Applications of the urban traffic control strategy TUC

European Journal of Operational Research 175 (2006) 1652–1665 www.elsevier.com/locate/ejor

Applications of the urban traffic control strategy TUC Vaya Dinopoulou, Christina Diakaki, Markos Papageorgiou

*

Dynamic Systems and Simulation Laboratory, Technical University of Crete, Greece Available online 9 April 2005

Abstract Despite the long-lasting research and developments in the field of urban traffic control systems, the continuously increasing mobility requirements urge for solutions that will release urban areas from the serious congestion problems and their consequences. From the control point of view, this may be translated into the employment of traffic-responsive systems that respond automatically to the prevailing traffic conditions. This is the aim of the signal control strategy TUC, whose basic philosophy, design methodology, characteristics and application results under both simulated and field conditions are presented in this paper. Based on a store-and-forward type of mathematical modelling and using well-known methodological tools from Automatic Control Theory, the TUC strategy addresses in a simple but efficient way, as demonstrated from the applications so far, the problem of co-ordinated, traffic-responsive signal control in large-scale urban networks.  2005 Elsevier B.V. All rights reserved. Keywords: Traffic control; Optimal control; Urban traffic control

1. Introduction Urban traffic control systems constitute a scientific field with long-lasting and extensive research and development activities. Many methodologies have been proposed so far, but the problem of traffic-responsive network-wide signal control still calls for adequate and efficient solutions particularly under saturated traffic conditions. In fact, *

Corresponding author. Tel.: +30 28210 37289; fax: +30 28210 37584. E-mail address: [email protected] (M. Papageorgiou).

widely used strategies like SCOOT (Hunt et al., 1982) and SCATS (Lowrie, 1982), although applicable to large-scale networks, have been judged to have a limited traffic-responsive behaviour during rapidly changing conditions such as those occurring during daily business peaks or in case of incidents. On the other hand, more advanced, recently developed, traffic-responsive strategies, like OPAC (Gartner, 1983), PRODYN (Farges et al., 1983), RHODES (Mirchandani and Head, 1998), employ algorithms with exponential complexity, which does not permit a straightforward network-wide application of their basic optimisation concept.

0377-2217/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2005.02.032

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

As a consequence, they use hierarchically superior control levels with the aim of network-wide coordination in a heuristic way. Another shortcoming of the aforementioned strategies is their limited capability to respond adequately to saturated traffic conditions that are frequently observed in modern metropolitan areas. The new signal traffic control strategy TUC (Traffic-responsive Urban Control) has been developed so as to provide co-ordinated, trafficresponsive control in large-scale urban networks, even in cases of saturated traffic conditions. This objective has been pursued via the utilisation of appropriate methodological tools that allow for efficient application to large-scale networks and give rise to the following characteristics (Diakaki, 1999): • Considerable efficiency as suggested by the results of all the investigations to date, under both simulated and real-life traffic conditions. • Robustness with respect to measurement inaccuracies and disturbances. • Reliability with respect to hardware failures (detectors, communication links, etc.). • Generality that leads to easy applicability (via available software tools) in networks of arbitrary characteristics and dimensions, with virtually no need for calibration or fine-tuning. • Extreme simplicity of design and implementation code. • Limited measurement requirements (one detector per link at arbitrary link locations). • Low computational effort and communication requirements (central control decisions once per cycle). The aim of this paper is to briefly describe the basic philosophy, methodology and characteristics of the TUC strategy, along with application results under both simulated and real-life traffic conditions. TUC was originally conceived to control the green splits for each junction. Although the strategy has been recently extended to also control cycle time and offsets (Diakaki et al., 2002), this paper focuses on split control only. Section 2 provides a description of the TUC strategy, while Sections 3 and 4 present the characteristics and

1653

application results under simulated and field conditions, respectively, for the two example networks. Finally, Section 5 summarizes the general conclusions and the future plans.

2. The TUC strategy The aim of the TUC strategy is to provide, at each cycle, traffic-responsive signal settings, taking into account the overall traffic conditions within an urban network. An urban network may be represented as a digraph with links z 2 Z and junctions j 2 J. According to the basic store-and-forward modeling approach (Gazis and Potts, 1963), vehicles experience constant travel times along a link and are stored at the end of the link if the corresponding inflow is higher than the outflow. The outflow from a link is forwarded according to the applied signal control. Consider a signal controlled junction j with the sets Ij and Oj of incoming and outgoing links, respectively. It is assumed that all the permissible movements of an incoming link receive the right of way (r.o.w.) simultaneously. The following assumptions are made: • The cycle time Cj and the total lost time Lj of junction j are fixed; for simplicity, it is assumed Cj = C for all junctions j 2 J. • The offsets are fixed (i.e. the beginning of the main stage of each cycle is fixed). • The signal control of junction j is based on a fixed number of stages that belong to the set Fj, and mz denotes the set of stages where link z has r.o.w. • The saturation flows Sz, z 2 Ij, are known. • The turning rates tzw, z 2 Ij, w 2 Oj, are fixed and known. By definition the following constraint applies at junction j: X gj;i þ Lj ¼ C; ð1Þ i2F j

where gj,i is the effective green time of stage i at junction j. Additionally, the following constraints

1654

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

are introduced to guarantee allocation of green time to all stages gj;i P gj;i;min

8i 2 F j ;

ð2Þ

where gj,i,min is the minimum permissible effective green time for stage i at junction j. Consider now a link z connecting two junctions M, N such that z 2 OM and z 2 IN (see Fig. 1). The dynamics of link z are described by the following equation xz ðk þ 1Þ ¼ xz ðkÞ þ T ½qz ðkÞ  sz ðkÞ þ d z ðkÞ  uz ðkÞ; ð3Þ where xz is the number of vehicles within link z; qz and uz are the inflow and outflow, respectively, of link z over the period [kT, (k + 1)T] with T the control time interval and k = 1, 2, . . . a discrete time index; and dz and sz are the demand and the exit flow, respectively. For the exit flow the following formula holds sz ðkÞ ¼ tz;0 qz ðkÞ

ð4Þ

with exit rates tz,0 considered fixed and known. Assuming that the demand flow is constant and equal to dz, and taking into account Eq. (4), the following is obtained from (3) xz ðk þ 1Þ ¼ xz ðkÞ þ T ½ð1  tz;0 Þqz ðkÞ þ d z ðkÞ  uz ðkÞ: ð5Þ The inflow to the link z is given by X qz ðkÞ ¼ tw;z uw ðkÞ;

ð6Þ

outflow uz of a link is equal to the saturation flow Sz if the link has r.o.w., and equal to zero else. However, if the control interval T is chosen not less than the cycle time C, an average value is obtained as follows: uz ðkÞ ¼

S z Gz ðkÞ ; C

ð7Þ

where Gz is the effective green time of link z, calculated as X Gz ðkÞ ¼ gN ;i ðkÞ: ð8Þ i2mz

Substituting (6)–(8) into (5), Eq. (9) yields " P X S w i2mw gM;i ðkÞ xz ðk þ 1Þ ¼ xz ðkÞ þ T ð1  tz;0 Þ tw;z C w2I M # P S z i2mz gN ;i ðkÞ þd z ðkÞ  : ð9Þ C Assume a nominal fixed time plan gN consisting of nominal splits gNj;i for each stage i of each junction j; assume that, under a corresponding constant nominal demand dN, the time plan gN leads to a T stationary state xN ¼ ½xN1 xN2 . . .  . Then we have due to (9) " P X S w i2mw gNM;i 0 ¼ T ð1  tz;0 Þ tw;z C w2I M # P S z i2mz gNN ;i þ d Nz  : ð10Þ C

w2I M

where tw,z with w 2 IM are the turning rates of the links entering junction M towards link z. Assuming that space is available in the downstream links and that xz is sufficiently high, the

Subtracting the steady-state equation (10) from (9), the following state equation is obtained: " xz ðk þ 1Þ ¼ xz ðkÞ þ T ð1  tz;0 Þ



M

uz

qz

sz

dz

Fig. 1. An urban road link.

N

X

Sz

P

i2mz Dg N ;i ðkÞ

#

C

w2I M

;

tw;z

Sw

P

i2mw Dg M;i ðkÞ

C

ð11Þ

where Dg = g  gN. Applying (11) to an arbitrary network of several signalized junctions j 2 J, the following state equation (in vector form) describes the evolution of the system in time: xðk þ 1Þ ¼ AxðkÞ þ BDgðkÞ;

ð12Þ

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

where x is the vector of the numbers of vehicles xz within links z 2 Z, Dg is the vector of Dgj;i ¼ gj;i  gNj;i , "i 2 Fj, "j 2 J, and A = I, and B are the state and input matrices, respectively. A quadratic criterion to be minimized has the general form I¼

1 1X 2 2 ðkxðkÞkQ þ kDgðkÞkR Þ; 2 k¼0

ð13Þ

where Q and R = rI are nonnegative definite, diagonal weighting matrices. The first term in (13) is responsible for the balancing of the numbers of vehicles within the network links. To this end, each diagonal element of Q is set equal to the inverse of the maximum permissible number of vehicles within the corresponding link. Furthermore, the magnitude of the control reactions can be influenced by the choice of the weighting parameter r. For this reason, the choice of r is performed via a trial-and-error procedure so as to achieve a satisfactory control behavior for a given application network. Minimization of the performance criterion (13) by applying the LQ methodology leads to a LQ control law (Anderson and Moore, 1990) gðkÞ ¼ gN  LxðkÞ;

ð14Þ

where L is the constant feedback gain matrix (the control matrix) which depends upon the problem matrices A, B, Q, and R and may be calculated off-line from the well-known stationary Riccati equation (Anderson and Moore, 1990). Simulation investigations indicate a low sensitivity of the gain matrix L with respect to variations of traffic parameters (such as turning rates, saturation flows, etc.) (Diakaki, 1999). Because the LQ methodology does not take into account the existence of constraints, a suitable nap-sack algorithm (see McLean et al., 1997, for details) modifies the calculated green time durations so as to satisfy the constraints (1) and (2). Finally, it should be noted that the derived state-feedback regulator (14) requires availability of measurements of all state variables in real-time. However, the numbers of vehicles xz are not directly measurable. Occupancy measurements oz, available in real-time, may be transformed into

1655

(approximate) numbers of vehicles via suitable non-linear functions xz = fz(oz) (see McLean et al., 1997, 1998, for details). The control law (14) suggests availability of nominal values gN, i.e. values of the effective green times that are optimal for a given historical demand and may be obtained through available techniques (e.g. through TRANSYT optimization). If such values are not available, the control law (14) may be employed in the following form: gðkÞ ¼ gðk  1Þ  L½xðkÞ  xðk  1Þ which is obtained by subtracting Eq. (14) for period k  1 from Eq. (14) for period k. A further control law that eliminates the need of nominal values gN may be obtained through the formulation of the urban traffic control problem as a LQI (linear-quadratic-integral) (Papageorgiou, 1996) optimal control problem under the same assumptions, based on the same modeling approach, and using a similar control objective as before. The LQI approach leads to the following multivariable regulator gðkÞ ¼ gðk  1Þ  L1 xðkÞ  L2 xðk  1Þ;

ð15Þ

where L1 and L2 are the control gain matrices. The efficiency of the TUC strategy was tested both under simulated and real-life traffic conditions that will be presented in the rest of the paper.

3. Simulation investigations of TUC For the simulation investigations of TUC, two existing urban networks have been utilised. Both networks have been modelled via the METACOR modelling and simulation tool (Diakaki and Papageorgiou, 1996), and simulation tests were conducted for several scenarios of demands and incidents with a duration of 4 hours each. In both cases, TUC has been compared to fixed-time signal control of the considered networks including offline optimized offsets; these fixed signal settings were developed for one specific peak demand scenario by experienced traffic engineers using stateof-practice tools. The utilized fixed signal settings are also used as nominal plan gN in TUC according to (14).

1656

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

(ii) High demand (approximately 40% higher than in scenario (i)) in almost all network origins. (iii) Demands present high fluctuations between the extremes of scenarios (i) and (ii). (iv) Demands like scenario (i) and a major incident occurring before the peak period. (v) Demands like scenario (i) and a major incident occurring during the peak period.

The first application network consists of 13 signal controlled junctions and 61 links (Fig. 2) from the urban network of Glasgow, in a part of which the first field-implementation and evaluation of TUC took place within the European project TABASCO (Diakaki et al., 2000). The investigations are based on a 4-hour simulation with TUC strategy running every 2 minutes, a control time interval that is equal or twofold to the cycle time of all considered junctions. Initially, simulations are performed with fixedtime signal control for five different scenarios of demands and incidents. Then, the control law (14) is applied and tested with the METACOR simulator. The utilized demand and incident scenarios carry the following characteristics:

In all investigations, it is assumed that the numbers of vehicles within the urban links are measurable in real-time (e.g. through a video detection system). Table 1 summarizes the results of the simulation tests in terms of the performance indices total waiting time at the network origins (of vehicles that wish to enter the network but their entrance is hampered due to congestion spillback at the

(i) Moderate demand in all but a few network origins.

1 2

3

42

11

40

2

49

9

9 8 12 13 17

3

35

61

52

20

4

8

18

LEGEND

7

32

33 27

28

6

...

23 24

......

25

5 19

15

31

36 29

37 21 22

38

14 16

48

11

34

39

10

13 b 58

30 41

7

6

13a 55

51

57

45 44 43

10

5

1b

59

12 b

47

4

56

53

12a

1a

60

54

50 46

urban junction number ( a, and b, where applicable, denote junctions with common signal staging) signal controlled urban link non-controlled urban link

26

Fig. 2. The Glasgow application network.

Table 1 Simulation results for fixed-time signal control, and TUC strategy for the Glasgow network

Scenario Scenario Scenario Scenario Scenario

(i) (ii) (iii) (iv) (v)

Waiting time

Travel time

Total time spent

Fuel consumption

Veh h

Percentage change

Veh h

Percentage change

Veh h

Percentage change

Veh lt

Percentage change

FSC

TUC

FSC

TUC

FSC

TUC

FSC

TUC

128 2042 4 128 120

100 100 100 100 100

2129 3383 2365 2166 2108

34 26 19 34 32

2257 5424 2369 2294 2228

38 54 20 38 35

3875 5500 4237 3920 3849

23 18 13 23 21

FSC: fixed-time signal control.

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

corresponding origins; this index reflects to some extent the impact of congestion beyond the simulated network part), total travel time within the simulated network, total time spent (this is the sum of the two previous indices), and total fuel consumption for all vehicles during the 4-hour simulation horizons. The figures of Table 1 indicate that the TUC strategy leads to a significant reduction of all performance indices. More specifically, the waiting time at the network origins is reduced by 100% for all investigated scenarios (i.e., no vehicles awaiting to enter the network), while the total travel time, the total time spent, and the total fuel consumption are reduced in the range of 19– 34%, 20–54%, and 13–23%, respectively, depending upon the investigated scenario. Fig. 3 displays the time evolution of the number of vehicles within some selected links under fixedtime signal control and the TUC strategy, for the demand scenario (i). The vertical axis in Fig. 3 represents the number of vehicles xz of a link z over the maximum storage capacity xz,max of the link. By inspection of the network sketch in Fig. 2 and the diagrams of Fig. 3, one may see that under fixed-time signal control, congestion develops in link 34 at junction 8. This congestion spills back through links 38, 20, 17, and 13, and reaches junction 2 where it is resolved. Under the TUC strategy the same congestion does not even reach junction 9. Similar performance is also achieved in the other investigated scenarios. Although the high improvements achieved by TUC are also due to the inadequacy of the same fixed-time signal settings gN applied to several different demand sce-

narios, the results indicate the capability of TUC to adapt to different demand patterns based on the same (partly inadequate) nominal plan gN. If the numbers of vehicles within urban links are estimated through occupancy measurements, the achieved amelioration of the traffic conditions is lower but still significant as compared to the fixed-time signal control. More specifically, in this case, the waiting time at the network origins, the travel time, the total time spent, and the total fuel consumption are reduced in the range of 73–100%, 10–30%, 14–34%, and 6–20%, respectively, depending upon the investigated scenario. The simulation investigations of both (15) and (16) using measured or (occupancy-based) estimated values of numbers of vehicles within links indicate a similar performance with the control law (14). Table 2 summarises the values of the performance indices for the five examined scenarios of demands and incidents, with measured values of numbers of vehicles within links. Given the similar performance of the three regulators, the selection of the approach to be employed may be based on other criteria like e.g. requirement of network authorities to utilise nominal values or lack of nominal values, etc. The second application network consists of 17 signal controlled junctions and 79 links (Fig. 4) and represents the urban network of the city centre of Chania, in two junctions of which the second field-implementation and evaluation of TUC took place within the Greek project CHANIASYN (Dinopoulou et al., 2000, see section 4). The investigations are based again on 4-hour simulations with TUC being activated every

Fixed-Time Control

TUC

1

1

0.8

0.8 34 38 20 17 13

0.6 0.4 0.2

x z (k )/x z,max

x z (k )/x z,max

1657

34 38 20 17 13

0.6 0.4 0.2

0 0

20

40

60

80

control interval (2 min)

100

120

0

0

20

40

60

80

100

120

control interval (2 min)

Fig. 3. Comparison of fixed-time signal control and TUC for scenario (i) of the first example network.

(i) Moderate demand in all network origins. (ii) High demand (approximately 40% higher than in scenario (i)) in all network origins. (iii) Extreme demand. (iv) Demands present high fluctuations between the extremes of scenarios (i) and (iii). (v) Demands like in scenario (iv) and a major incident occurring during the peak period.

2978 4541 3686 3022 3027 2985 4510 3664 3029 3046 1394 2530 1913 1430 1434 1399 2500 1895 1436 1449 1399 2486 1905 1431 1444 1394 2526 1913 1430 1434 1399 2500 1895 1436 1449 TUC-(1) refers to the multivariable regulator (14). TUC-(2) refers to the multivariable regulator (15). TUC-(3) refers to the multivariable regulator (16).

1399 2486 1905 1431 1444 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 (i) (ii) (iii) (iv) (v) Scenario Scenario Scenario Scenario Scenario

TUC-(2)

90 seconds, the utilized cycle duration. Initially, simulations are performed with fixed-time signal control for five different scenarios of demands and incidents. Then, the control law (14) is applied and tested with the METACOR simulator. The utilized demand and incident scenarios carry the following characteristics:

2985 4494 3677 3023 3039

TUC-(3) TUC-(2) TUC-(1) TUC-(3) TUC-(2) TUC-(3) TUC-(2)

Travel time (veh h)

TUC-(1) TUC-(1)

TUC-(3) Waiting time (veh h)

Table 2 Simulation comparison of alternative control laws for TUC for the Glasgow network

Total time spent (veh h)

Fuel consumption (veh lt)

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

TUC-(1)

1658

Table 3 summarizes the results of the simulation tests in terms of the same performance indices as in the first example network. As before, the figures of Table 3 indicate that the TUC strategy leads also in this case, to a significant reduction of all performance indices. More specifically, the waiting time at the network origins is reduced by 100% for all investigated scenarios, while the travel time, the total time spent, and the total fuel consumption are reduced in the range of 19–78%, 32–91%, and 23–86%, respectively, depending upon the investigated scenario. Clearly the unrealistically high improvements achieved under some scenarios are mainly due to the inadequacy of the fixed settings for these scenarios. However, since TUCÕs nominal plan gN is identical to the fixed settings, this again demonstrates the capability of TUC to adapt, via the real-time measurements, automatically to different demand patterns. Fig. 5 displays an example of the time evolution of the relative occupancies xz/xz,max within some selected links under fixed-time signal control and the TUC strategy applied to the Chania network, for the demand scenario (iv). Under fixed-time signal control, congestion develops in link L11 at junction 7A. This congestion spills back through links L39, L48, L47, L43, L6, L4, L7, L8 and reaches L10, thus creating a kind of gridlock. Under the TUC strategy the same congestion does not even reach junction 5A. Similar effects are also observed in other investigated scenarios.

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665 O10

D1 O1 1A L61

D2

O2

L1

D3 L6

2A

L62

L4

2B

L8 L7

4A

L2

4B

L9

L10 L11

5

7

L39

L44 L46 1C

L47

3A

L48

3B

L35

6

O7 L18

O9

D8

16A

L20

D9

16B

L36

O11 D11

L24 L25

L21

L19

12

L22 O8

D20

L28

L26 L27

14

D24

O18

O19

L23 L17

L34

L38 D21

8

L40

L41

13

D7

D14

L42

L37 O20

L13 L14 L15 L63 L16

D10

D6 O6

O5

O21 L43

L45

D5

O4

D4

L12

1B D22

O3

1659

O14 L49

O24

L50

L51

D12

D15 D23

D18

L58 17

L56 L59

O17

9

D19

L53 L54

10 L57

L60

O15 11

O12

18 O23 O13

LEGEND

D16

L55 D17

O22

D13

...

O16

... ...

urban junction number (A,B and C, where applicable, denote junctions with common signal staging) signal controlled urban links non-controlled urban links

Fig. 4. The Chania application network.

Table 3 Simulation results for fixed-time signal control and TUC strategy for the Chania network

Scenario Scenario Scenario Scenario Scenario

(i) (ii) (iii) (iv) (v)

Waiting time

Total travel time

Total time spent

Total fuel consumption

Veh h FSC

Percentage change TUC

Veh h FSC

Percentage change TUC

Veh h FSC

Percentage change TUC

Veh lt FSC

Percentage change TUC

78 392 5682 225 225

100 100 100 100 100

393 764 3662 1583 1583

19 39 78 67 62

471 1156 9344 1808 1808

32 60 91 71 67

831 1770 11 750 2573 2573

23 47 86 60 57

FSC: fixed-time signal control.

Fig. 5. Comparison of fixed-time signal control and TUC for scenario (iv) of the Chania network.

If the numbers of vehicles within urban links are estimated through occupancy measurements, the achieved amelioration of the traffic conditions is slightly lower but still significant as compared to the fixed-time signal control. More specifically, in

this case, the waiting time at the network origins, the travel time, the total time spent, and the total fuel consumption are reduced in the range of 97– 100%, 19–75%, 32–90%, and 23–85%, respectively, depending upon the investigated scenario.

1660

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

In conclusion, in both aforementioned investigation cases, the application of TUC largely avoids the development of extended oversaturated conditions (including gridlocks) thereby leading to a significant amelioration of the traffic conditions.

4. Field implementations and evaluations of TUC 4.1. Implementation of TUC in Glasgow The first field-implementation and evaluation of the TUC strategy took place for a part of the M8 corridor network in Glasgow (McLean et al., 1998) within the TABASCO project. In this field implementation, TUC was part of the integrated traffic control strategy IN-TUC (INtegrated-Traffic-responsive Urban Control). IN-TUC (Diakaki, 1999) has been designed so as to integrate three different control applications, the urban traffic control strategy TUC, a ramp metering strategy, and a route guidance strategy. For ramp metering, the ALINEA (Asservissment LINeaire dÕEntre´e Autoroutie´re) strategy, a local feedback control law derived by use of classical feedback methods is used (Papageorgiou et al., 1991). Finally, route guidance is activated via available VMSs (Variable Message Signs) that display recommendations to the drivers on the routes to follow so as to mini-

mise their individual travel times. For this part of the strategy, a simple feedback control law is applied to each VMS in the aim of equalising the travel times between both corresponding alternative routes, which leads to user-optimal conditions (Pavlis and Papageorgiou, 1999). The aforementioned parts of the strategy are integrated in the sense of the mutual exchange of measurements and decisions. Each part may run with a different control interval and each part may be used as an independent control strategy. The M8 corridor network in Glasgow has serious congestion problems especially during the pm peak period that become more severe in presence of incidents or road works. The control elements included in the network area (Fig. 6) are ramp metering at Craighall on-ramp (junction 16), three VMSs installed in the urban area around junction 16, and signal control of the urban junctions along the urban routes parallel to the M8 motorway. The efficient and integrated utilisation of these control elements was expected, according to past simulation studies (Diakaki et al., 1997), to lead to a sensible improvement of the network management and reduction of traffic problems. IN-TUC has been applied to the Glasgow network with control intervals of 2 minutes for the signal control and route guidance, and 20 seconds for ramp metering. Regarding the control

Fig. 6. The Glasgow site.

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

decisions of TUC, the road authorities specified that the following operational constraint should be respected (McLean et al., 1997). The final control output should be one out of 6 pre-specified signal control plans available for every junction. This constrains the TUC strategy from optimal operation since the number of available plans is extremely limited compared to all possible outcomes of TUC. Despite this imposed operational constraint, TUC and IN-TUC as a whole demonstrated, as discussed below, a rather high efficiency. The field implementation and evaluation in Glasgow was phased. It started with the installation of ramp metering with ALINEA in July 1997. TUC was launched in November 1997, while IN-TUC became fully operational in February 1998. The evaluation was completed in March 1998. This approach allowed an understanding of the effect of individual control elements upon the network. The evaluation of the system considered a network wider than the one actually manipulated by the control system. This was done in order to enable a network-wide analysis of the effects of the system rather than an analysis constrained to the area directly affected by the operation of the system. Table 4 (McLean et al., 1998) summarises some of the performance indicators calculated throughout the evaluation period for the Glasgow corridor network. The lines ÔM8EÕ and ÔUrban Diversion RoutesÕ refer to the eastbound directions of the corresponding routes. The ÔTotal Urban NetworkÕ-line refers to the whole considered urban network, while the ÔTotal Evaluation NetworkÕ-

1661

line refers to the sum of the aforementioned network parts including also the metered on-ramp link. Furthermore, the Ôveh/hÕ-column displays summations of traffic volume data from all available detectors in the corresponding network parts, while the ÔsÕ-column displays summations of journey times of the motorway and urban stretches of the corresponding network parts. Finally, it should be mentioned that the evaluation considered several cases from which the following four main cases are presented in Table 4: • Base case: Fixed urban traffic control only (TRANSYT optimized), without ramp metering nor VMS operation. • Case 1: Fixed urban traffic control and ALINEA ramp metering. • Case 2: ALINEA ramp metering and TUC signal control. • Case 3: IN-TUC with ramp metering, signal control, and route guidance. The comparison of the results of the aforementioned cases presented in Table 4 leads to a series of conclusions. To start with, the introduction of ramp metering (case 1) increases (5%) the throughput of the motorway while decreasing (5%) the journey times therein. At the same time, having fixed urban traffic control at the urban diversion routes, the load (due to the driversÕ diversion in order to avoid the metered on ramp) and the journey times of the urban diversion routes increase significantly (13% and 4%, respectively). With the introduction of TUC strategy (case 2), the load

Table 4 Effect of control on throughput and journey times in Glasgow network Time period: 16:00–17:00 Throughput

M8E motorway Urban diversion routes Total urban network Total evaluation network (including the metered on-Ramp) * Not statistically significant.

Journey times

Veh/h

Percentage change

Base case

Case 1

Case 2

36 721 3087 20 157 60 324

+5 +13 –3 +2

+6 +20 –10 *

s

Percentage change

Case 3

Base case

Case 1

Case 2

Case 3

+6 +23 –6 *

210 440 1174 1567

–5 +4 * –2

* * –11 –10

* +1 –15 –13

1662

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

of the urban diversion routes increases further (from 13% to 20%). In contrast, the journey times of the urban diversion routes decrease as compared to case 1 (from 4% to 0%) and return to the levels of the base case. From this, it may be concluded that the observed increased throughput and the amelioration of the journey times despite this increase, are due to the efficient operation of the TUC strategy. The introduction of VMSs (case 3) leads to a further increase of load on the urban diversion routes (from 20% to 23%), as in this case the VMSs may explicitly suggest the alternative routes to the drivers. However, the corresponding journey times present only a slight increase (from 0% to 1%), a fact that further supports the previous conclusion. In conclusion, TUC specifically and IN-TUC as a whole demonstrated high efficiency in the corresponding field-investigated cases. 4.2. Implementation of TUC in Chania The second field-implementation and evaluation was undertaken within the Greek project CHANIASYN for a two-junction network of the city of Chania (Fig. 7) (Dinopoulou et al., 2001). These two junctions are somehow isolated from

the rest of the network and carry heavy loads, since they represent one of the major entrances to and exits from the city. In this implementation, TUC was applied and compared with the TASS strategy (Siemens, 2000) that was recently introduced in this network. For comparison purposes, the two strategies were applied in weekly alternation for a total period of six weeks (August–September 2001). The measurements collected during the first two weeks were used for the comparative evaluation of both strategies, while the measurements collected during the rest of the evaluation period allowed for the reliability check of the TUC strategyÕs performance. The implementation of TUC took place under several constraints that favor the existing TASS strategy. More specifically: • The TUC strategy was applied with constant cycle times of 90 seconds in contrast to TASS that may modify also the cycle time, if necessary. • The second constraint refers to the offsets. Although TUC can also modify the offsets in real-time, this TUC option was disabled in this implementation (again in contrast to TASS that also modifies the offsets).

Fig. 7. The urban network of Chania showing the two-junction network of the TUC implementation.

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

• The nominal green times used by TUC were not the optimal ones. Moreover, they were different than the green times used by TASS. This has some importance because, based on the nominal values, TUC modifies the green times so as to respond to the prevailing traffic conditions. In periods, however, of low traffic in the network, the TUC settings are close to their non-optimal nominal values (see (14)). • The implementation took place in a 2-junction network. As a consequence, several of the significant TUC characteristics remain practically unused (e.g. the avoidance of gridlocks).

1663

Table 5 summarizes some of the performance indicators calculated for the TASS and TUC strategies during the first two weeks of the evaluation period. More specifically, the table displays the total distance traveled, the mean speed, and the mean travel time, in daily averages and averages of the peak hours. The peak hours for this particular network at this particular period of the year were identified, based on volume measurements, to be 14:00–15:00 at noon and 21:00–22:00 at night. The figures of Table 5 make clear that the application of TUC leads to the increase of mean speeds

Table 5 Evaluation results for Chania network TASS

TUC

Daily averages

Peak hours

14:00–15:00 Mean speed (km/hour)

Daily averages 21:00–22:00

Peak hours 14:00–15:00

21:00–22:00

% Change

Wednesday Thursday Friday Saturday Sunday Monday Tuesday

18.16 16.87 15.05 14.11 18.81 16. 99 16.32

15.05 12.03 13.47 12.65 30.54 12.06 16.46

12.06 10.12 6.81 5.65 9.26 11.33 9.63

+13 +9 +15 +12 +20 +6 +15

+11 +27 +7 +43 +4 +16 12

+26 +15 +33 +97 +60 +7 +54

Total

16.42

14.29

8.79

+13

+13

+40

Total travel distance (veh km) Wednesday Thursday Friday Saturday Sunday Monday Tuesday Total

17 518.99 19 965.60 19 965.60 19 214.20 17 116.75 19 530.34 18 441.60

1193.96 1172.66 1196.00 1113.63 812.01 1192.98 1242.55

1068.83 1155.06 1079.93 957.31 1033.11 1102.05 1226.34

+12 1 1 +1 1 0 3

+6 +7 +5 +7 3 +4 2

+6 +5 +5 +12 +8 0 +1

131 456.98

7923.79

7622.63

+2

+4

+5

Mean travel time (hour) Wednesday Thursday Friday Saturday Sunday Monday Tuesday

0.06 0.06 0.07 0.07 0.05 0.06 0.06

0.07 0.08 0.07 0.08 0.03 0.08 0.06

0.08 0.10 0.15 0.18 0.11 0.09 0.10

12 9 13 11 17 6 13

10 21 7 30 4 14 +10

21 13 25 49 38 7 35

Total

0.06

0.07

0.11

11

12

29

1664

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665

in the range 6–20%, usually with a parallel increase of throughput as the criterion of total distance traveled indicates. At the same time, the mean travel time reduces in the range 6–17%. Totally, the weekly average increase of mean speed is 13% while the corresponding decrease of the mean travel time is 11%. A more detailed examination of the results indicate that the performance of TUC during the peak hours is even better. In the peak hour 14:00–15:00, the mean speed increases in the range 4–43%, while the corresponding mean travel time decreases in the range 4–30%, despite an increase of the traffic load observed in most of the evaluation days. In the peak hour 21:00–22:00 the increase of mean speed is even higher. It lies in the range 7–97% with an average of 40%, while the corresponding mean travel time decreases in the range 7–49%, despite the 5% (in average) increase of the traffic load. A similar performance of TUC is observed also during the rest of the evaluation period. TUC responds with the same high efficiency to similar traffic conditions, thus demonstrating an excellent reliability of performance. Conclusively, the TUC strategy led to a significant improvement of the traffic conditions in the considered network despite the constraints imposed to the application. It is also worthwhile to mention that, although there was no publicity for the tests that were taking place in this particular network part, users of the network (bus and taxi drivers in particular) confirmed and emphasized the aforementioned conclusions.

5. General conclusions and future plans The investigations of TUC in both simulated and real-life traffic conditions indicate the efficiency of the strategy. This efficiency in combination with its exceptional simplicity and easy applicability suggest that TUC is a significant innovation in the area of urban traffic control systems. In June 2001, a new European project (SMART NETS) was launched where TUC is being implemented in large parts of three European cities: Southampton (UK), Munich (Germany), and Chania (whole network). Within this

particular project, the most recent extensions of TUC for cycle and offset control as well as provision of public transport priority are being further investigated and implemented. Finally, it should be mentioned that simulation tests for the application of TUC (including all the aforementioned extensions) in parts of the urban networks of Jerusalem and Tel Aviv were completed with very successful results.

Acknowledgements TUC was initially developed with partial support of the European Commission under the TABASCO (TR1054) Project. The part of work that refers to the network of Chania was partially supported by the Greek General Secretariat of Research and Technology (GGET) and the Municipality of Chania within Project CHANIASYN (96SYN194). The contents of the paper reflect the views of the authors, who are responsible for the accuracy of the data presented herein. The contents do not necessarily reflect the official policy of the European Commission.

References Anderson, B.D.O., Moore, J.B., 1990. Optimal Control— Linear Quadratic Methods. Prentice Hall, Englewood Cliffs, NJ. Diakaki, C., 1999. Integrated control of traffic flow in corridor networks. PhD Thesis. Technical University of Crete, Department of Production Engineering and Management, Chania, Greece. Diakaki, C., Papageorgiou, M., 1996. Integrated modelling and control of corridor traffic networks using the METACOR modelling tool. Internal Report 1996-8. Technical University of Crete, Dynamic Systems and Simulation Laboratory, Greece. Diakaki, C., Papageorgiou, M., McLean, T., 1997. Simulation studies of integrated corridor control in Glasgow. Transportation Research C 5, 211–224. Diakaki, C., Papageorgiou, M., McLean, T., 2000. Application and evaluation of the integrated traffic-responsive urban corridor control strategy IN-TUC in Glasgow. Transportation Research Record 1727, 101–111. Diakaki, C., Dinopoulou, V., Aboudolas, K., Papageorgiou, M., 2002. Final System Development Report. Deliverable 9, Project SMART NETS (IST-2000-28090), Report for the Information Society Technologies Office, Brussels, Belgium.

V. Dinopoulou et al. / European Journal of Operational Research 175 (2006) 1652–1665 Dinopoulou, V., Diakaki, C., Papageorgiou, M., Hourmouziadou, Z., 2000. Real-time control strategy of urban traffic: Development and implementation in Chania (in Greek). Progress Report for Phase I of the Research Project CHANIASYN of the Greek Ministry of Research and Technology. Dynamic Systems and Simulation Laboratory, Technical University of Crete, Greece. Dinopoulou, V., Diakaki, C., Marinakis, G., Papageorgiou, M., 2001. Real-time control strategy of urban traffic: Development and implementation in Chania (in Greek). Progress Report for Phase II of the Research Project CHANIASYN of the Greek Ministry of Research and Technology. Dynamic Systems and Simulation Laboratory, Technical University of Crete, Greece. Farges, J.L., Henry, J.J., Tufal, J., 1983. The Prodyn real-time traffic algorithm. In: Proceedings of the 4th IFAC Symposium on Transportation Systems, Baden Baden, Germany, pp. 307–312. Gartner, N.H., 1983. OPAC: A demand-responsive strategy for traffic signal control. Transportation Research Record 906, 75–84. Gazis, D.C., Potts, R.B., 1963. The oversaturated intersection. In: Proceedings of the 2nd International Symposium on Traffic Theory, London, UK, pp. 221–237. Hunt, P.B., Robertson, D.L., Bretherton, R.D., Royle, M.C., 1982. The SCOOT on-line traffic signal optimisation technique. Traffic Engineering & Control 23, 190–199. Lowrie, P.R., 1982. SCATS: The Sydney co-ordinated adaptive traffic system—principles, methodology, algorithms. In:

1665

Proceedings of the IEE International Conference on Road Traffic Signalling, London, UK, pp. 67–70. McLean, T., Brader, C., Diakaki, C., Papageorgiou, M., Hangleiter, S., Tsavahidis, M., Damas, C., 1997. Urban integrated traffic control implementation strategies. Deliverable 8.2, Project TABASCO (TR1054). Transport Telematics Office, Brussels, Belgium. McLean, T., Brader, C., Hangleiter, S., Tsavahidis, M., Damas, C., Maxwell, B., Barber, P., 1998. Urban integrated traffic control evaluation results. Deliverable 8.3, Project TABASCO (TR1054). Transport Telematics Office, Brussels, Belgium. Mirchandani, P., Head, L., 1998. RHODES: A real-time traffic signal control system: Architecture, algorithms, and analysis. In: TRISTAN (Triennal Symposium on Transportation Analysis), San Juan, Puerto Rico. Papageorgiou, M., 1996. Optimierung—Statische, Dynamische, Stochastische Verfahren Fu¨r Die Anwendung, second ed. Oldenbourg, Munich, Germany. Papageorgiou, M., Haj-Salem, H., Blosseville, J.-M., 1991. ALINEA: A local feedback control law for on-ramp metering. Transportation Research Record 1320, 58–64. Pavlis, Y., Papageorgiou, M., 1999. Simple decentralized feedback strategies for route guidance in traffic networks. Transportation Science 33, 264–278. Siemens, 2000. TASS, Traffic-actuated signal plan selection in MIGRA Central. Planning Manual, Pef. No. V24713Z1991-B2, Edition 002, 2000-03-30.