Analysis of artificial neural network models for freeway ramp metering control

Arti®cial Intelligence in Engineering 15 (2001) 241±252

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Analysis of arti®cial neural network models for freeway ramp metering control Chien-Hung Wei* Department of Transportation and Communication Management, National Cheng Kung University, Tainan 701, Taiwan Received 12 March 2000; revised 20 April 2001; accepted 30 April 2001

Abstract Traf®c along a freeway varies not only with time but also with space. It is thus essential to model dynamic traf®c patterns on the freeway in order to derive appropriate metering control strategies. Existing methods cannot ful®ll this task effectively. Due to the learning capability, arti®cial neural network models are developed to simulate typical time series traf®c data and then expanded to capture the inherent time± space interrelations. The augmented-type network is proposed that includes several basic modules intelligently af®liated according to traf®c characteristics on the freeway. Inputs to neural network models are traf®c states in each time period on the freeway segments while outputs correspond to the desired metering rate at each entrance ramp. The simulation outcomes indicate very encouraging achievements when the proposed neural network model is employed to govern the freeway traf®c operations. Also discussed are feasible directions for further improvements. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Ramp metering rate; Arti®cial neural network; Time±space interrelation; Traf®c state; Learning capability

1. Introduction Satisfactory research results have been frequently obtained in processing time-dependent data with arti®cial neural networks. Forecasting based on time series data is a typical example. These applications usually refer to a ®xed point in the space coordinate. Conventional statistical methods exhibit similar capability. In a number of circumstances, however, data vary not only with time but also with space. For example, vehicle traf®c on a freeway is changing over time due to driving maneuvers, entering and leaving volumes, and various traf®c controls. While the roadway condition is affected by traf®c from upstream moving downstream, the downstream condition may in¯uence the on-coming traf®c as well. Our task is to identify traf®c characteristics or patterns at various combinations of time and space to de®ne appropriate management methods. Conventional methods cannot deal with this situation effectively. Recently, several studies report promising outcomes of applying the arti®cial neural network (ANN) approach to two categories of transportation problems along this line [1,2]. One category is to de®ne unstable states of traf®c by investigating traf®c patterns and leads to detection of incidents, e.g. Refs. [3±7], etc. The other is to control freeway * Tel.: 1886-6-2757-575 ext. 53233; fax: 1886-6-2753-882. E-mail address: [email protected] (C.-H. Wei).

traf®c operations by ramp metering in order to retain desired level of service at various locations and times. Readers may refer to Stephanedes and Liu [8], Papageorgiou et al. [9], Wei and Wu [10], Zhang and Ritchie [11] and others for details. Ramp metering control is often deployed when a freeway is congested to reduce the traf®c entering that freeway. Metering rates should be determined properly based on the real-time traf®c conditions on the freeway. Traf®c movement in turn is affected by the actual volume joining the mainline ¯ow. It is therefore essential to model the dynamic traf®c movement along a freeway in order to optimize metering rates for each entrance ramp. A number of methods have been proposed for this modeling process [12]. This paper presents an alternative way to ful®ll this task. First, a few typical neural network models are developed to simulate typical time series traf®c data. Then, the better performing models are expanded to capture time±space relations inherent in traf®c data. Each of the augmented networks includes several basic models that are effectively associated according to practical observations. Inputs to the neural network are the current traf®c states at each ramp area while outputs correspond to desired metering rates. Relatively simple ideas are demonstrated to characterize the ANN models and the overall achievement is quite appealing. Several experiments are conducted on the best network. The application potential is assessed by

0954-1810/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0954-181 0(01)00019-X

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C.-H. Wei / Arti®cial Intelligence in Engineering 15 (2001) 241±252 Table 1 Data sets for metering rate estimation

Fig. 1. Typical multileg neural network.

comparing the proposed neural network model with a popular freeway control model Ð FREQ10PC [13]. 2. Spatiotemporal neural networks The spatiotemporal neural network is designed to deal with a time-correlated sequence of spatial patterns [14]. In the literature, the family of neural networks that possess spatiotemporal capability may be divided into three categories. The multileg network (MLN) is the most popular type that has been applied to time series data analysis, e.g. Refs. [15±17]. The basic structure is to feed the network with a set of time sequence data and generate the timedependent output. Fig. 1 shows a three-layer feedforward network exhibiting such capabilities. A typical relation between the output Z at time t affected by factors X and Y from time period t 2 n through t is as follows: Zt ˆ R‰…Xt ; Yt †; …Xt21 ; Yt21 †; ¼; …Xt2n ; Yt2n †Š The recurrent network (RN) has loops and brings information back to the same processing element (PE). A standard recursive PE is shown in Fig. 2. Feedback loops permit trainability and adaptability while recurrency provides necessary nonlinearity [18]. Ivan [6] applied RN to arterial street traf®c incident detection and showed satisfactory results. The spatiotemporal pattern recognition network (STN) for time±space characteristics identi®cation is fairly new in the neural network community. Most existing studies deal with noise ®ltering and speech recognition. The basic idea is to develop dynamic associative memory for temporal patterns [19]. A learning algorithm for STN is more dif®cult

Fig. 2. Recursive processing element.

Data set

Time interval (min)

# Inputs

Variables

1 2 3 4

10 1 10 1

7 7 4 4

S, V, ONQS S, V, ONQS D, NQS D, ONQS

to develop than for ordinary neural networks and prevalent reports are not readily available in the literature. Many fundamental investigations must be conducted before STN is practical for the purpose of this study. Consider that the traf®c characteristics at different locations and time on the freeway affect the corresponding metering rates. MLN and RN seem more suitable for mapping the time±space relationships between traf®c variables and the desired control strategy Ð metering rate. In light of the above discussion, a series of systematic experiments are designed with MLN and RN in the following sections. Actual freeway traf®c data are used to investigate the properties of MLN and RN in dealing with typical sequential traf®c data. Then, a further extension is undertaken to facilitate the capability of capturing the time± space relations among freeway traf®c data. 3. Traf®c data The traf®c data are adopted from the northern section origin/destination ¯ow of the Sun-Yat-Sen freeway, Taiwan, based on the traf®c counts at the entrance/exit ramps [20]. The study area consists of 10 interchanges around the Taipei metropolitan area. Southbound traf®c in the morning peak period (4 h) is used here. Note that ramp metering control had not yet been implemented when the data were collected. Also note that, since the original survey only sought volume counts, the data collection interval was 10 min. A secondary purpose of this study is to ®nd appropriate traf®c variables that determine meaningful freeway metering control strategies, i.e. metering rates. The preliminary study indicates fairly promising results using volume to capacity and on-ramp queue to storage ratio (ONQS) as input variables of a typical back propagation neural network [10]. A number of practitioners and researchers suggest occupancy (density) or combinations of several factors as primary variables. Since the current research is intended to capture both spatial and temporal characteristics of the freeway system, the time interval for collecting relevant data should be determined appropriately. Therefore, the four sets of data in Table 1 are used for training the time±space neural networks. Since ramp metering control is often considered for reducing traf®c entering a freeway, it seems desirable to include the prevailing traf®c ¯ow level as the affecting

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Table 2 Correlation between metering rate and preceding intervals (10 min interval)

Fig. 3. Volume-speed relation.

variable. The basic traf®c ¯ow theory indicates the possibility of similar traf®c volumes (V) under different traf®c conditions, as shown in Fig. 3. Hence, prevailing traf®c speed (S) should serve as a complementary variable if V is used. Consider an alternative way of identifying traf®c characteristics. According to the traf®c ¯ow theory, traf®c condition is a monotonic function of density (D), which may be reasonably represented as volume divided by speed. Note that in ®eld implementation, some kind of data transformation is needed for variable conversion. In the context of traf®c control variables, using density alone may yield similar effects to using both volume and speed. In light of the basic neural network properties, fewer inputs might lead to a smaller network and faster training. Nevertheless, the desirability of certain combinations of traf®c information for this type of application should be veri®ed through systematic experiments. One or 10 min data collection intervals are considered for real world data. The idea is to investigate the trade-offs between detailed information and the resulting performance. The 10 min interval is the original format of traf®c data. A transformation to 1 min interval is made by ®rst assuming that traf®c conditions do not vary signi®cantly. Then, 10 min data are transformed into 1 min data by adding small random variations. Note that this treatment is applied just for demonstrating data manipulation. More realistic traf®c variations are considered in Section 6.2. For all cases, the ONQS is used as an input variable. It is assumed that relevant traf®c information could be obtained via suitable detectors allocated in the freeway system as shown in Fig. 4. Consequently, metering rates of each entrance ramp depend on the information obtained from three sets of detectors measuring mainline S, V, and D, and the fourth set for entry demand. The above mentioned origin/destination traf®c counts are needed for the FREQ10PC model and for simulation, given in Section 6.

Fig. 4. Locations of traf®c detectors.

Interval

Correlation coef®cient

Interval

Correlation coef®cient

t t21 t22 t23 t24 t25 t26 t27 t28

20.49799 20.48921 20.48736 20.51800 20.80404 20.67832 20.53669 20.42626 20.29195

t29 t 2 10 t 2 11 t 2 12 t 2 13 t 2 14 t 2 15 t 2 16 t 2 17

20.28874 20.24665 20.19694 20.14342 20.09952 20.03375 0.02448 0.09046 0.19379

Apparently, all these data sets exhibit quite complex time±space relations among the inputs and outputs. Below, an ef®cient approach is shown for developing suitable neural networks to secure the spatiotemporal characteristics inherent in these traf®c data. 4. Neural networks for time-dependent data In this section, the construction and performance of MLN and RN models for time-related traf®c data is shown. Relevant data from only the ®rst interchange are chosen in order to temporarily discard the in¯uence of interchanges. In addition, data set 3, which has the smallest size, is tentatively used at this stage to reduce the computational burden. 4.1. Multileg model The typical MLN shown in Fig. 1 leaves two questions for practical applications, namely, time intervals and the numbers of input variables. The former relies on the data set used while the latter might be application speci®c. It is needed to specify the correlation between the metering rate at time t and preceding time intervals for the traf®c data under consideration. Based on our traf®c data, statistical test results indicate the correlation between metering rates and preceding traf®c conditions in Table 2. While statistical outcomes show a close relation among intervals t back to t 2 6; several test runs also show better results in seveninterval cases. Therefore, we now modify the basic MLN into the structure shown in Fig. 5. For each input variable, the corresponding values for interval t back to t 2 6 are connected laterally and linked to all elements in the hidden layer. 4.1.1. Improving network input process Ð Hashing According to the modi®ed MLN structure, the number of input elements and connections to hidden layer PEs would increase fairly quickly if more time intervals and traf®c variables are involved. This tends to worsen the training process and to require a large memory. The following approach is proposed to enhance computational ef®ciency, particularly for dealing with freeway traf®c data.

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Fig. 7. Input layer element with hashing. Fig. 5. Modi®ed MLN.

Consider the evolution of certain traf®c variables over several periods of time as illustrated in Fig. 6. All the corresponding values of the traf®c variables must be sent to input and hidden layers while they altogether just stand for a particular traf®c state. It thus seems highly preferable to feed the network with only the key trait rather than a complete set of numerical ®gures. A code that represents a certain combination of traf®c variables over several time intervals may be obtained for each type of traf®c conditions. Neural network size in terms of connection weights may be reduced in this fashion while essential characteristics of data are still preserved. Hashing is proposed for this purpose. The idea is to transfer vital features of data by a suitable hash function into a single key or code [21]. A crucial concern is to prevent hash collision, which means the same code is generated for different data. Effectiveness of hashing depends heavily on the hash function selected. An illustrative hash function below is shown as the weighted sum of traf®c variable values (TP) over the relevant time interval i: X Code ˆ TPi £ HWi i

Fig. 6 shows an example of the weights for each time interval. Since the traf®c condition is seldom symmetric within the relevant duration, the above hash function is considered effective to prevent hash collision. Additionally, this procedure tends to exhibit signi®cant differences among

Fig. 6. Evolution of traf®c variable.

the resulting codes, a desirable situation for neural network training. The input layer portion of each traf®c variable is adjusted for hashing as shown in Fig. 7. The hash weight HW between the code and each original input element is a constant value computed by HWi ˆ …1=n†…i 2 …n 2 nmod 2†=2† 4.1.2. MLN architecture improvement Although the above method is simple and effective enough in most situations, it is desirable to consider the possibility of symmetric traf®c conditions and to improve model accuracy. Besides hashing, incorporating a little more information at certain time intervals is proposed. The twofold purpose is to increase neural network accuracy and avoid hash collision. Experiments are conducted on the ®ve networks shown in Table 3. Data set 3 in Table 1 is used and three types of time legs are considered for training. Numerical outputs clearly indicate that arbitrary length of related time intervals is unlikely to yield satisfactory training results. Data with seven-interval interrelations tend to exhibit better results, regardless of network types. Network types 2, 3 and 5 adopt more information of recent status and lead to better performance. Figs. 8 and 9 depict the structures and training results of these encouraging networks. It is conjectured that metering rate is so strongly dependent upon very recent traf®c situations that network type 1 performs well in many time series cases, but not in this one. 4.2. Recurrent model A possible drawback of the above multileg models is the large number of connections, leading to great computational load and memory requirements. The recurrent model uses feedback loops representing time-related information. Explicit elements and connections may be reduced, which often results in faster training and better performance. The speci®c structure of a PE with a feedback loop is shown in Fig. 10. It differs from a typical PE by the register that is used for storing the activation status at the previous time interval. This information is conveyed back to the same PE, mixing with next interval inputs. Effects of the feedback information are determined by the feedback weight r.

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Table 3 Modi®ed MLN models with hashing Net work type

# PEs for each traf®c variable

1 2

n 4

3

6

4

4

5

4

a

a

Additional information

Feature

None Most recent interval, midinterval, most preceding interval Most recent 3 intervals, midinterval, most preceding interval Most recent 3 intervals, mid-3 intervals, most preceding 3 interval Most recent interval, mid-3 intervals, most preceding 3 intervals

Base case shown in Fig. 5 Preventing hash collision due to symmetry Emphasizing effects of most recent status Incorporating moving average to avoid large deviation Highlighting effects of recent status and moving average

n is 7 in this case.

The structure of the RN model is similar to conventional feedforward network trained with the back propagation algorithm, except that some elements are associated with feedback loops. Each input unit corresponds to a traf®c variable pertinent to metering rates. For example, two types of input units are needed if data set 3 is used. Six recurrent models listed in Table 4 are tested. Computational results clearly denote the inef®ciency of ®xed recurrent weights since the ®rst ®ve neural networks do not converge after signi®cant training cycles. On the other hand, recurring information in the hidden layer with variable weights exhibits outstanding performance. Network type 6 is chosen for further study based on the above ®ndings. 5. Neural networks with time±space feature In this section, the more promising networks obtained in Section 4.2 are expanded to incorporate a spatial feature. Spatial effects of freeway traf®c data and the determination of metering rates are mutually affected. Not only is the downstream metering in¯uenced by the upstream entering traf®c, but also the upstream metering should take into account downstream demand. Traf®c demand and movement is highly stochastic. The complex interrelations among possible factors have not been well understood. The neural network architecture developed in this study is shown to be fairly effective in capturing the inherent time± space characteristics. 5.1. Time±space networks for freeway traf®c data

Fig. 8. Favorable MLN models.

The preliminary time±space architecture suggested for the ramp metering control purpose is shown in Fig. 11. Since the metering rate of each ramp is mainly affected by the immediately upstream and downstream mainline traf®c and partially dependent on traf®c elsewhere, it seems wise to consider partially connected networks. The proposed network is composed of several subsystems, one for a ramp. The subsystem is in fact the time-related network obtained in Section 4. Full connections exist in

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Fig. 10. Recursive PE with register.

architecture is actually a three-layered, feedforward neural network that can be trained with the conventional back propagation algorithm. Since the theoretical background is quite solid for this type of network, there is no need to develop special training methods at this stage. Besides, the back propagation neural network guarantees the proposed network to model any arbitrary functions, including the dynamic time±space traf®c interrelations. An auxiliary advantage of this structure is to make distributed processes workable. Namely, data collection and computation between input and hidden layers may be conducted at local processors and the central computer computes the metering rates. Four candidate time-dependent networks yielding encouraging performance are employed, respectively, as the subsystem to construct the complete time±space network (TSN). Pertinent information about these four networks is provided in Table 5. Among the desirable features of this time±space structure is that the network size scales favorably with the numbers of variables and ramps under consideration. The occurrence of related time legs would not affect the neural network structure nor the network scale. For the same traf®c variables of concern, TSN type 4 requires the fewest connections while the others are signi®cantly larger. 5.2. Time±space network training So far, 10 min traf®c characteristics are solely used as the training data. In practice, one might expect to update freeway control every minute so that traf®c condition is fully

Fig. 9. Training of favorable MLN models.

each subsystem, representing the interrelations among the variables associated with the metering rate of each ramp. The inter-subsystem relations, representing mutual in¯uences among ramps at different locations, are handled by linking hidden units with output units. The resulting Table 4 Recurrent network models Network type Recurrent layer Recurrent weight

1 Input 0.5

2 Hidden 0.5

3 Output 0.5

4 All 0.5

5 Input a 0.5

6 Hidden Variable

a

Each variable has two units, one for the current interval and another for information recurring.

Fig. 11. Time-space neural network structure for freeway data.

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Table 5 Candidate time±space networks Network type

Subsystem

# Links with variable weight a

1 2 3 4

Multileg type 3 Multileg type 2 Multileg type 5 Recurrent type 6

5100 3900 3900 1830

a Consider D and ONQS as input variables for the 10-ramp freeway system.

accounted for. Hence, data set 4 in Table 1 is applied to train these time±space networks. Also, traf®c conditions for 70 min are correlated for the multileg type networks as indicated in Table 2. It is surprising that the recurrent type TSN cannot be reasonably trained. The error is so signi®cant that one would regard it unsuitable for spatiotemporal traf®c data although potentially recurrent networks are ef®cient for time related problems. Macroscopically, all other networks perform equally well, as shown in Fig. 12. TSN type 3, incorporating moving average and recent status effects, exhibits a smooth training process. However, its ®nal resulting error is the largest among the three multileg networks. TSN type 1 retains the smallest training error although it takes longer to converge. Table 6 lists the ®nal training results of the three multileg networks. TSN type 1 takes into account the most recent 3-interval status and reveals the best training outcome. Such a situation con®rms the principal concerns in determining the most favorable metering rates. 5.3. Further testing Before approving TSN type 1 for the freeway control system, some experiments are conducted to explore its properties in depth. First, it is trained on different traf®c variables to identify suitable ones. The proposed neural network is trained with data sets 1 and 3 in Table 1, and the results are shown in Fig. 13. It shows that using density as the only traf®c variable is suf®cient in this type of application. In addition to allowing for a smaller network, it generates more accurate results. The second test is to verify the size of related time legs. Here we rearrange data set 4 to produce three training sets with 71, 11, and 7 min correlations, respectively. It is observed that cases with shorter time legs behave quite smoothly and the resulting errors are acceptably

Fig. 12. Training of TSN models.

low. On the other hand, the 71 min correlation data give better outputs if enough training is allowed. Fig. 14 illustrates the training processes in detail. One might conclude that the longer the related duration is, the more information the TSN model obtains and the higher accuracy the network generates. A trade-off often exists in real time traf®c control, in considering long-term trend to develop better strategies or short-term variation to ful®ll prevailing demand. The comparative bene®ts may be assessed by appropriate simulation models, which are presented in Section 6. 6. Simulation experiments A mesoscopic traf®c simulation model is developed and validated for evaluating the proposed metering rate estimation model [22]. It is a stochastic, event-based model that could incorporate several types of ramp metering control. Vehicle operations on freeway mainlines, entrance ramps and exit ramps are all simulated. Below, several experimental runs are executed to test the relative performance of various control modes. All these experiments are compared under the same freeway con®guration and equivalent traf®c conditions as presented in Section 3. Three control modes are implemented in the simulation processes: 1. NoCtrl: No ramp metering control is deployed. Vehicles may enter the freeway without any restriction if the traf®c condition itself is permitted. 2. FREQ: Entrance ramps are controlled by the metering rates computed from the FREQ10PC model.

Table 6 Training results of multileg TSN models TSN type

Output target/computed

Max error (veh/h)

Avg error (veh/h)

1 2 3

0.670/0.651 0.670/0.642 1.000/0.916

38 56 168

13.2 15.4 37.6

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Fig. 13. TSN 1 trained with different variables.

3. ANN: Entrance ramps are controlled by the metering rates adaptively furnished from the proposed arti®cial neural networks. Note that the FREQ10PC model is embedded with a macroscopic, deterministic model that simulates traf®c ¯ows in a freeway for the given set of metering rates. Its SYNODM subroutine is used to estimate the origin/destination (O/D) table based on the arrivals on the entrance ramps. Then, the most appropriate metering rate of each ramp is solved with the linear programming method for each time period. Since only periods longer than 10 min can be processed, the resulting metering rates are practically pretimed for the given traf®c pattern. In contrast, the arti®cial neural network model for metering rate estimation may handle periods with arbitrary duration. Traf®c dynamics may be considered in greater detail. It thus seems more ¯exible and reliable than the FREQ10PC model. Section 5.3 illustrates comparable accuracy in TSN type 1 training results for different time legs. The ®rst task in this section is to ®nd the suitable length of related time legs as the metering control is actually executed. Since freeway operations tend to be fairly sensitive to short term occurrences, such as incidents and sharply increasing demand, longer time legs are less likely to deliver ef®cient control. Based on the preliminary trials, one would consider the long periods not sensible for the purpose of real time freeway traf®c control. Therefore, we choose the neural network model with 11 min correlation to link with the traf®c simulation model. 6.1. Ordinary traf®c demand The simulation is executed for 4 h, 6:00±10:00 a.m., after 40 min of transition time. In general, freeway users desire higher speeds or shorter travel times while the management authorities wish to maximize the overall system utilization. Theoretically, the user optimum may hardly approach the system optimum. Neither objective might be uniquely attained in practice. Performance of different control modes is thus assessed with such factors that cover the wishes of both sides.

Fig. 14. TSN 1 trained with various time legs.

The highest demand occurs from 8:00 to 9:00 a.m. The operations of vehicles entering and leaving the freeway during the above 1 h period are collected and listed in Table 7. The operational results for the entire control period are shown in Table 8. One may note that the ANN and FREQ control modes behave quite differently, although the ANN metering rate is learned from the FREQ10PC model. In the FREQ mode, the metering rates are generated with a macroscopic approach. When the neural network metering rate estimation model is linked with the simulation model, inputs to the neural network are not exactly the same as those to the FREQ mode. Hence, the resulting sets of metering rates are likely dissimilar, leading to divergent outputs. From Tables 7 and 8, one may notice that no single control mode dominates others in all respects. In particular, the average travel speed within the entire control period is indeed the same for three modes although minor variance exists for the peak hour period. It implies that under a moderate demand level, users may perceive analogous level of service regardless of the control modes. This situation changes as traf®c demand increases. The FREQ mode implements more restrictive control on the vehicles entering the freeway since the associated average waiting time on ramp is the highest among all. Since FREQ10PC obtains the metering rates by solving a linear programming problem for 10 min periods, it may not ®t the actual traf®c condition very well. As a result, the total

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Table 7 Peak hour performance for ordinary demand NoCtrl # Vehicles entering freeway # Vehicles leaving freeway Average waiting time on ramp Average running time on mainline Total vehicle-kilometers Average travel speed (KPH) a

FREQ (% change) a

ANN (% change) a

18,379 17,109 608 1432

18,177 (21.1) 15,820 (27.5) 725 (119.2) 1391 (22.9)

18,470 (10.5) 17,004 (20.6) 574 (25.6) 1428 (20.3)

263,575 53.5

228,236 (213.4) 56.0 (14.7)

260,152 (21.3) 53.9 (10.7)

Compared to NoCtrl.

vehicle kilometers (TVK) of the FREQ mode is the lowest. Highway agencies, from the system optimum point of view, may not be satis®ed with the outcome. Alternatively, the ANN mode generates higher TVK and favorable total travel time. One might accept it as superior to, or at least as good as the other modes in facilitating traf®c control. 6.2. Increased traf®c demand To investigate the characteristics of various control modes at higher traf®c demand, 25% more traf®c and larger variations are added to the simulation process within the control periods. Simulation runs are conducted and relevant data are collected as were done in the ordinary demand case. The results are shown in Tables 9 and 10. Here one would easily detect notable differences in TVK and average travel speeds among the three control modes. The FREQ mode is the best and the NoCtrl mode is the worst, according to the above two criteria. However, the FREQ mode suffers from much higher average waiting time on ramp due to its rigid nature and increased demand. The linear programming method ensures no congestion on the mainline, which corresponds to much shorter average running times than the other modes. Contrarily, the ANN mode takes into account queues on entrance ramps and utilizes the freeway capacity more ef®ciently. It is also due to relevant local and system wide traf®c state information processed in the proposed time±space neural network structure. The advantageous ANN result is a lower total travel time than FREQ and higher average travel speed than NoCtrl mode.

6.3. Discussions Based on the above simulation experiments, one might preliminarily conclude that the ANN control mode is a compromise between the FREQ and NoCtrl modes under a realistic congested traf®c condition. It tends to yield a lower total travel time and satisfactory TVK, which satis®es both the general public and authorities. On the other hand, the FREQ mode follows the basic rule to maximize system throughputs subject to available capacities. Preserving smooth movements on mainlines is the ultimate concern of the FREQ mode. Users tend to criticize the FREQ mode for its very long waiting time on ramp. The original data for ANN training were obtained from FREQ10PC. Given the input traf®c variables, FREQ10PC generates optimized metering rates for each ramp with the embedded deterministic mathematic model. Although it seems that ANN models are just used to replicate the algorithm embedded in FREQ10PC, these ANN models turn out to perform better in freeway traf®c control. The primary reason is that ANN models are capable of generalizing the complex dynamic traf®c ¯ows [2] while FREQ10PC is mainly a static optimization mechanism. Several other unique features make the ANN approach superior to FREQ10PC model and potential competitors. Given the availability of traf®c information in the entire control area, the ANN model can be trained in advance off-line and then used on-line with real-time information. Numerous reports have con®rmed such function. Mathematical approaches solve speci®c quantitative problems, but they are not as ef®cient in dealing with traf®c control

Table 8 Performance of entire period for ordinary demand NoCtrl # Vehicles entering freeway # Vehicles leaving freeway Average waiting time on ramp Average running time on mainline Total vehicle-kilometers Average travel speed (KPH) a

Compared to NoCtrl.

35,861 31,342 900 1648 461,309 54.8

FREQ (% change) a 35,285 (21.6) 29,966 (24.4) 1043 (115.9) 1619 (21.8) 431,571 (26.4) 55.2 (10.7)

ANN (% change) a 35,066 (22.2) 31,551 (10.7) 984 (19.3) 1636 (20.7) 480,130 (14.1) 55.1 (10.5)

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Table 9 Peak hour performance for increased demand NoCtrl # Vehicles entering freeway # Vehicles leaving freeway Average waiting time on ramp Average running time on mainline Total vehicle-kilometers Average travel speed (KPH) a

FREQ (% change) a

ANN (% change) a

20,245 15,772 1016 1821

19,102 (25.6) 16,184 (12.6) 1486 (146.3) 1477 (218.9)

19,919 (21.6) 15,984 (11.3) 1078 (16.1) 1679 (27.8)

200,198 50.8

230,830 (215.3) 54.6 (17.5)

210,614 (15.2) 51.5 (11.4)

Compared to NoCtrl.

involving many uncertainties. It is also very tough to set up speci®c rules for expert systems to manage dynamic traf®c conditions. In particular, the ANN model estimates suitable metering rates rather than calculating them for the prevailing traf®c states. Neural networks sometimes contribute errors and inappropriate metering rates, just as humans do. Perhaps its greatest potential for this particular application is its capability to learn from its own mistakes. Experiences of making mistakes may be taken into account while con®guring the neural network structure to ensure the error adjustment function. Then, a retraining procedure can be designed to take full advantage of the inherent nature of neural networks [23]. A preliminary suggestion for exploiting this idea is illustrated in Fig. 15. The neural network model can be updated continuously to incorporate more traf®c patterns for recognition. Additional algorithms might be employed as well to enhance the training process and/or improve the network architecture. With this module, the freeway ramp metering control systems may be represented by Fig. 16. Work is still needed to develop ef®cient procedures for judging the metering rates and determining how they should be revised. 7. Conclusions Based on the above discussion, it is concluded that the proposed spatiotemporal arti®cial neural networks possess great potential for solving freeway metering control problems. Traf®c on freeway is a typical example of time±space interrelations. In this study, several types of

freeway traf®c data are used to test neural network applicability in this context. The computational results indicate considerable promise in capturing time±space characteristics, leading to very small errors. The proposed network structure is basically an extension of multileg feedforward networks. Nothing except the typical back propagation training algorithm is needed, which makes the proposed model simple and workable. Improved network performance is demonstrated by incorporating suf®cient information in the input layer. Evaluating related time intervals and hashing input data is included to well manipulate training data and enhance network architecture. A number of experiments are conducted to evaluate the neural network structures and their comparative performance. A mesoscopic traf®c simulation model is developed and validated for evaluating the proposed metering rate estimation model. It is a stochastic, event-based model that could incorporate several types of ramp metering control. Three control modes are implemented in the simulation processes for a freeway section with 10 interchanges. Macroscopically, analogous level of service was observed under a moderate traf®c demand level regardless of the control modes. However, the FREQ mode implements more restrictive control on entering vehicles since the associated average waiting time on ramp is the highest among all. As a result, the TVK of the FREQ mode is the lowest. Highway agencies, from the system optimum point of view, may not be satis®ed with the outcome. Alternatively, the ANN mode generates higher TVK and favorable total travel time. Road users might consider it superior to, or at least as good as the other modes in facilitating traf®c control.

Table 10 Performance of entire period for increased demand NoCtrl # Vehicles entering freeway # Vehicles leaving freeway Average waiting time on ramp Average running time on mainline Total vehicle-kilometers Average travel speed (KPH) a

Compared to NoCtrl.

FREQ (% change) a

ANN (% change) a

38,533 30,663 1437 2134

36,469 (25.4) 30,810 (10.5) 2053 (142.9) 1801 (215.6)

37,949 (21.5) 30,564 (20.3) 1495 (14.0) 2094 (21.9)

397,591 49.3

443,471 (111.5) 53.9 (19.3)

401,233 (10.9) 51.0 (3.4)

C.-H. Wei / Arti®cial Intelligence in Engineering 15 (2001) 241±252

251

Fig. 15. Self-adjusting module of ANN model.

25% more traf®c and larger variations are added to the simulation runs to further examine the characteristics of various control modes at higher traf®c demand. The simulation outcomes indicate very encouraging performance when the proposed neural network model is used to control freeway traf®c operations. The advantageous ANN result is a lower total travel time than FREQ and higher average travel speed than NoCtrl mode. It is conjectured that the ANN mode does not always provide the best control strategies although the neural network model may theoretically capture the actual traf®c

conditions. In other words, errors of the ANN control mode may arise that result in undesirable traf®c situations. A retraining mechanism should be added to form a more comprehensive model that identi®es any ¯aws and learns from experience under suitable supervision. The establishment should make complete use of the inherent learning features of the neural networks. Eventually, mistakes would be amended and better performance is achieved. This issue is highly worth pursuing in future research. Without learning capability, the FREQ mode can hardly make progress toward better performance.

Fig. 16. A comprehensive freeway ramp metering control system.

252

C.-H. Wei / Arti®cial Intelligence in Engineering 15 (2001) 241±252

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