x  c $IA$] A   Zbd޽h ?"` CCC___PPT10i..F+D=' == @B + { 0L0 ($(  (r ( S lv _^   r ( S 0 _^  H ( 0޽h ? ___ff3ff___PPT10i..0D r+D=' == @B +m { 0 4$(  4r 4 S  A _^  A r 4 S A /G A H 4 0޽h ? ___ff3ffy___PPT10Y+D=' == @B +y { 0 0(  x  c $: _^  : x  c $ : /G : H  0޽h ? ___ff3ffy___PPT10Y+D=' == @B +m { 0 ,$(  ,r , S A _^  A r , S ܻA GH A H , 0޽h ? ___ff3ffy___PPT10Y+D=' == @B + { 0L0 0*(  0r 0 S A _^  A x 0 c $A _, A f 0 Nb޽h ? ___ff3ffy___PPT10Y+D=' == @B + { 0L0 0(  x  c $f _^  f x  c $f _^ f f  Nb޽h ? ___ff3ffy___PPT10Y+D=' == @B + { 0L0 0(  x  c $xf _^  f x  c $Tf _^ f f  Nb޽h ? ___ff3ffy___PPT10Y+D=' == @B +} { 0 P$(  Pr P S  f _^  f r P S f _^ f H P 0޽h ? ___ff3ff___PPT10i.2PC+D=' == @B +- {  0 D< T(  Tr T S f _^  f r T S p'f  &^ f   T ZA  xi"`/G&5 fH T 0޽h ? ___ff3ff___PPT10i.2@č+D=' == @B + {  0 `1d;(  dr d S Jf _^  f  ,d PA  riz `} f^ /d s 6A  neriz0 1 0d 6$Df P   queue length xxxxxx splits Above: manual control Bellow: optimal control Results: The situation on the first arm worsened but the global situation was better. F f3 N.   RB 1d s *D8cH d 0޽h ? ___ff3ffy___PPT10Y+D=' == @B +A {  0 h` |(  |r | S <; _^  ; r | S ; _^  ;  | BAV i6 qThank you for your attention!,  | 6`A G {] Jitka Homolov jkratoch@utia.cas.cz 6^0FPB~        0BVH | 0޽h ? ___ff3ffy___PPT10Y+D=' == @B +M{  0 tlP(    BVff qThank you for your attention!,   6sf  tY {] Jitka Homolov jkratoch@utia.cas.cz 6^0FPB~        0BVH  0޽h ? CCCy___PPT10Y+D=' == @B + 0  (  X  C    =  S 8= 0  = " H  0޽h ? 3380___PPT10.u`d 0  (  X  C    =  S = 0  = " H  0޽h ? 3380___PPT10.u`d 0  (  X  C    =  S = 0  = " H  0޽h ? 3380___PPT10.u`d 0   (  X  C    =  S Բ= 0  = " H  0޽h ? 3380___PPT10.u`d 0 0 (  X  C    =  S = 0  = " H  0޽h ? 3380___PPT10.u`d 0 @ (  X  C    =  S t= 0  = " H  0޽h ? 3380___PPT10.u`d 0 P (  X  C    =  S = 0  = " H  0޽h ? 3380___PPT10.u`d 0 ` (  X  C    =  S t= 0  = " H  0޽h ? 3380___PPT10.u`d 0 p (  X  C    =  S = 0  = " H  0޽h ? 3380___PPT10.u`d  0  (  X  C    =  S { 0  = " H  0޽h ? 3380___PPT10.u`d  0  (  X  C    {  S { 0  { " H  0޽h ? 3380___PPT10.u`d 0  (  X  C    {  S  { 0  { " H  0޽h ? 3380___PPT10.u`d 0  (  X  C    {  S { 0  { " H  0޽h ? 3380___PPT10.u`dr?8pj{ !&۩0g7 j: 5Me} %8=I1T2( ;  z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.czz(jkratoch@utia) .. 5  HH  21 21    21    5     )   2    !"#$%&'()*+4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$2$w焅T 0 $  e               <Traffic Systems  <Data = detector measuring Intensity = amount of passing vehicles per time [veh/h] Occupancy = proportion of sample time when a detector is being activated [%] Velocity, density = Control variable = Splits (relative greens) impacting the capacities of all junction approaches, i.e. the amount of passed cars0c,T 6 DT^@    b    Our Approach   Multi-level control system Local level  control of a microregion Coordination level  global control State space approach to the actual traffic situation Individual traffic variables do not bring full information Queue length as a state  intuitively understandable Optimal signal traffic control as LP task Linearity of local relations and restrictions ZKZ5ZrZZ*Z/ZK5q  *  .     e  &Local traffic control of a microregion''  '  Linear model of a microregion for queues Basic equation  hydrodynamic analogy Supplementary equation for occupancy (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities)&% X )M   X    (     p :&Local traffic control of a microregion''  '  Formulation of the linear control task Optimization by LP Criterion  weighted sum of queues Restrictions  traffic nature of all variables and relations between them State space model Non-negativity Total sum of splits Restricted increments of splits z'6JV '7J  V*  85Coordination level - control of the whole macroregion66 p       Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the optimization task Optimization by LP Several strategies  the easiest one is the analogy of the local level!%Z !% Y                Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)}( ~:D   B 7/l=     " !#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{|}~>?@ABCDEF G H I rYI1[2( ;  z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.czz(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.cz/ 0DArialardeBk BThhy 0DTimes New Romanhhy 0 DAvantGarde Bk BThy 0"0DWingdings Bk BThy 0@DSymbolgs Bk BThy 0PDAvantGardeBk BThy 0t " A . @n?" dd@  @@``  ..,,   () .. 5  HH  21 21    21    5     )   2    !"#$%&'()*+4$$2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ$$2$w焅T 0 $  e               <Traffic Systems  ]Data = detector measuring Intensity = amount of passing vehicles per time [veh/h] Occupancy = proportion of sample time when a detector is being activated [%] Velocity, density = not always measured Control variable = Splits (relative greens) Signal scheme To impact the capacities of all junction approaches, i.e. the amount of passed cars0v,b 6 DbD@      Our Approach   Multi-level control system Local level  control of a microregion Coordination level  global control State space approach to the actual traffic situation Individual traffic variables do not bring full information Queue length as a state  intuitively understandable Optimal signal traffic control as LP task Linearity of local relations and restrictions ZKZ5ZrZZ*Z/ZK5q  *  .     e  &Local traffic control of a microregion''  '  Linear model of a microregion for queues Basic equation  hydrodynamic analogy Supplementary equation for occupancy (Kalman) filtering + estimation Estimation of model parameters Estimation of non-detected and non-measurable quantities)&% X )M   X    (     p :&Local traffic control of a microregion''  '  Formulation of the linear control task Optimization by LP Criterion  weighted sum of queues Restrictions  traffic nature of all variables and relations between them State space model Non-negativity Total sum of splits Restricted increments of splits z'6JV '7J  V*  85Coordination level - control of the whole macroregion66 p       Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the optimization task Optimization by LP Several strategies  the easiest one is the analogy of the local level!%Z !% Y                Testing Data: Real data as the inputs  measured in Prague Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation Kalman filter Common version of linear Kalman filter with point estimates inserted. UE. SE  ?  +      &  Simulated and estimated queues  lNote: a disturbance was added to the first state, i.e. length of the queue on the first arm of the junction(mZg m & Testing 0 Conclusions  All reached results are very promising. Observable and stable models. Good state estimates by Kalman filter. Noticeable improvement over against the manual control. B)}( ~:D   B 7/l=>?@ABCDEF G H I y { 0 0(  x  c $: _^  : x  c $ : /G : H  0޽h ? ___ff3ffy___PPT10Y+D=' == @B +r<9iq<I1z;( ; r z(jkratoch@utia.cas.cz6mailto:jkratoch@utia.cas.czLRovnice Equation.30"Editor rovߍέy)g*gey15+Hj,[T28GMNuS!R=BZq6OMIPR}+οA>>/柎k~aR+My9۷39?K|\v)?-R~`Q^Q㔯bC\S3)P`hk'W?|N~:crUZ2ޖ~ͣj}pAջOl>KFl\_nGka~1{ f;emu&8S^ߑZs0/X s {4?`!棼smn! `0xcdd``db``baV !,&FF(`T)WRcgbR /P=7T obIFHeA*CL N`A $37X/\!(?71aǒXk4:]b mHgI%gܨPG벡/fE?͈*ycdl`< g%W#;g 7* ;*+**o0B䱄ȝI9 n\*τۜ s 85 a/(3 ٫&Ł^i`\2BnO73o-Pϋx=`Tb=\^h``;F&&\ @ ] @BO`U`!m*%7a>az `P0xcdd`` @c112BYL%bpuFs`wT vG;q ~%F1nw1{^pO 1J@(\uDf _cmŞ\qۃ\F=\TN`%wLLJ% s:@ !t?1nic 3.0ORovnice Equation.30"Editor rovnic 3.0PRovnice Equation.30"Editor rovnic 3.0QRovnice Equation.30"Editor rovnic 3.0RRovnice Equation.30"Editor rovnic 3.0/ 0DArialrdeBk BThhy 0DTimes New Romanhhy 0 DAvantGarde Bk BThy 0"0DWingdings Bk BThy 0@DSymbolgs Bk BThy 0PDAvantGardeBk BThy 0t "`DTahomardeBk BThy 0 A . @n?" dd@  @@`` 80H" ..,,   () .. 5  HH  21 21    21    5     )   2    !"#$%&'()*+ /012 78`2$q"p]ij2$棼smn!d2$HQRIX/Ʌ2$h{2ZEj&RHvd?{~Ʌ2$m*%7a>aB2$)Wg/832$w焅T /     e               <Traffic variables  xData = detector measuring Intensity = amount of passing vehicles per time [veh/h] Occupancy = proportion of sample time when a detector is being activated [%] Velocity, density = not always measured Control variable = Splits (relative greens) Signal scheme = course of light signals Impact on the capacities of all junction approaches, i.e. the amount of passed carsX0w,| 6 D  lD@    !  Our Approach   Multi-level control system Local level  control of a microregion Coordination level  global control State space approach Queue length as a state intuitively understandable, fully expresses an actual traffic situation non-measurable Optimal signal traffic control as LP task Linearity of local relations and restrictions ZKZZZXZ*Z.ZZKX  *. e  Model of a microregion   Linear model of a microregion for queues Basic equation  hydrodynamic analogy Supplementary equation for occupancy State space model )'' )         x  )   # :Estimation on the local level  Estimation of states Linear Kalman filter Output model Output intensities (sum of Pi;t) Identity for occupancy Estimation of model parameters or non-detected and non-measurable quantities Non-linear Kalman filterZ$Z9ZMZZ#  M  Z  2  r   MControl on the local level   Formulation of the linear control task Optimization by LP Criterion  weighted sum of queues Restrictions  traffic nature of all variables and relations between them State space model Non-negativity Total sum of splits Restricted increments of splits '7JV '7J U*  8Control of the macroregion&     Linear model of a macroregion Analogy of local model No estimation Using estimates from local level Formulation of the optimization task Optimization by LP Several strategies  the easiest one is the analogy of the local level!%Z !%  Z                STesting  Data: Real intensities as the inputs  measured in Prague area Simulation: Digital simulation - model with fixed parameters, computed output AIMSUN simulation  traffic micro-simulator Kalman filter Linear Kalman filter with point estimates inserted DD1, EKF, & Z9Z ZnZZ?Z 0 ?  J  +       2 Model in pictures  Data: Real intensities as the inputs Microregion: Junction with two input and only one output arms Simulation: Digital simulation Kalman filter LKF  1  1   f&   >       Queue estimation  1Note: a disturbance was added to the first state(2Z, 2 & Control 0 Conclusions  6All reached results are very promising: Models of  micro and  macro regions Estimation of states, model parameters, etc. Control strategies Fixed or dynamically setting of weights Control on horizon  dynamic approach Noticeable improvement over against the manual (fixed) controlZ)fN?)fN?  7/=>?@ABCDEF G H I N T   0` 33PP` 13` 3333` Q_{` 333fpKNāvI` j@v۩ῑ΂H>?" dd@,?n<d@ `7 `2@`7``2 n?" dd@   @@``PR    @ ` ` p>> @ 8   (    <0"" H 0    Td" H 0    < "U_ H 0    Tpd">& H 0    N"P H 0    <@'"p H 0    C x0?d?"bUv H 0  (   <: #" `   XKlepnutm lze upravit styl pYedlohy nadpiso.--    0= "   Klepnutm lze upravit styly pYedlohy textu. Druh roveH TYet roveH tvrt roveH Pt roveH,   `    6B "]}  b*0    6K "] }   \*0     6V "]T}  \*0  B  s *޽h ? 333380___PPT10.(г% Smsice<   0   B (  T +  "+bb P@ # "Dwoh  s *"PP  Bd" P@bb P 0  # "Nyh  s *"P    Bd"P 0 z   <" a*h   s *"    f?d?"+).   B@e ?#" ` p  XKlepnutm lze upravit styl pYedlohy nadpiso.--    0h " `    ^Klepnutm lze upravit styl pYedlohy podnadpiso.00   6lm "`p   f* 0   6Tx "`p   `*"0    6 "`  `*"0  B  s *޽h ? 333380___PPT10.(г% 0L0 00(  x  c $HA Mp A x  c $IA ] A P  s *޽h ?"` CCC___PPT10i..F+D='  = @B +  0L0 (0(  (x ( c $lv     x ( c $0    H ( 0޽h ? ___ff3ff___PPT10i..0D r+D='  = @B +s  0 4*(  4x 4 c $ A    A r 4 S A @G A H 4 0޽h ? ___ff3ffy___PPT10Y+D='  = @B +  0 6(  ~  s *:    : x  c $ : i : H  0޽h ? ___ff3ffy___PPT10Y+D='  = @B +s  0 ,*(  ,x , c $A    A r , S ܻA GH A H , 0޽h ? ___ff3ffy___PPT10Y+D='  = @B +  0L0  0(  0x 0 c $A    A x 0 c $A  A  00 NA ? ?      00  `A ? ? "` =   {t  0 s *A ? ?"` = f 0 Nb޽h ? ___ff3ffy___PPT10Y+D='  = @B +  0L0 r(  ~  s *f    f   s δ0e0e  #" 0eY   0  `A ? ? "` F   "f  Nb޽h ? ___ff3ffy___PPT10Y+D='  = @B +]   0L0 ld(  ~  s *K=    = ~  s *q=  =  0 NA ? ? % j~    f  Nb޽h ? ___ff3ffy___PPT10Y+D='  = @B +  0L0 <(  ~  s *xf    f ~  s *Tf   f f  Nb޽h ? ___ff3ffy___PPT10Y+D='  = @B +  0 p6(  ~  s *lA     x  c $  _^  H  0޽h ? ___ff3ff___PPT10i.2PC+D='  = @B +  0 P*(  Px P c $ f    f r P S f _^ f H P 0޽h ? ___ff3ff___PPT10i.2PC+D='  = @B +3   0 JB T(  Tx T c $f   f r T S p'f   f   T ZA  xi"`/G&5 fH T 0޽h ? ___ff3ff___PPT10i.2@č+D='  = @B +   0 `1dA(  dx d c $Jf    f  ,d PA  riz `} f^ /d s 6A  neriz0 1 0d 6$Df P   queue length xxxxxx splits Above: manual control Bellow: optimal control Results: The situation on the first arm worsened but the global situation was better. F f3 N.   RB 1d s *D8cH d 0޽h ? ___ff3ffy___PPT10Y+D='  = @B +y   0  |0(  |x | c $<;    ; x | c $;   ; H | 0޽h ? ___ff3ffy___PPT10Y+D='  = @B +M  0 tlP(    BVff qThank you for your attention!,   6sf  tY {] Jitka Homolov jkratoch@utia.cas.cz 6^0FPB~        0BVH  0޽h ? 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