Integrated variable speed limit and ramp metering control study on flow interaction between mainline and ramps

Abstract

During peak periods, bottlenecks are often triggered by excessive demand from both on-ramp and mainline input flows. To relieve bottleneck severity and improve traffic safety, ramp metering and variable speed limit are implemented to control the on-ramp and mainline input flows, and sometimes they are integrated. This article presents a proactive integrated control, with goals to save network-wide travel time and increase traffic flow. A METANET-based macroscopic traffic model was adopted as a prediction model. Micro-simulation tests were performed to evaluate and compare the control approaches among integrated and isolated control scenarios. By decoupling the traffic prediction and simulation models, the control error sources were analyzed. The evaluation revealed that both isolated and integrated controls benefit the traffic network to different extents under varying demand scenarios. Under proactive integrated control, ramp metering is activated solely during slight congestion; or it is activated during high-congestion periods to assist variable speed limit and thus integration maximizes the infrastructure utility.

Introduction

Active traffic and demand management (ATDM) methods, including ramp metering (RM),^1,2 variable speed limit (VSL),^3,4 and route guidance (RG) ⁵ effectively and efficiently alleviate freeway congestion and improve traffic safety. Over the past decade, several ATDM methods that incorporate real-time data collection and traffic control coordination have been implemented in the field.^1–3,6 So far, RM and VSL are the most commonly studied methods. RM is a ramp flow control that regulates on-ramp traffic flow entering the freeway mainline. The benefit of RM is subject to mainline and on-ramp demand levels. If on-ramps yield a low demand, there is little need for RM; conversely, if on-ramp demand is high, RM sometimes needs to be switched off in the case that the on-ramp queue spills back to surface streets to balance the metering rate and the queue overspill issue. ⁷ Thus, RM alone might be insufficient for freeway control in many cases. In contrast, VSL control is a traffic flow control for mainline, which carries more controllable traffic. Whereas, over-control of VSL may spread low speed to upstream traffic and the mainline queue may cover upstreamoff-ramps. Thus, much recent research has focused on the integrated control of RM and VSL.^8–10

Depending on how the control strategy is designed, it can determine RM and VSL rates successively or simultaneously. For example, Lu et al. ¹¹ determined VSL before RM. In their method, VSL is determined first, based on the current traffic state. With the determined VSL rates, a first-order density dynamics is linearized and can be used to optimize RM rates. Likewise, Carlson et al. ¹² integrated RM and VSL by considering RM first. The basic principle is that RM is applied for downstream congestion as long as the on-ramps are not full; otherwise, VSL is switched on.

Recently, many researchers have applied a tightly coupled second-order traffic dynamics to combine RM and VSL and consider their optimal coordination and integration.^9,13,14 The METANET model ¹⁵ has been commonly applied. The original METANET model was extended to the Advanced Motorway Optimal Control (AMOC) tool to incorporate RM and VSL signals. The common objective function takes the total time spent (TTS) on both mainline and ramps, sometimes with a term that penalizes abrupt variations in RM and VSL signals. However, different studies differ in the applied control methods and optimization techniques. Hegyi et al. ⁹ fulfilled proactive integration using model predictive control (MPC). The nonlinear optimization problem was solved by a sequential quadratic programming (SQP) algorithm. Furthermore, Zegeye et al. ¹⁴ proposed a receding-horizon parameterized control approach based on MPC and state feedback control. A multi-start SQP algorithm was used to solve the optimal control variables. However, for real-life applications, computation time is the major concern. To this end, Ghods et al. ¹⁶ introduced a game theory to obtain optimal control inputs for the integration. The proposed optimization algorithm was verified in a macro-simulation, and its computation time was significantly reduced.

In previous research, although the performance of the model-based integrated control has been confirmed, some problems still exist. First, the aforementioned evaluation research applied the same macroscopic model in both traffic modeling and prediction. In other words, prediction in the proactive strategies was assumed to perfectly match future traffic measurements. This assumption is not achievable in real-world implementation. As a result of this infeasible assumption, real-life traffic demand, disturbances, and model errors are rarely considered, which may lead to overestimation of the control performance. Second, it is questionable whether integrated control always surpasses isolated control. Both RM and VSL have their own strengths and weaknesses, as explained before. Integration only takes the advantages of both strategies and ideally avoids their disadvantages. However, the true effect of integrated or isolated control remains unknown in real-world applications. Finally, but most importantly, it is still unclear how RM and VSL cooperate and how their control rates change simultaneously in the design stage of an optimal controller based on a nonlinear model. Mainline and ramp flows interact at weaving, merging, or diverging segments. Traffic conditions on those segments are susceptible to recurrent congestion. Investigating the integration of RM and VSL can reveal the interaction between ramp flow and mainline flow under an optimal controller. Few previous researches have examined the integration results or explained how RM and VSL integrate, especially for the proactive algorithms that RM and VSL are determined simultaneously. Clarifying the relationships between RM and VSL and between mainline flow and ramp flow can help in integrated control algorithm design. To bridge these research gaps, this article evaluates a proactive integrated control strategy. Traffic evolutions are predicted by an extended METANET model, and driver responses are simulated within a micro-simulation environment. In this way, this study decouples traffic modeling and prediction. The evaluation varies mainline and ramp flow by changing mainline and ramp demand, and looking into the control variables to assess integration performance. The main objectives of this article are to (1) identify the performance of integrated and isolated control in decoupled prediction and simulation environments, and explain control error sources; (2) evaluate the variations in control performance under different combinations of demand scenarios; and (3) investigate control variable profiles from the tested integrated control strategy and explain the integration process and interaction between mainline and on-ramp flows.

The remainder of this article is organized into sections: section “Control method” briefly introduces the integrated control method; section “Simulation test and evaluation results” is devoted to the investigation of integration performance; and finally, the last section presents the concluding remarks and future work.

Control method

Mainline and ramp flows interact at freeway weaving, merging, or diverging segments. Traffic conditions vary when mainline and ramp demand levels are varied. RM and VSL work by limiting upstream mainline and ramp discharge flows from entering the downstream bottlenecks. The analysis attempts to demonstrate the cooperation between RM and VSL in variation relationships of control variables.

Control strategy

The applied integrated control of RM and VSL aims to achieve optimal network performance according to traffic states predicted in real time. Its MPC framework has a multi-module structure to collect field traffic data, predict traffic conditions, and optimize and apply control variables. ¹⁷

Traffic-state prediction model

A METANET-based dynamic traffic model, DynaTAM-RM&VSL (Dynamic Analysis Tool for Active Traffic and Demand Management- Ramp Metering and Variable Speed Limit), was used to perform traffic-state prediction and coordinate mainline and on-ramp flows. DynaTAM is an application-oriented software tool; its branches, DynaTAM-RM and DynaTAM-VSL, were developed and presented by Wang et al. ¹⁸ and Hadiuzzaman et al., ¹⁹ respectively. In addition to the original METANET model proposed by Messmer and Papageorgiou, ¹⁵ DynaTAM-RM&VSL applies several physical constraints to estimate segment boundary flows. Estimated capacity drop from a triangular fundamental diagram was also introduced to model active bottlenecks.

To apply the dynamic traffic flow model, the freeway corridor was divided into several segments $(i=1,2,\dots ,N)$ of length $L_i$ and lanes ${\lambda }_i$ . The evolutions of traffic density ${\rho }_i(k)$ in vehicles per kilometer per lane (veh/km/ln) and traffic speed $v_i(k)$ in kilometers per hour (km/h) at each time index t ( $t=\mathrm{kT}$ ,T is the discrete time step, k = the time step presently in the calculation) were calculated by the following two equations. For RM, the density dynamics takes on-ramp meter rates as the value of r. For VSL, $V[{\rho }_i(k)]$ in the original METANET is replaced by the suggested speed limit u

$$\begin{array}{c}\multicolumn{1}{c}{{\rho }_i(k+1)={\rho }_i(k)+\frac{T}{L_i{\lambda }_i}({\lambda }_{i-1}{q}_{i-1}(k)-{\lambda }_i{q}_i(k)}\\ \multicolumn{1}{c}{+r_i(k)-s_i(k))}\end{array}$$

(1)

where q is the boundary flow between segments in vehicles per hour per lane (veh/h/ln), r is the on-ramp flow in vehicles per hour (veh/h), and s is the off-ramp flow in veh/h

$$\begin{array}{c}\multicolumn{1}{c}{v_i(k+1)=v_i\left(k\right)+\frac{T}{\tau }\{u_i\left(k\right)-v_i\left(k\right)\}}\\ \multicolumn{1}{c}{+\frac{T}{L_i}{v}_i\left(k\right)[v_{i-1}\left(k\right)-v_i\left(k\right)]-\frac{\upsilon T[{\rho }_{i+1}(k)-{\rho }_i(k)]}{\tau L_i[{\rho }_i(k)+\kappa ]}}\end{array}$$

(2)

where $\tau$ is the reaction term parameter in hours (h), $\upsilon$ is the anticipation parameter (km² per hour, km²/h), $\kappa$ is the positive constant (veh/km/ln); these are global parameters that were calibrated from traffic measurements.

In addition, several segment-specific constraints and capacity drops were introduced when calculating boundary flows among successive segments. The boundary flow values (see the equations below) are loaded into the density dynamics (equation (1)). The segment-specific constraints originate from the cell transmission model (CTM). ²⁰ The following equations are applied

$$q_i(k)=\min \left\{\begin{array}{c}{v}_i\left(k\right){\rho }_i\left(k\right)+\frac{r_{i+1}\left(k\right)-s_{i+1}\left(k\right)}{{\lambda }_i}\hfill \\ \multicolumn{1}{c}{Q_{max,i+1},{\omega }_{i+1}({\rho }_{\mathrm{Jam},i+1}-{\rho }_{i+1}\left(k\right))}\end{array}\right\}$$

(3)

where $\omega$ is the shockwave speed (km/h), $Q_{max}$ is the segment capacity in veh/h/ln, and ${\rho }_{\mathrm{Jam}}$ is the jam density (veh/km/ln).

In equation (3), at any time step k, the transition flow from i to $i+1$ , that is, $q_i(k)$ depends on the average segment flow at i, the capacity of downstream segment $i+1$ , and the supply from the segment $i+1$ . However, for a segment on which a bottleneck is triggered, the actual capacity is reduced below the free-flow capacity, which results in a capacity drop. Thus, equation (3) is modified as

$$q_i(k)=\min \left\{\begin{array}{c}{v}_i\left(k\right){\rho }_i\left(k\right)+\frac{r_{i+1}\left(k\right)-s_{i+1}\left(k\right)}{{\lambda }_i}\hfill \\ \multicolumn{1}{c}{{Q\prime }_{max,i+1},{\omega \prime }_{i+1}({\rho \prime }_{\mathrm{Jam},i+1}-{\rho }_{i+1}\left(k\right))}\end{array}\right\}$$

(4)

where $\omega {\prime }_{i+1}(\rho {\prime }_{\mathrm{Jam},i+1}-{\rho }_{i+1}(k))=(\rho {\prime }_{\mathrm{Jam},i+1}-{\rho }_{i+1}(k))/$ $(\rho {\prime }_{\mathrm{Jam},i+1}-{\rho }_{\mathrm{cr},i+1}(k)){Q\prime }_{max,i+1}$ , $\omega \prime$ is the shockwave speed related to bottleneck capacity (km/h), $Q{\prime }_{max}$ is the bottleneck capacity, and ${\rho }_{\mathrm{cr}}(k)=Q_{max}/v_f$ .

Objective function

The objective function in the control framework is a weighted summation of the total travel time (TTT) on the mainline, the total waiting time (TWT) on ramps and the total travel distance (TTD) on the mainline. TTT is determined by traffic density, while TTD is determined by the product of traffic density and speed, that is, traffic flow. Thus, as proved in much previous research,^11,18,19,21 minimizing TTT reduces mainline density and mitigates congestion; whereas, maximizing TTD accommodates more vehicles in the mainline. As RM and VSL may improve freeway mobility at the cost of preventing vehicles entering the traffic network and detouring a portion of traffic to local roads, TTD is included in the objective function. Meanwhile, excessive ramp delay caused by ramp control may raise the public’s doubts about efficiency. To alleviate extremely long delays, the waiting time of vehicles, which are forced to stop by ramp meters should be weighted more than the absolute travel time. ⁷ In summary, the optimization problem is to find optimal control values to obtain the minimal value of the objective function J (as shown in the equations below) over a prediction horizon $N_p$ . This optimization problem balances traffic mobility and infrastructure utility, as well as temporal equity of the mainline and on-ramp vehicles. The weighting factors ( ${\alpha }_{\mathrm{TTT}}$ , ${\alpha }_{\mathrm{TWT}}$ , and ${\alpha }_{\mathrm{TTD}}$ ) were selected in the simulation stage. To include time and distance indexes in one objective function, values of ${\alpha }_{\mathrm{TTT}}$ and ${\alpha }_{\mathrm{TWT}}$ should be related to speed. Typically, ${\alpha }_{\mathrm{TTD}}$ is held at 1, and the values of ${\alpha }_{\mathrm{TTT}}$ and ${\alpha }_{\mathrm{TWT}}$ are tuned in the range of 20–100 and determined by comparing the resulted values of the objective function using the method in an existing research. ²² In this study, ${\alpha }_{\mathrm{TTT}}$ and ${\alpha }_{\mathrm{TWT}}$ were 55 and 100

$$J={\alpha }_{\mathrm{TTT}}\mathrm{TTT}+{\alpha }_{\mathrm{TWT}}\mathrm{TWT}-{\alpha }_{\mathrm{TTD}}\mathrm{TTD}$$

(5)

$$\begin{array}{c}\mathrm{TTT}=T\sum _{j=1}^{N_p-1}\sum _{i=1}^N{\lambda }_i{L}_i{\rho }_i(k+j)\hfill \\ \mathrm{TWT}=T\sum _{j=1}^{N_p-1}\sum _{i=1}^N{w}_{0,i}(k+j)\hfill \\ \mathrm{TTD}=T\sum _{j=1}^{N_p-1}\sum _{i=1}^N{\lambda }_i{L}_i{\rho }_i(k+j)v_i(k+j)\hfill \end{array}$$

(6)

where j is the time step in the prediction horizon $(j=1,2,\dots ,N_p-1)$ .

Constraints

Two inequality constraints are adopted for optimizing the RM rate r

$$q_{i-1}\left(k\right)+r_i\left(k\right)\le Q_{max,i}$$

(7)

where k is the time-step index

$$r_i\left(k\right)\ge r_{\min ,i}\left(k\right)\left(\mathrm{when}{w}_{o,i}\left(k\right)>95\%w_{cap}\right)$$

(8)

where $r_{min}$ is the minimum RM rates in vehicles per hour (veh/h); $w_o$ is the on-ramp queue length in vehicles (veh); $w_{\mathrm{cap}}$ is the on-ramp queue capacity in vehicles (veh).

Equation (7) makes an applicable flow rate lower than the difference between the mainline capacity $Q_{max}$ and current flow rate q. Equation (8) considers the limited storage space to avoid spillback from on-ramps to surface streets.

The control strategy also constrains VSL rates for the VSL-controlled segments by two inequality constraints

$$V_{min}\le u_i\left(k\right)\le V_{max}$$

(9)

$$|u_i(k+1)-u_i\left(k\right)|\le V_{\max ,\mathrm{diff}}$$

(10)

First, equation (9) restricts the optimal speed limit between the maximum and minimum values ( $V_{max}$ and $V_{min}$ ). Second, equation (10) limits the absolute speed change between two consecutive time steps within a maximum speed difference $V_{\max ,\mathrm{diff}}$ to maintain safe operation. This temporal constraint avoids abrupt speed limit change and ensures driver safety and comfort.

Simulation test and evaluation results

Study site

A westbound section (between 122 Street and 159 Street) of an urban freeway corridor, called Whitemud Drive (WMD), in Edmonton, Canada, was chosen (Figure 1). The posted speed limit on this 8-km freeway section is 80 km/h. As observed from historical data, two recurrent bottlenecks are often activated along this urban freeway. One is a two-sided weaving segment from the on-ramp of 122 Street to the off-ramp of Terwillegar Drive. The other one originates at the sharp curve before 149 Street, where the deceleration of vehicles causes a backward shockwave. However, in coordinated control, further upstream RM and/or VSL control restricts flow and affects downstream bottleneck traffic. To eliminate the effect from upstream control, this analysis starts with integrated local control at the first bottleneck. Weaving segments bear frequent weaving maneuvers, which are representative of the interaction between mainline and ramp flow. Thus, the performance of Segments 1–4 (the weaving segment and its adjacent three segments) was demonstrated.

Figure 1.

Study corridor, WMD, Edmonton, Canada.

The City of Edmonton has installed vehicle detection stations (VDSs) and traffic video cameras along this corridor. The VDSs collect 20-s intervals of volume, speed, and occupancy data and send the data to the city’s central computer system for archival. To replicate real-world traffic conditions, the prediction and micro-simulation models were calibrated and validated with field data. Similar to a previous study by Wang et al., ¹⁸ five steps were performed to construct the prediction and micro-simulation models: (1) identified geometric features from the field; (2) collected and processed field traffic data; (3) analyzed traffic data and identified bottlenecks; (4) coded for the prediction/micro-simulation network model; and (5) calibrated the prediction/micro-simulation model from the observations from step 3. During model validation, measurements from the prediction/micro-simulation model and the field were compared to validate the constructed prediction/micro-simulation model.

Micro-simulation setup

To implement the proactive strategy, an online optimization method was developed based on traffic measurements and prediction using VISSIM ²³ and Visual C++ (Figure 2). To change the RM and VSL rates assigned to the freeway segments during the simulation, the VISSIM component object model (COM) application programming interface (API) was used. Moreover, the Visual C++ program was used to load the traffic network through the VISSIM API and to start the simulation process.

Figure 2.

Simulation setup.

For RM implementation, a signal control strategy, namely “single-lane one car per green,” was applied in the signal-state generator. It allows one vehicle to enter the freeway during each signal cycle with a minimum duration of 4.5 s. ²⁴ An uncontrolled single-lane on-ramp is capable of a throughput of 1800 veh/h. The minimum admissible ramp flow is typically 200–400 veh/h. ²⁵ With this in mind, in the simulation, the cycle length was set from 5 to 10 s at 1-s intervals. Each signal cycle consisted of 1-s green, 1-s yellow, and remaining red signal indications. Once a ramp meter was required to shut off, its signal indication was set to green (cycle length is 0 s). It is important to note that the signal cycle length was converted from on-ramp flow obtained by solving the optimization problem.

In Canada, the implemented speed limits on freeways are multiples of 10 km/h. Thus, VSL signs update in increments or decrements of a value that is a multiple of 10 km/h; hence, $V_{\max ,\mathrm{diff}}$ is 10 km/h. Furthermore, the upper and lower bounds of the posted speed limit are $V_{max}=80\mathrm{km}/\mathrm{h}$ and $V_{min}=20\mathrm{km}/\mathrm{h}$ . The VSL sign locations along the studied corridor are shown in Figure 1. VSL-1 was located 1.5 km upstream of the bottlenecks, and it urged drivers to decelerate so that the capacity at VSL-1 was lowered. VSL-2 provided higher speed limits ahead of the bottleneck for drivers to accelerate and pass through the bottleneck as quickly as possible. In this study, VSL-2 was given a fixed value of 80 km/h. Thus, VSL-2 was not considered in the optimization problem.

The sequence of ramp and mainline inputs that minimizes the performance criterion over a given future prediction horizon $(N_p=5\min )$ was determined. The control horizon $(N_c)$ was 1 min. In this study, a 5-min prediction horizon was equivalent to a 15-step prediction, as length of each prediction time step $(T)$ was 20 s. The values of $N_p$ , $N_c$ , and T were selected based on previous research. ⁶ At each control horizon, these meter and speed limit rates were generated using a C++ program based on a decision tree–based solver.

Simulation results

The control performance at the four segments was considered in the analysis. The simulation tests replicated traffic conditions during PM peak hours (4:30 PM to 6:30 PM) after a 5-min warm-up period (4:25 PM to 4:30 PM). The warm-up period allowed vehicles to spread everywhere in the network. Then this analysis removed the warm-up period. The peak hours contained low-demand and high-demand periods. Low demand was loaded into the network from 4:30 PM to 4:40 PM and from 6:00 PM to 6:30 PM, and high demand was loaded for the time period in between. The demand level in the high-demand period varied for the mainline and on-ramp. Moreover, as explained before, traffic conditions at weaving segments are sensitive to weaving maneuvers. Weaving maneuvers increase as weaving flow grows. The growth of congestion is much faster than the increase of weaving flow. This study selected mainline demand ranging from 3600 to 4000 veh/h and on-ramp demand from 800 to 1000 veh/h. Traffic congestion is sensitive to even a 100 veh/h increase in either mainline or on-ramp demand.

Possible sources of suboptimal or even adverse control performance are explained before presenting the results:

• VSL limits flow by lowering the upstream speed limit. Assuming all drivers comply with VSL, the upstream of the bottleneck experiences lower speed, even though it may be free flow in the no-control case. In this way, VSL may actively spread a relatively low-speed upstream. The overall mobility performance is improved by VSL at bottlenecks but lowered at upstream segments;

• RM limits flow by stopping on-ramp vehicles at entrances to the freeway mainline. Stopped vehicles at on-ramps may cause excessive waiting time. Thus, RM improves mainline mobility but meanwhile results in delay to ramp vehicles;

• Proactive integration considers a tradeoff among network-wide mainline travel time, ramp waiting time, and network flow. However, the tradeoff may not be achieved in real-world applications due to the following: (1) the selection of control variables is limited to several discrete values for the convenience of signal setting. The assumption of discrete signals loses some control performance; (2) occasional mistakes from the queue estimation model may generate incorrect RM control signals; (3) traffic dynamics cannot promise to perfectly match real traffic evolutions even though they have been calibrated and validated; (4) several constraints are applied to the optimization for safety concerns. For example, as the speed limit becomes lower and lower, it cannot recover to the normal value quickly once congestion is about to be alleviated; and (5) proactive control optimizes the traffic performance over a short term, but the resulting traffic condition may not be optimal over the whole peak period.

In summary, in real implementation, the aforementioned factors keep control performance from reaching its optimum level. The following analysis examines control performance under different scenarios of traffic demand. Table 1 lists the control performance results from the simulation tests. Each case was run 10 times with random seed numbers in the micro-simulation, and the performances have been averaged. Overall, in the no-control cases, TTT and TTD increased as the ramp and mainline demand grew. In other words, congestion became more severe as the demand increased and the network carried more vehicles. When control strategies were applied, the performance generally improved by a distinct difference. After comparing TTS (TTS = TTT + TWT) among control scenarios in each demand combination, the control performance was assessed, as shown by font styles in Table 1. The performance decreases in order of the following font styles: bold-italic, bold, italic, and regular. We can observe that the integrated control performed best among all control options when both mainline and on-ramp demand were relatively high (the bottom right side). Otherwise, isolated control may be a better option. In conclusion, integrated control is not always better than isolated control. On one hand, VSL is enough for low on-ramp demand (see the rows when on-ramp demand is 800 veh/h). At this time, integration with RM adds excessive ramp waiting time (TWT) and thus loses some performance in TTS. RM performs better if on-ramp demand grows (see the column when mainline demand is 3600 veh/h). Similarly, integration with VSL increases mainline travel time (TTT). On the other hand, if we look at the bottom right of Table 1, integration of RM and VSL acts as a combination of isolated RM and VSL. The TTT and TWT values under integration are between those under isolated RM and VSL, which provides evidence for the balancing effect of integration on the mainline travel time and ramp waiting time.

Table 1.

Control performance under different traffic demands.

On-ramp demand (veh/h)			Mainline demand (veh/h)
			3600	3700	3800	3900	4000
800	No control	TTT a	237.99	247.89	285.21	311.85	326.68
		TWT b	2.04	2.10	2.15	2.10	2.09
		TTD c	16405.57	17010.34	17121.66	17312.67	17726.24
	VSL	TTT	219.65	234.65	241.61	252.12	323.70
		TWT	2.04	2.09	2.09	2.09	2.20
		TTD	16405.05	17009.07	17294.86	17676.83	17835.85
	RM	TTT	218.42	233.58	271.22	304.78	308.44
		TWT	5.18	3.61	3.27	4.68	4.61
		TTD	16405.08	17010.11	17294.92	17219.50	17765.35
	RM&VSL	TTT	221.74	235.22	257.90	280.76	301.50
		TWT	3.67	3.59	3.31	3.24	3.17
		TTD	16405.05	17009.88	17295.41	17640.25	17699.56
900	No control	TTT	262.53	268.17	273.38	325.28	329.59
		TWT	2.59	2.54	2.39	2.64	2.52
		TTD	16853.21	17168.73	17529.43	17390.54	17542.15
	VSL	TTT	257.19	234.95	280.08	333.8	329.12
		TWT	2.54	2.56	2.34	2.57	2.56
		TTD	16861.96	17166.91	17528.25	17394.44	17635.70
	RM	TTT	223.94	253.81	269.94	305.04	329.00
		TWT	5.48	5.28	4.04	4.83	7.72
		TTD	16846.23	17157.93	17530.20	17539.99	17389.18
	RM&VSL	TTT	227.55	252.03	262.67	281.78	322.71
		TWT	4.88	3.57	3.47	3.67	6.03
		TTD	16840.04	17167.42	17454.28	17838.77	17679.23
1000	No control	TTT	276.42	328.95	338.51	334.81	355.85
		TWT	2.39	2.82	2.79	2.39	3.44
		TTD	17040.57	16774.49	17243.51	17548.01	17236.82
	VSL	TTT	251.00	315.12	335.23	328.88	347.76
		TWT	2.3881	2.39	2.61	2.34	2.74
		TTD	17037.81	17057.53	17348.43	17602.64	16882.69
	RM	TTT	223.64	294.72	294.16	324.89	332.83
		TWT	12.29	7.45	6.58	8.93	7.87
		TTD	16863.70	17290.00	17330.01	17161.77	17521.57
	RM&VSL	TTT	228.50	285.97	295.29	321.44	322.57
		TWT	12.26	3.82	5.08	5.43	7.36
		TTD	16842.89	17347.12	17355.20	17568.99	17036.60

TTT: total travel time; TWT: total waiting time; TTD: total travel distance; RM: ramp metering; VSL: variable speed limit.

The performance decreases in order of the following font styles: bold-italic, bold, italic, and regular.

Note: ^adenotes TTT in vehicle hours (veh*h); ^bdenotes TWT in vehicle hours (veh*h) and ^cdenotes TTD in vehicle kilometers (veh*km).

An interesting phenomenon can be observed from Table 1: VSL or RM sometimes leads the traffic condition to become even worse (on-ramp demand is 900 veh/h and mainline demand is 3800–4000 veh/h). The reasons why traffic control may obtain unsatisfactory effects, no matter whether it is isolated or integrated were explained qualitatively before. The following analysis will look at a set of simulation results from a typical scenario (mainline demand is 3900 veh/h and on-ramp demand is 900 veh/h), quantitatively investigate the causes, and detail how integrated control coordinates RM and VSL.

Figure 3 shows the control performance under different control strategies. In particular, Figure 3(a) profiles speed to show traffic evolutions. It is obvious that without any control, congestion originates from Segment 3 and propagates to the farthest upstream segment. The low speed on the farthest upstream segment prevents vehicles from entering the traffic network. It can be shown from Table 1 that the TTD even decreased from 17,529.43 to 17,390.54 veh*km when the mainline demand increased from 3800 to 3900 veh/h.

Figure 3.

Network performance: (a) speed profiles; (b) RM and VSL rates; (c) measures of effectiveness; and (d) flow profiles under integrated control.

When VSL was applied to Segment 2, the backward shockwave caused by VSL propagated upstream. The low average speed on Segment 1 blocked the freeway mainline entrance. Even though some improvement was achieved on downstream segments, the overall TTT increased (no-control: 325.28 veh*h and VSL: 333.8 veh*h), and TTD remained the same (no-control: 17390.54 veh*km and VSL: 17394.44 veh*km). Figure 3(b) profiles the control variable variations. Isolated VSL control generated very-low-speed limits during peak hours. The unsatisfactory performance of VSL was due to the formed mainline queue. Other than the general error sources explained before, two other factors were attributable to the unsatisfactory performance. First, as neither estimation nor a constraint for mainline queue length was built into the control algorithm, the mainline queue was not predictable. If the bottleneck kept getting worse, the algorithm continued suggesting lower speed limits for the upstream VSL-controlled segment. Once low-speed limits were achieved, the algorithm could not recover speed limits immediately as a result of the safety constraint (equation (10)). Second, the traffic dynamics took flow measurements on Segment 1 as the demand for downstream traffic prediction. No measurement or prediction of speed and density was taken for Segment 1. The algorithm mistakenly assumed that the low flow from Segment 1 was due to low mainline demand rather than congestion. Therefore, VSL led to a negative improvement. It is crucial to ensure the farthest upstream segment does not encounter congestion before and after deploying the proactive control algorithm. The high TTT and low TTD profiles of VSL in Figure 3(c) can also come to this conclusion.

The control performance of isolated RM on Segment 3 was better than that of isolated VSL. The TTT was reduced by 6.2% (no-control: 325.28 veh*h and RM: 305.04 veh*h). An apparent correlation between RM cycle length and speed profiles was that the longer a cycle length was, the higher the mainline speed will be. RM with a longer cycle length discharged less ramp flow so that it prevented mainline traffic becoming worse. However, the control horizon lasted for 1 min, suggesting that a long RM cycle length may form a long ramp queue and spillback to the surface street. Hence, most RM cycle lengths were less than 7-s long. The resulting ramp queue can be calculated from the TWT profile, as shown in Figure 3(c). The maximum TWT of isolated RM happened at around 5:00 PM, reaching 0.334 veh*h. The stopped vehicle number equaled to 20 veh (0.334 veh*h multiplied by 1 min). Assuming vehicle length and spacing equaled to 10 m per vehicle (m/veh), the queue length was 200 m (20 veh multiplied by 10 m/veh). This queue length almost exceeded the ramp length of 250 m. Thus, in the next time-step, the RM cycle length decreased so that TWT decreased. In conclusion, RM control impacts the network performance little when on-ramp demand is high, due to the limited on-ramp storage length.

In contrast, integrated control maximizes the utility of both control strategies. Combining VSL on Segment 2 with RM on Segment 3, traffic congestion was notably alleviated (Figure 3(a)). The bottleneck speed was remarkably higher, and the duration of a low-speed upstream was much shorter than in other scenarios. The integrated control obtained a 13.3% reduction in TTT (no-control: 325.28 veh*h, RM&VSL: 281.78 veh*h). In addition, the alleviation of speed drops on the farthest upstream segment attracted more vehicles to enter the network. The TTD increased from 17390.54 to 17838.77 veh*km. TWT under integrated control was 1 veh*h more than that in no-control scenario, but it was still 1 veh*h less than that in the RM scenario. From the control signals in Figure 3(b), RM reacted earlier than VSL at the onset of congestion. In the case of an excessive queue, VSL then took over. The average speed limits were higher than those determined by isolated VSL. Thus, the mainline queue was shorter. In the middle of the congested period, VSL itself could not control the congestion as the mainline queue length increased. At this time, RM helped in restricting ramp flow, resulting in a TWT increase. The speed at the bottleneck and the farthest upstream segment increased. Then RM stopped working until the demand was reduced. Traffic congestion recovered, but there were still occasional traffic instabilities. It is important to note that the number of stopped vehicles were different between high- and low-demand periods even though RM cycle lengths were the same. That is why, although the RM cycle lengths were high, RM did not lead to an extremely long ramp waiting time during low-demand periods.

RM and VSL are basically flow control measures. To illustrate their effectiveness in flow control, Figure 3(d) presents the flow profiles under integrated control. The upstream mainline (Segment 2) and on-ramp discharge flow was adjusted by VSL and RM, respectively. Then the mainline and on-ramp flows interacted at the weaving segment (Segment 3) and became the bottleneck flow. During the high-demand period, bottleneck flow slightly fluctuated around 4800 veh/h. VSL and RM worked together to maintain this stable bottleneck flow. Most of the time, the upstream mainline and on-ramp discharge flows were negatively correlated. To put it simply, on-ramp flow reduced when the mainline flow increased, and vice versa. By this means, VSL and RM cooperated through limiting mainline and on-ramp input flows and sustained a stable traffic condition.

Figure 3(c) confirms that the proactive integrated control is superior to isolated control under high mainline and ramp demand. Integrated control shortens mainline travel time by mitigating the mainline queue, and meanwhile controls the on-ramp waiting time by balancing mainline and ramp travel time. This is done by proactive integration. The integration synthetically considers all possible control scenarios, takes advantage of both control strategies, and coordinates RM and VSL rates. The effect of the prediction is reflected in how RM and VSL react before the onset of congestion. Other than control signal profiles, the effect of the prediction is more obvious in speed profiles on Segment 2 (Figure 3(a)) and TWT profiles on Segment 3 (Figure 3(c)). The prediction module forecasts traffic evolutions and proposes control countermeasures. By responding to the predicted traffic condition, it is promising that bottleneck congestion can be prevented if demand is light. In the presented case, the demand was so high that the bottleneck congestion could not be prevented but could still be greatly alleviated. In addition, proactive integration is not always better than isolated control due to some potential errors in real implementation. RM improves freeway mobility but only for short congestion scenarios with relatively high ramp demand. As the mainline carries more controllable flow, VSL outperforms RM when mainline demand is high. However, if the demand is extremely high at both the mainline and on-ramp flows, isolated control cannot operate optimally. In this case, the integration of RM and VSL maximizes their benefits and infrastructure utility.

Conclusion and future research

Recurrent bottlenecks often limit discharge flow and lower freeway mobility and safety. This study emphasized the applicability and effectiveness of a proactive integrated approach. It adopted a METANET-based traffic flow model within an MPC framework. By implementing this proactive control approach in a micro-simulation model, there were three major findings:

1. Proactive RM and VSL, no matter whether they are isolated or integrated, generally improve freeway mobility. After decoupling prediction and simulation models, the unsatisfactory performance originates from the built-in prediction model and control algorithm. The control benefits of integrated control can achieve improvements of up to 13.65% in TTS and 3.41% in TTD, varying with different combinations of mainline and on-ramp demand.

2. Considering the same demand scenario, the control performance among strategies differs. The light congestion that is caused by on-ramp flow can be alleviated by RM. When mainline demand becomes higher, VSL can control mainline flow and achieve more control benefits. However, isolated control fails to achieve the best control performance once mainline and ramp demands are both high. The integration of RM and VSL maximizes their own benefits.

3. For integrated control, RM reacts before VSL. When the demand keeps increasing, VSL takes over the control. During the most congested period, RM and VSL work simultaneously. Later, RM is deactivated in the case of a long ramp queue. At the end of congestion, RM is activated occasionally to deal with the remaining traffic disturbances.

This analysis could guide strategy selection during the ATDM planning stage. Prior to implementation, the causes of recurrent congestion must be carefully analyzed. Flow and corridor origin-destination surveys are recommended. Geometric and traffic situations vary among cases, so it is hard to provide a quantitative guideline for strategy selection. However, the results from this article can still help. RM is beneficial for alleviating short-period congestion during peak hours without disturbing mainline traffic. Appropriate metering rates can improve freeway mobility and balance temporal equality between mainline and ramp vehicles. VSL functions under a higher demand, taking the risk of spreading congestion upstream. The performance of integrated RM and VSL exceeds isolated strategies for more severe congestion.

Proactive integrated control is potentially implementable in the field. If appropriately designed, the proposed integrated approach can lead to better network-wide mobility performance. Further research will consider the effect of ramp flow arrival pattern in RM simulation tests in order to investigate the influence of continuous ramp platoon on mainline traffic. In addition, VSL can be legally enforced or advisory in practice. Driver compliance is a major concern for VSL implementation. In future research, the integrated control strategy will consider driver compliance based on the results of a VSL field test.