Scholarly article on topic 'Integrated Ramp Metering and Mainstream Traffic Flow Control on Freeways Using Variable Speed Limits'

Integrated Ramp Metering and Mainstream Traffic Flow Control on Freeways Using Variable Speed Limits Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Rodrigo C. Carlson, Diamantis Manolis, Ioannis Papamichail, Markos Papageorgiou

Abstract We integrate local Ramp Metering (RM) with Mainstream Traffic Flow Control (MTFC) enabled via Variable Speed Limits (VSL), which is a recently proposed freeway traffic management tool. The integration is performed by the extension of an existing simple local cascade feedback MTFC controller via a split-range-like scheme. The integrated controller remains simple yet efficient and suitable for field implementation. The controller is evaluated in simulation and compared to stand-alone RM or MTFC via VSL, as well as optimal control results. The controller's performance is shown to meet the specifications and to approach the optimal control results for the investigated scenario.

Academic research paper on topic "Integrated Ramp Metering and Mainstream Traffic Flow Control on Freeways Using Variable Speed Limits"

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Procedía - Social and Behavioral Sciences 48 (2012) 1578 - 1588

Transport Research Arena- Europe 2012

Integrated ramp metering and mainstream traffic flow control on freeways using variable speed limits

Rodrigo C. Carlsona'b9 Diamantis Manolisa9 Ioannis Papamichaif'*,

Markos Papageorgioua

"Dynamic Systems and Simulation Laboratory, Technical University of Crete, Chania 73100, Greece bThe Capes Foundation, Ministry of Education of Brazil, Brasilia, Brazil

Abstract

We integrate local Ramp Metering (RM) with Mainstream Traffic Flow Control (MTFC) enabled via Variable Speed Limits (VSL), which is a recently proposed freeway traffic management tool. The integration is performed by the extension of an existing simple local cascade feedback MTFC controller via a split-range-like scheme. The integrated controller remains simple yet efficient and suitable for field implementation. The controller is evaluated in simulation and compared to stand-alone RM or MTFC via VSL, as well as optimal control results. The controller's performance is shown to meet the specifications and to approach the optimal control results for the investigated scenario.

©2012Publishedby ElsevierLtd. Selectionand/or peerreview underresponsibilityoftheProgrammeCommittee of the Transport Research Arena 2012

Keywords: Integrated freeway traffic flow control; mainstream traffic flow control; ramp metering; feedback control

1. Introduction

Traffic flow congestion on freeways is an increasing problem of modern societies. Congestion is known to reduce the nominal capacity of the freeway infrastructure (Papageorgiou & Kotsialos, 2002), with serious impact on travel times, traffic safety, fuel consumption and environmental pollution.

Various traffic control measures have been proposed to alleviate traffic congestion but are known to face limitations. Ramp Metering (RM), for example, is the most direct and efficient tool for freeway traffic flow control, but because the ramp storage space may be limited, RM may have to be deactivated

* Corresponding author. Tel.: +30-282103-7422; fax: +30-282103-7584. E-mail address', ipapa@dssl.tuc.gr.

1877-0428 © 2012 Published by Elsevier Ltd. Selection and/or peer review under responsibility of the Programme Committee of the Transport Research Arena 2012

doi:10.1016/j.sbspro.2012.06.1133

for most of the peak period due to full ramps (Papamichail, Kotsialos, Margonis, & Papageorgiou, 2010).

To overcome these limitations, the integration of different traffic control measures has been investigated in the past, for example, RM integrated with route guidance (Kotsialos, Papageorgiou, Mangeas, & Haj-Salem, 2002; Karimi, Hegyi, De Schutter, Hellendoorn, & Middelham, 2004), or RM integrated with variable speed limits (VSL) (Hegyi, De Schutter, & Hellendoorn, 2005; Zhang, Chang, & Ioannou, 2006). However, most of these works were based on approaches that may face difficulties in field applications; in some cases even simulation results were not satisfactory.

Recently, Carlson, Papamichail, Papageorgiou, and Messmer (2010a, 2010b) proposed Mainstream Traffic Flow Control (MTFC) on freeways by the use of VSL and investigated its integration with RM via an optimal control approach. Because of the limited practicality of the approach employed, Carlson, Papamichail, and Papageorgiou (2011) designed a simple but efficient feedback MTFC controller that is deemed suitable for field implementation, without considering, however, the integration with RM.

We propose the integration of MTFC via VSL with RM using a feedback control approach. The cascade feedback MTFC controller developed by Carlson et al. (2011) is extended via a split-range-like scheme (Stephanopoulos, 1984) such that MTFC is only applied when the metered on-ramp storage space is about to be exhausted. Simulation-based investigations for a hypothetical freeway using a second-order macroscopic traffic flow simulator (METANET) demonstrate the features of the proposed integrated control strategy and compare its efficiency against stand-alone RM, MTFC, and optimal control.

In the next section, the congestion-caused infrastructure degradation and the MTFC concept are reviewed, along with an outline of the METANET simulator (Messmer & Papageorgiou, 1990) and the AMOC optimal control tool (Kotsialos et al., 2002) used for the evaluation of the proposed strategy. Section 3 presents a brief review of the feedback control strategies employed in this paper and the design of the integrated controller based on RM and MTFC via VSL. The efficiency of the proposed strategy is evaluated in Section 4. Finally, Section 5 concludes the paper.

2. Background

2.1. Congestion-caused infrastructure degradation and theMTFC concept

A (latent) bottleneck on a freeway is a location where the How capacity upstream is higher than the flow capacity gd°pwn downstream of the bottleneck location (Fig. 1(a)). If the arriving flow qm (which naturally verifies qm < ) is higher than q^™ , the bottleneck is activated, i.e., a congestion is formed (Fig. 1(a)). The congestion forming at an active bottleneck has two kinds of detrimental effects on the freeway capacity and throughput (Papageorgiou & Kotsialos, 2002):

• Capacity drop (CD) at the congestion head, i.e., an active bottleneck outflow qout that may be 5-20% lower than the nominal capacity gd°pwn . A main contributing factor for CD is deemed to be the acceleration of vehicles while exiting the congested area.

• Blocking of off-ramps (BOR)\ vehicles that are bound for exits upstream of the active bottleneck are delayed due to the blocking of off-ramps by the congestion body, whereby off-ramp flow is reduced. The basic idea of MTFC is to regulate the mainstream traffic flow sufficiently upstream of (otherwise)

active bottlenecks so as to avoid the CD (since vehicles will have accelerated before reaching the bottleneck area). The bottleneck of Fig. 1(b) is not activated (and no MTFC is needed) as long as qm < q1^ , in which case we have qout « qm . If qm grows bigger than the bottleneck capacity gd°pwn, the bottleneck would be activated in absence of control as in Fig. 1(a), and qout would be reduced due to CD; while MTFC can implement a controlled mainstream flow qc such that qout is equal to the gd°pwn . Clearly, the mainstream congestion cannot be avoided via MTFC because qm > , but the congestion outflow in the MTFC case is higher than in the no-control case because the CD is avoided. In this paper,

Upstream capacity

Downstream

Congestion q^ tail moves-* upstream

On-ramp

aup Active

Congestion

capacity bottleneck qff"

Off-ramp

a < adown

■lo ut ^ cap

Congestion q^ tail moves ^ upstream

Controlled > <

congestion

Upstream Flow capacity Downstream

control ¿7up capacity

^ cap ,

^ _ i i ..down

\Rottleneck £/cap

down /cap

"/out Pout

| (capacity drop) Congestion

Vehicle acceleration area

(covered by the congestion) Fig. 1. (a) Active bottleneck notions; (b) A local aspect of MTFC

we use VSL as an MTFC actuator to impose the controlled flow qc on the freeway mainstream. 2.2. METANET andAMOC tools

A validated macroscopic second-order traffic flow model included in the METANET simulator (Messmer & Papageorgiou, 1990) was extended to incorporate VSL control measures (Carlson et al., 2010a) and is used in this work. In METANET the freeway network is represented by a directed graph, whereby the links of the graph represent freeway stretches with uniform characteristics. The nodes of the graph are placed at locations where a major change in road geometry occurs, as well as at junctions and on-/off-ramps. The macroscopic description of traffic flow implies the definition of adequate variables expressing the aggregate behavior of traffic at certain times and locations, while the time and space arguments are discretized. For details, see (Messmer & Papageorgiou, 1990; Carlson et al., 2010a).

The freeway network traffic control problem may be formulated as a discrete-time nonlinear dynamic optimal control problem with constrained control variables over a given optimization horizon, and is incorporated in the open-loop optimal control tool AMOC (Kotsialos et al., 2002). The cost criterion is the total time spent (TTS) by all vehicles in the network; penalty terms are added to penalize (abrupt) time variations of VSL and RM rates, see (Carlson et al., 2010b). The solution determined by AMOC consists of the optimal VSL and RM rate trajectories as well as the corresponding optimal state trajectory.

2.3. VSL as an MTFC actuator

The reasons and ways of using VSL as an MTFC actuator have been thoroughly discussed by Carlson et al. (2010a, 2010b; 2011). In short, lower VSL values induce lower capacity values. This implies that, if the mainstream demand qm (Fig. 1(b)) arriving from upstream is higher than the VSL-induced capacity, then the VSL application area may become an active mainstream bottleneck that limits the area's outflow qc to values corresponding to the (lower) VSL-induced capacity. Thus, a controllable mainstream congestion may be created upstream of a bottleneck location to avoid its activation and the related reduction of throughput because of the capacity drop. Additionally, lower VSL values shift the critical density of the fundamental diagram toward higher values.

2.4. Practical VSL application aspects

This section summarizes some practical VSL implementation aspects detailed by Carlson et al. (2011). To start with, VSL can only take discrete values in practice. Therefore, we introduce a set of admissible discrete VSL rates b e {0.2,0.3,...,1.0}, where a VSL rate is defined as the displayed VSL divided by the legal speed limit without VSL. The VSL to be applied is obtained by rounding-off the VSL rate b (k) delivered by the MTFC control strategy (see Section 3.2) to the nearest discrete value, k being the

discrete-time index. Additional VSL may be activated within and upstream of the controlled congestion in a way that leads to equal VSL displays along the congested stretch; while vehicles driving towards the congestion tail encounter gradually decreasing VSL. Furthermore, the difference between two consecutive posted VSL rates at the same gantry is limited to 0.2, while the same limit applies to the difference between the posted VSL rates at two consecutive gantries. Finally, a constant VSL rate of 0.9 is applied in the acceleration and bottleneck areas Fig. 1(b)) whenever MTFC via VSL is active. These aspects are only considered when applying feedback concepts, not with optimal control (AMOC).

3. Freeway Traffic Feedback Control

This section outlines two freeway traffic feedback control strategies that are used in the simulations of Section 4, and details the design of the integrated control strategy proposed in this paper.

3.1. PI-ALINEA

PI-ALINEA (Wang & Papageorgiou, 2006) is a feedback RM strategy corresponding to a PI controller structure. PI-ALINEA orders suitable on-ramp inflows to the freeway based on the bottleneck density pout (veh/km/lane), and reads:

qT (k) = qr (k -1) + (Kp + K,) ep (k)- Kpep (k -1) (1)

where qr (veh/h) is the ordered ramp flow, bounded within q.r e[grmm, grmax ] , Kl and Kp are the integral and proportional gains, respectively, and ep (&) = pout - pout (k) is the density control error with pout, the set-point, usually set around the critical density pCI at which qout is maximized.

When the on-ramp storage space is limited, queue management operates in conjunction with RM to avoid over-long ramp queues. A proportional (P) controller with feed-forwarded on-ramp demand d (veh/h) may be used (Smaragdis & Papageorgiou, 2003):

& (k ) = - y [ * " w (k -1)]+d (k -*) W

where qr e[0, ^rmax ] is the queue-management ordered flow, Tc is the control period, w (veh) is the on-ramp queue length, and -w (veh) is the maximum admissible on-ramp queue (set-point). The final ordered on-ramp inflow to the freeway is qr = max[qr, qr} .

3.2. FeedbackMTFC via VSL

The control problem here is to regulate the traffic density pont (Fig. 1(b)) via real-time changes of the mainstream flow qc enabled by VSL (Carlson et al., 2011). Thus, we have the VSL rate b as the control input and the bottleneck density pont as the control output.

The basis for the design of the feedback MTFC via VSL is a discrete-time linearised model. Fig. 2(a) depicts the MTFC feedback cascade controller structure designed by Carlson et al. (2011) with a, p, t> 0, K' > 0, and K > 0 being model parameters, where 0 < p <a< 1 ; and z the discrete-time complex variable. The secondary loop in Fig. 2(a) is affected by the VSL rate b delivered by the secondary controller that will determine the outflow qc of Fig. 1(b). This flow is measured downstream of the VSL application area and is fed back and compared to the reference flow qc delivered by the primary controller. The primary controller uses the measured density pout at the bottleneck area. The secondary controller of Fig. 2(a) was designed as an integral (I) controller:

b (k ) = b (k -1) + Kl eq (k), (3)

Fig. 2. (a) Feedback cascade MTFC controller structure; (b) Integrated feedback controller structure

with Kl the integral gain and eq (k) = qc (k)- qc (k) the flow control error, given per lane. The primary controller was specified to be a proportional-integral (PI) controller:

<?c (*) = I (* -1) + (K + K) (*) - k;ep (k -1) (4)

where K[ and K'^ are the integral and proportional gains of the controller, respectively. Similarly to RM, the density set-point pout may be set equal to the critical density pcr for maximum throughput. For more details about the controller design, tuning and operation, the user is referred to Carlson et al. (2011).

3.3. Integrated traffic control

The idea in the integrated case is to specify combined mainstream flow and on-ramp flow values in order to keep the bottleneck density pout around the critical density (set-point). Since there are now two input flows to control the bottleneck density, there is an additional degree of freedom that may be used to apply some desired policy. The policy pursued in this paper is to apply RM for as long as the ramp storage space is not full; and to switch to MTFC only when ramp queue management is activated. This policy may be implemented if the feedback cascade control structure of Fig. 2(a) is extended via an appropriate split-range-like control scheme (Stephanopoulos, 1984) as depicted in Fig. 2(b). In Fig. 2(b) the PI controller of the primary loop delivers a reference flow qt, i.e., the total desired inflow into the bottleneck. The total desired inflow qt is split into the desired mainstream flow qc, which is handled by the respective secondary loop (as in Fig. 2(a)), and into the desired RM flow qx which is directly implemented via an appropriate metering policy of the traffic lights (Papageorgiou & Papamichail, 2008) to produce the real respective outflows q[ and q'T that enter the bottleneck area.

In the split block, any change of qt ordered by the primary controller is conveyed to qY unless one of two restrictions applies: i) the lower RM bound qrmin has been reached, or ii) the queue management orders a value qr higher than qr. In either of the two cases, any ordered flow changes are transmitted to qc . More precisely, if is the mainstream capacity and gcrap is the on-ramp capacity, we have 91 ^ C + ¿p by definition and

if qt - qm > max (q . , q )

Jt J cap \Jr,min'Jr/ (5)

% ) elSe

if ât - qm > max ( q q)

Jt J cap \Jr,min'Jr/

U - maX (^n* I ) elSe

In essence, the controller operates as PI-ALINEA until one of the two restrictions applies, at which point it starts operating as MTFC via VSL, and the term max ( qx min, qT ) becomes a feed-forward element affecting the output of the primary controller. The gains of the primary controller should be scheduled based on the split decision, i.e., Kl and KF (PI-ALINEA gains) are used if the first condition in (5) and

(6) applies, otherwise K[ and K'F (MTFC via VSL gains) are used. Similarly, the set-point pout of the primary controller must be changed accordingly, since the constant VSL value applied at the acceleration and bottleneck areas in the MTFC case shifts the critical density to higher values.

4. Simulation Results

The simulated scenarios and respective results are summarized in Table 1. Because stand-alone RM or MTFC using either feedback or optimal control, have been investigated in previous works (Papamichail et al., 2010; Carlson et al., 2011), the related detailed results of optimal control are omitted, except for the integrated control case. The resulting total time spent (TTS) for all optimal control scenarios are provided in Table 1 as a reference of achievable performance. The model parameters were taken from (Carlson et al., 2010a).

4.1. Network and demand

A hypothetical 21.5 km long three-lane freeway stretch, sketched in Fig. 3 (upper part), is used in the simulations that follow. The mainstream is divided in 15 links (L00-L14) with two on-ramps (01 and 02) and one off-ramp (Dl). The VSL application area, acceleration area, and bottleneck area as well as both real-time measurements for feedback control, are also indicated in Fig. 3 (lower part). Depending on the control scenario, only the arriving mainstream flow is controlled (MTFC via VSL), or only the 02 on-ramp flow (RM), or both (integrated control). The 01 on-ramp is left uncontrolled in all scenarios.

The demand profiles and exit rates displayed in Fig. 4 are used and allow for control testing under all possible traffic flow conditions (free, critical, congested), including dynamic transitions among them. The model time step is T = 10 s. The minimum admissible VSL rate is 6mm = 0.2 and the minimum admissible RM rate is qimm = 200 veh/h. The control period, that determines the frequency of VSL changes and RM rate updates, is Tc = 60 s, see (Papageorgiou et al., 1991; Carlson et al., 2011).

4.2. No control

In absence of control, the resulting flow, density and ramp queue at the bottleneck area are shown in Fig. 5. The flow in the bottleneck area reaches the factual capacity (6240 veh/h) at i = 0.4 h, and, despite the strong reduction of inflow at the origins and increase of exit rate at Dl that follows, a mainstream congestion appears there at i = 0.5 h; this leads to a gradual mainstream flow decrease (capacity drop).

Table 1. Summary of simulated control scenarios

Control strategy Description TTS (veh-h) %

No control - 4196 -

RM-AMOC Optimal RM without ramp queue constraint. 3279 -21.9

RM-AMOC/Q Optimal RM with maximum ramp queue of 100 veh. 3506 -16.4

PI-ALINEA Feedback RM without ramp queue constraint. 3282 -21.8

PI-ALINEA/Q Feedback RM with maximum ramp queue of 100 veh. 3506 -16.4

MTFC-AMOC Optimal MTFC via VSL. 3363 -19.8

MTFC-FB Feedback MTFC via VSL. 3370 -19.7

Integrated-AMOC Optimal integrated control, i.e., constrained RM and MTFC via VSL. 3335 -20.5

Integrated-FB Feedback integrated control, i.e., constrained RM and MTFC via VSL 3324 -20.8

L12 L13

LOO L01 L02 L03 L04 L05 LOÓ L07 L08 L09 LIO Lll 0.7 km 0.8 km L14 1.5 km^l.5 knr /1.5 km^l.5 km^l.5 km*** 1.5 km**!. 5 km^l.5 km^l.5 km** 1.5 km** 1.5 km ,1.5 km . >K >K 2.0 km"

Ul|—i—|—|—i—|—|—i—|—|—i—|—|—i—|—|—i—r—|—i—I—|—i—I—|—i—I—|—i—I—■—i—I—|—i—r

N0 N1 N2 N3 N4 N5 N6 N7

N9 NlO N11

II I |D2

Bottleneck

_ L1° _ 1.5 km

_ Lll _

1.5 km

-Acceleration area->i<

L12 _ "0.7 km

_ L13 _

0.8 km

_ L14_

—1> _ _ __ _ _ —> _ _ _—>____=>____—> _ _ _ _D2

VSL application area oí Flow measurement di 02 Density measurement

Fig. 3. Hypothetical freeway stretch

Fig. 4. Demand at the origins and turning rates

The created congestion travels upstream (not shown) and covers the Dl exit as well as the 01 on-ramp short after. Despite the lower demand entering the network after t = 2 h, it takes about 40 minutes before congestion is completely dissolved. The resulting TTS is 4,196 vehh.

4.3. Ramp metering

For the application of RM, two cases are considered in order to highlight the effect of limited on-ramp storage space. In the first case, the on-ramp's storage capacity is unlimited. In the second case, the on-ramp storage space is limited to 100 veh. The PI-ALINEA gains are Kl = 120 km/h/lane and KF = 300 km/h/lane and the set-point is /3out = 29 veh/km/lane.

4.3.1. Unlimited on-ramp storage space

The resulting TTS for PI-ALINEA is 3,282 veh h, which is a 21.8 % improvement compared to the no-control case. The flow, density and ramp queue at the bottleneck area are shown in Fig. 6.

The situation is identical to the no-control case until short before t = 0.4 h, but eventually the feedback controller is activated and maintains the bottleneck density close to the set-point (dashed line in the density plot), leading to maximum freeway exit flow (and hence to minimization of TTS). To achieve this, a ramp queue is created at the 02 on-ramp in two occasions and, since there are no queue constraints, the queue exceeds 300 vehicles in the second one. The congestion is completely avoided, and in fact RM is even de-activated for about 20 minutes between the two demand peaks. (Recall that in the no-control case the first demand peak creates a congestion that lasts uninterrupted for the next two hours.)

Fig. 5. No-control: flow, density and ramp queue at the bottleneck area

Fig. 6. PI-ALINEA: flow, density and ramp queue at the bottleneck area

4.3.2. Limited on-ramp storage space

The resulting TTS for PI-ALINEA/Q is 3,506 vehh, which is a 16.4 % improvement compared to the no-control case, but 5 % worse than in the case of unlimited ramp storage space. Note that a storage space of 100 veh is relatively large, and such a big value was chosen to allow for a better demonstration of the integrated control scenario. The flow, density and ramp queue at the bottleneck area are shown in Fig. 7. The dotted curve appearing in the queue plot corresponds to w .

The situation is identical to the previous scenario until short before t = 1.4 h, when the on-ramp storage space is about to be exceeded and queue management is activated. As a consequence, the critical density at the bottleneck cannot be sustained anymore, in contrast with the PI-ALINEA case. Hence, congestion is formed thereafter, leading to a corresponding drop in the exit flow.

4.4. Mainstream traffic/low control

For the application of MTFC-FB the links from L01 to Lll are considered each as a cluster (each with an independent VSL), and another cluster comprises links L12, L13 and L14. VSL is not applied at link LOO. Link Lll is the application area where the VSL rate delivered by the control law (3) is applied after any constraints are imposed. The VSL rates at the other links (clusters) follow the rules outlined in Section 2.4. The measurements are taken as shown in Fig. 3. The set-point of the primary controller is pouX = 32 veh/km/lane. The controller gains are Kl = 0.0007 h/veh/lane for the secondary controller and K[ = 3 km/h/lane and K¿ = 50 km/h/lane for the primary controller (Carlson et al., 2011).

The resulting TTS is 3,370 veh h, which is a 19.7 % improvement compared to the no-control case. The flow, density and ramp queue at the bottleneck area, and the VSL rates are shown in Fig. 8. The situation is identical to the no-control case until t = 0.4 h, when VSL is first activated at both clusters of

Fig. 7. PI-ALINEA/Q: flow, density and ramp queue at the bottleneck area

Fig. 8. MTFC-FB: flow, density and ramp queue at the bottleneck area, and the VSL rates

links so as to decrease the flow arriving at the bottleneck and increase the critical density in the bottleneck merge area, respectively. This short VSL action is sufficient to avoid the onset of congestion, and thus further VSL action is not needed for the next 20 minutes, similarly to the PI-ALINEA case. A second control action is started short before t = 1.3 h. The bottleneck congestion is again avoided and the outflow is maintained close to capacity by maintaining the bottleneck density close to its set-point pout (dashed line in the density plot). Note that the resulting improvement is slightly lower than in the RM case with unlimited storage; this is because MTFC restricts the mainstream flow upstream of the off-ramp, and hence the off-ramp outflow is reduced accordingly; thus, some delays are incurred for the vehicles bound for the off-ramp (which are avoided with RM).

4.5. Integrated control

For the application of Integrated-AMOC, only link Lll and the cluster comprising links L12, L13 and L14 are controlled. Except for the lower bound, no further constraints are applied to the VSL rate, see (Carlson et al., 2010a). The on-ramp queue is limited to 100 veh. The resulting TTS is 3,335 vehh, which is a 20.5 % improvement compared to the no-control case and obviously superior to the constrained RM case, as well as to the MTFC case (for reasons mentioned earlier). The flow, density and ramp queue at the bottleneck area, and the VSL rates are shown in Fig. 9.

Up to around t = 1.4 h, there is no significant difference from the two RM scenarios investigated previously. AMOC has a clear "preference" for RM over MTFC (again for mentioned reasons) in the first peak period where only RM is applied and is sufficient to avoid the congestion. In the second peak period, AMOC starts applying both control measures quasi simultaneously. VSL enters in operation at both clusters of links reaching values close to the lower bound at Lll. AMOC efficiently keeps the on-ramp queue within the stipulated limit. Congestion is completely avoided in both peak periods.

When Integrated-FB is used, the resulting TTS is 3,324 veh h, which is a 20.8 % improvement compared to the no-control case and slightly lower than in the corresponding optimal control case. The latter is because the activation of VSL upstream of the application area affects favorably the performance of the system for this specific scenario. The flow, density and ramp queue at the bottleneck area, and the VSL rates are shown in Fig. 10. The controller gains and set-point are the same as in Sections 4.3 and 4.4.

The results in Fig. 10 are quite similar to the corresponding optimal control scenario of Fig. 9, with two slight differences. First, the on-ramp queue formed during the second peak period in the feedback case is maintained for a longer period. This is because the structure of the control strategy requires in the

Fig. 9. Integrated-AMOC: flow, density and ramp queue at the bottleneck area, and the VSL rates

Fig. 10. Integrated-FB: flow, density and ramp queue at the bottleneck area, and the VSL rates

present case a full deactivation of MTFC before handing control over to RM again. Second, the dashed line in the density plot shows the controller set-point which is switched because of the constant VSL rate applied at the acceleration and bottleneck areas during MTFC operation. In the VSL rates plot of Fig. 10 it is visible that the constraints of the VSL rate, as outlined in Section 2.4, apply. Furthermore, the VSL rates do not reach low values as in the Integrated-AMOC case, because of the activation of VSL upstream of the application area for safety reasons (Section 2.4).

5. Conclusions

Ramp Metering and Mainstream Traffic Flow Control via Variable Speed Limits were integrated for the efficient control of freeway traffic. An existing cascade feedback MTFC controller was extended by use of a split-range-like scheme so as to allow integration with RM in such a way that MTFC enters in operation only when the on-ramp queue is about to be exhausted. The integrated control strategy remains simple yet efficient as evidenced by its evaluation using the METANET simulator and its comparison with non-integrated control and with an optimal control approach for a hypothetical freeway network.

Ongoing research is investigating the integration of RM and MTFC at the network level (coordination), as well as the application of different splitting policies. A field test of the proposed strategy will be attempted in the near future.

References

Carlson, R. C., Papamichail, I., & Papageorgiou, M. (2011). Local feedback-based mainstream traffic flow control on motorways using variable speed limits. IEEE Transactions on Intelligent Transportation Systems, 12(A), 1261-1276.

Carlson, R. C., Papamichail, I., Papageorgiou, M., & Messmer, A. (2010a). Optimal motorway traffic flow control involving variable speed limits and ramp metering. Transportation Science, 44(2), 238-253.

Carlson, R. C., Papamichail, I., Papageorgiou, M., & Messmer, A. (2010b). Optimal mainstream traffic flow control of large-scale motorway networks. Transportation Research Part C: Emerging Technologies, 18(2), 193-212.

Hegyi, A., De Schutter, B., & Hellendoorn, H. (2005). Model predictive control for optimal coordination of ramp metering and variable speed limits. Transportation Research Part C: Emerging Technologies, 13(3), 185-209.

Karimi, A., Hegyi, A., De Schutter, B., Hellendoorn, J., & Middelham, F. (2004). Integrated model predictive control of dynamic route guidance information systems and ramp metering. The 7th International IEEE Conference on Intelligent Transportation Systems (pp. 491-496). Washington, D.C., USA: IEEE.

Kotsialos, A., Papageorgiou, M., Mangeas, M., & Haj-Salem, H. (2002). Coordinated and integrated control of motorway networks

via non-linear optimal control. Transportation Research Part C: Emerging Technologies, 10(1), 65-84.

Messmer, A., & Papageorgiou, M. (1990). METANET: a macroscopic simulation program for motorway networks. Traffic Engineering and Control, 31(8), 466-470.

Papageorgiou, M., & Kotsialos, A. (2002). Freeway ramp metering: an overview. IEEE Transactions on Intelligent Transportation Systems, 3(4), 271-281.

Papageorgiou, M., & Papamichail, I. (2008). Overview of traffic signal operation policies for ramp metering. Transportation Research Record: .Journal of the Transportation Research Board, 2047, 28-36.

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.

Papamichail, I., Kotsialos, A., Margonis, I., & Papageorgiou, M. (2010). Coordinated ramp metering for freeway networks - A model-predictive hierarchical control approach. Transportation Research Part C: Emerging Technologies, 18(3), 311-331.

Smaragdis, E., & Papageorgiou, M. (2003). Series of New Local Ramp Metering Strategies. Transportation Research Record, 1856, 74-86.

Stephanopoulos, G. (1984). Chemical process control: an introduction to theory and practice. Englewood Cliffs N.J.: Prentice-Hall.

Wang, Y., & Papageorgiou, M. (2006). Local ramp metering in the case of distant downstream bottlenecks. 2006 IEEE Intelligent Transportation Systems Conference (pp. 426-431). Toronto, ON, Canada.

Zhang, J., Chang, H., & Ioannou, P. A. (2006). A simple roadway control system for freeway traffic. 2006 American Control Conference (pp. 4900-4905). Minneapolis, MN, USA.