Adaptive traffic control system: Control strategy ... - Wiley Online Library

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pp. 323-347

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Adaptive Resolution, and Accuracy

IStrategy, Prediction

Hong K.Lo H. E Chow Recent advances in traffic control methods have led to flexible control strategies for use in an adaptive traffic control system (ATCS). ATCS aims at controlling the imminent traffic, which is yet to arrive and hence not known perfectly. Therefore, volume prediction is an essential part. Associated with the prediction are two aspects: resolution and accuracy. Recent studies indicate a tradeoff between prediction resolution and accuracy: finer resolutions, larger errors. It is imperative to study the relationship and tradeoff between the control strategy, prediction resolution, and its associated error, which are crucial to the development of ATCS. This study investigates this relationship through an extensive simulation of scenarios in Hong Kong with a recently developed dynamic traffic control model, DISCO.Based on the Hong Kong scenarios conducted with DISCO, the major findings include: (i) the importance of resolution outweighs that of error; (ii) dynamic timing plans generally outperform time-invariant timing plans; (iii) up to a certain extent, overestimated predictions lead to better results than underestimated predictions.

Introduction

Adaptive traffic control system (ATCS) aims at controlling the imminent traffic, which is yet to arrive and hence not known perfectly. An ATCS can use historical data based on time of day or day of week, or real-time detected data, to formulate control strategies, in the hope that the current or historical arrival profile will remain representative for the upcoming situation. More advanced ATCS may include a short-term traffic prediction module for improved prediction accuracy. In any case, the performance of ATCS depends on its ability to predict the upcoming traffic pattern.

Hong K. Lo and H.F. Chow are in the Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, P.R.China Received: March 2002; Accepted:July 2002

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In fact, the need and benefit of short-term traffic prediction are well recognized. Lan (2001) provides a summary of recent developments in traffic prediction models. Yin et a1 (2002) proposes a fuzzy-neural approach for short-term traffic prediction. Abdulhai et al. (2002) develops a short-term traffic prediction model based on a neuro-genetic algorithm. In particular, Abdulhai et al’s experiments indicated that prediction errors were related to the time-resolutions of the predictions. That is, if one were to predict traffic volume at 1-min intervals, the percentage errors would be higher than for prediction at 5-min intervals. Many factors could possibly contribute to this outcome. At larger time resolutions, the stochastic demand variations, the immediate effects due to the downstream and upstream signals, platoon dispersion, etc. are averaged out, leading to a more stable mean. This tradeoff between prediction resolution and accuracy has implications on ATCS design. Control strategies for dynamic traffic can be classified by three distinctive approaches, ranging from time-invariant “fixed green splits in a fixed cycle” (FGFC) plans, to time-variant “variable green splits in a fixed cycle” (VGFC), and eventually “variable green splits in variable cycles” (VGVC) plans. The performance of these strategies with perfect information is studied in Lo and Chow (2001,2002). In terms of control flexibility, VGVC includes VGFC as a special case, which in turn includes FGFC as a special case. One would expect VGVC to perform the best, if the available traffic prediction were perfect and that its resolutions were fine enough to support time-variant changes in phase durations. In terms of computational effort, the algorithm needs to search in an exponentially growing space as the control flexibility and hence the number of decision variables increase. For real-time operations, the system has a tight time budget to search for a good strategy. Even though theoretically VGVC is the best, given a tight time budget, it could happen that the algorithm finds a better performing FGFC plan due to its much smaller search space that allows for a more thorough search as compared with the more flexible strategies. When confronted with the limitations of real-time operations, it is imperative to study the relationship and tradeoff between the flexibility of the control strategy, prediction resolution, and its associated error. If the prediction were only good at 15-min intervals, would it be useful to determine a flexible VGVC plan that changes its duration from phase to phase (or from minute to minute)? Or, would it be better to use the predictions at a fine resolution of 1-min anyway, at the expense of larger

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prediction errors; what about determining a FGFC plan with the 15-min prediction intervals? To our knowledge, in the open literature, this relationship between Control strategy, data Resolution, and prediction Accuracy (notated in short as the CRA relationship herein), which is crucial to the development of ATCS, has neither been studied nor documented. Due to its complexity, it is not possible to derive analytical functions to express this CRA relationship. The relationship will depend on the control strategy of ATCS, traffic characteristics of the site, and the prediction model. In this study, as a first attempt, we conduct numerical simulations based on real scenarios to get a preliminary understanding. Many signal control models have been developed in the past; some can handle flexible phase sequences (e.g., Wong et al, 2002). However, to truly capture the dynamic control strategies discussed above, we consider the dynamic platform designated as Dynamic Intersection Signal Control Optimization (DISCO) (Lo, 1999,2001) recently developed as the ATCS platform. DISCO considers the entire Fundamental Diagram of traffic flow, which is essential for controlling congested and transient traffic. As a dynamic model, DISCO works with time-variant traffic patterns and derives dynamic adaptive timing plans. From this extensive simulation study, based on the scenarios evaluated with DISCO, the major findings include: (i) the importance of resolution outweighs that of error; (ii) dynamic timing plans generally outperform time-invariant plans; (iii) up to a certain extent, overestimated predictions leads to better results than underestimated predictions.

Background Dynamic Intersection Simal Control ODtimization (DISCO) DISCO (Lo, 1999; 2001) considers the entire range of the Fundamental Diagram by encapsulating the Cell-Transmission Model (CTM) (Daganzo, 1994, 1995). CTM provides a convergent approximation to the Lighthill and Whitham (1955) and Richards (1956) (LWR) model and covers the entire Fundamental Diagram. By encapsulating CTM, DISCO inherits the fust-order kinematic model of traffic flow as represented by the LWR model. It captures kinematic waves, physical queue formations and dissipations in an explicit manner -

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features that are important for modeling congested urban streets. We applied DISCO to a range of demand scenarios in Hong Kong (Chang, 1998;Lo et al., 2001). The results were promising. DISCO produced delay estimates that were in agreement with the on-site delay measurements; the difference between them was bounded by a few percent. When used to optimize the timing plans, DISCO outperformed TRANSYT by as much as 30+%in a wide range of scenarios ksted (Lo et al, 2001). These results establish DISCO as a reasonable dynamic signal control platform.

Due to its dynamic nature, DISCO supports not only fixed green splits in a fixed cycle (FGFC) plans, but also variable green splits in a fixed cycle (VGFC) plans. In addition, DISCO can allow each phase to vary in a time variant manner, referred as variable green splits in variable cycles (VGVC) plans. These various degrees of flexibility are illustrated schematically in Figure 1. The darker and lighter shades in Figure 1 refer, respectively, to the effective red and green durations.

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-*Cycle 1

Cycle 1

Cycle 2

Cycle 2

Cycle 3

Cycle 3

Fig. 1. Three Control Strategies Formulated as a mixed-integer program, DISCO can be solved formally with mathematical programming techniques. For real-sized problems, however, it takes an exceedingly long time to solve the formulation perfectly. Therefore, we adopted a heuristic solution approach based on Genetic Algorithm (GA) to find a good, rather than an optimal

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solution (Lo et al., 2001; Lo and Chow, 2002). The main advantage of this GA based solution approach is that the quality of the solution is scalable to the amount of computational time available. With a longer computational time, the algorithm can search the solution space more thoroughly, leading to better solutions. In terms of computational effort, this GA based algorithm needs to search in an exponentially growing space as the control flexibility and hence the number of decision variables increase. Even though theoretically VGVC offers the most flexible control strategy, given a fixed computational time, it could happen that the algorithm finds a better performing FGFC plan due to its small search space.

The site chosen for this study is a mixed residential-commercial district - Mongkok, Hong Kong, which is notorious for heavy congestion. For most of the day, intersections in this area operate with the cycle time of 120 s - the maximum allowed in the Transport Planning and Design Manual (Transport Department, 2002). During our surveys, we observed that these intersections operated in a state of over-saturation during peak hours. Figure 2 shows the plan view of the Argyle Street network in Mongkok. It has four origins where demands are loaded to the network and three signalized junctions, from right to left in Figure 2: Portland Street, Shanghai Street, and Reclamation Street. We collected traffic inflows into the network at 20-second intervals from 08:OO a.m. to 09:OO a.m. on three days: October 11, 18, and 23, 200 1 . An example of the inflow patterns to Argyle Street (the main eastwest corridor) on October 11, 2001 is shown in Figure 3. The pattern is somewhat cyclic due to the upstream signal.

Data Resolution

By aggregating the measurements in Figure 3 to I-min, 5-min, and 15-min intervals, we obtain Figure 4. Note that the variability is gradually removed as the resolution of aggregation becomes coarser.

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Plan Mew or Argyle Strcct

Fig. 2. Plan view of the Argyle Street Area

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m zoo

5"

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Fig. 3. Traflic Inflow Pattern to Argyle Street on 11 Oct, 2001

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900 8:OO:OO

8:lO:OO

8:05:00

8:15:00

Time Periods

Fig. 4. Aggregating the traffic inflow data to 1-min, 5-min, and 15-min intervals

Prediction Accuracy

In traffic control, one must have a way of predicting the imminent traffic that is to be controlled. Historical averages or real-time detected (but past) traffic patterns can be used as “predictions”, assuming that the traffic doesn’t vary significantly. Even with advanced techniques, prediction errors are unavoidable. In particular, Abdulhai et a1 (2001) demonstrated the relationship between prediction resolution and average percentage error, as summarized in Table 1. In general, finer prediction resolutions have higher errors due to the intrinsic traffic variability at fine resolutions. Many factors could possibly contribute to this outcome. For the time-resolutions of interest in this study (20 s - 1Smin), at larger time resolutions, the stochastic demand variations, the immediate effects due to the downstream and upstream signals, platoon dispersion, etc. are averaged out, leading to a more stable mean. We adopt this error relationship in the simulation study as discussed in the next section.

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Prediction resolution 1-minute 5-minute 15-minute

Average percentage error* (%) f 10 *5 f 2.5

Methodology of the Numerical Study This study aims at investigating the relationship between the Control strategy, data Resolution, and prediction Accuracy (CRA), which is crucial to the development of ATCS. The analysis is divided into three parts: first we study the effect of data resolution on the performance of the control strategy (i.e. the CR relationship). Then we investigate the effect of prediction accuracy on the control strategy (i.e. the CA relationship). Finally, we combine these two considerations to assess the CRA relationship. RelationshiD between Control Stratem and Data Resolution The traffic inflow data into the Argyle Street network were collected at 20-s intervals from 08:OO a.m. to 09:OO a.m. on three days: October 11, 18, and 23,200 1. These traffic data at the 20-s resolution are considered as the “real traffic”. Subsequently, we aggregate these original data into three different resolutions: 1-min, 5-min, and 15-min (see Figure 4) to simulate the available information predicted or estimated at these coarser resolutions. This aggregate but error-free information is used in DISCO to determine the appropriate control plans. Afterwards, the timing plans by DISCO are evaluated by simulating their performance back with the original traffic data in the resolution of 20-s. By doing so, we simulate the performances of the timing plans in the “real traffic” to assess how much the control strategy would be impaired by degrading information resolution. Figure 5 summarizes the simulation procedure.


33 1

Relationship between Control Strategy and Prediction Accuracv The time-dependent traffic volumes as shown in Figure 3 are only known after the fact. They are not available as inputs to DISCO prior to their occurrence. To find an optimal timing plan for the flow situation in Figure 3, DISCO must be fed with predicted traffic information, which is bound to have prediction errors. To simulate the different levels of prediction accuracy, we add a random error to the measurements in Figure 3 to represent the predicted information. These predicted volumes are then used in DISCO to determine an appropriate control strategy. The performance of this control strategy will then be evaluated back with the original flow measurements.

II

Aggregation

+

II

Traffic Info @ 1-min resolution; @5-min resolution; @15-min resolution 1

+

I

Apply DISCO to Traffic Info at respective resolutions

.t Control Plans

on Traffic Data @20s resolution

e---

Delay Performance at respective Traffic Info resolutions Fig. 5. Procedures for simulating the CR Relationship The prediction error is assumed to follow the normal distribution,


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whose mean is set to be the percentage error times the mean volume of the true traffic and its coefficient of variation (COV)taken as 25% (as reflected from the on site measurements):

where S is the percentage prediction error to be modeled, p is the mean volume of the real traffic. For example, to create a prediction realization with a +lo% error, we draw randomly from the error distribution (1) with S =+lo%, and then add the error to the actual mean p . For illustration purposes, Figure 6 (Figure 7) shows the simulated predicted volumes by adding (subtracting) a random noise of

_I

... .. ..

Fig. 6. A realization of the predicted volumes with a random error with mean +10%

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Fig. 7. A realization of the predicted volumes with a random error with mean -10% 10% average error to the measurements. The results in Figure 6 (Figure 7) illustrates that the prediction overestimates (underestimates) the flow by 10%.Note that the realizations in both cases deviate around 10% from the original data. The exact deviations come from the errors drawn randomly according to (1). To investigate the effect of the random prediction errors on the performance of control plans, we set up this simulation study. Random errors of *lo%, f5%, and 0% are added to corrupt the traffic data. Note that the case of 0% error only refers to the error distribution (1) having a zero mean; its standard deviation is nonzero. So, 0% error here does not imply the perfect forecast. Thirty realizations of the predicted volumes are constructed for each error rate. These realizations represent the available information or predictions prior to the occurrence of the real traffic. DISCO is then applied to search for the control plans based on these prediction realizations. The DISCO timing plans are then evaluated back with the “real” traffic. Finally, we calculate the expected delay to summarize the performance of the control plans under each error rate. The procedure is summarized in Figure 8.

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/

Traffic Data @2Os resolution

+

+

Generate Traffic Info with -10% random error; -5% random error; 0% random error; W’ random error; and 10% random error .(

30 sets of “predicted” Traffic Info for each error profile .(

Apply DISCO to these “predicted” Traffic Info .(

Control Plans

II

I

Traffic simulation of the Control Plans on Traffic Data @20s resolution

Delay Performance with respective error profiles

Fig. 8. Procedures for simulating the CA Relationship

Relationship between Control Stratem Data Resolution. and Prediction Accuracy To investigate the CR4 relationship, first we aggregate the collected traffic data into resolutions of 1 min, 5 min, and 15 min. Then, according to Table 1, we adopt the random error rate of f10% for the information at 1-min resolution, f5% for the information at 5-min resolution, and f2S% for the information at 15-min resolution. For each information resolution, we generate thirty realizations of the predictions by first drawing random errors according to (1) based on the above error rates, and then adding the errors to the true means. DISCO is then applied to generate the control plans for each prediction realization. Finally, similar to before, the control plans are evaluated back with the “real” traffic. The overall procedure is summarized in Figure 9.

Adaptive Traffic Control: Control Strategy...

I

+

335

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Aggregation & Traffic Info @l-min resolution; @5-min resolution; Q 15-min resolution

+

i

Generate Traffic Info a l - m i n resolution with f10% random error; @5-min resolution with f5% random error; Ql5-mln resolution with *2.5% random error

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30 sets of ‘predicted”Traffic Info for each resolution

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I Apply DISCO to these “predicted” Traffic Info I + I Control Plans I

+

Traffic simulation of the Control Plans on Traffic Data Q20s resolution I

Delay Performance with respective resolutions and error profiles Fig. 9. Procedures for simulating the CRA Relationship

Results Relationship between Control Stratem and Data Resolution Table 2 shows the delay performance of the DISCO control plans determined from aggregated but error-free information on three days: 11, 18,23, October 2001. The reported delays are the control plans’ simulated performances in the real traffic. The last column in Table 2 shows the delay performance of the control plans as determined with the original data at 20-s resolution. Theoretically, as full information is utilized, these control plans should give the best performance as compared with the

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Hong K. Lo and H.R Chow

control plans obtained with the aggregate information. In fact, this is the case, as shown in Table 2.

Total Delay (veh-hr) Plans

FGFC VGFC VGVC

Total Delay (veh-hr) FGFC Plans VGFC VGVC c) 23 October 2001

L

Total Delay (veh-hr) FGFC Plans VGFC VGVC

15 min 12.45 11.97 11.97

Data Resolution 5 min 1 min 12.00 12.42 12.75** 11.52 12.75** 11.42*

20-sec 10.74 10.11 10.11

15 min

Data Resolution 5 min 1 min

20-sec

8.96 8.68 8.68

9.45 9.3 1 9.36**

15 min

Data Resolution 5 min 1 min

12.28 12.55** 12.55**

12.91 12.19 12.19

8.90 8.77 8.77

12.74 12.15 12.15

8.59 8.21 8.21

20-sec 12.12 11.98 11.98

Comparing the results down each column in Table 2, for the same data resolution, with a few exceptions marked with "**", the dynamic VGFC and VGVC plans outperformed the FGFC plans. It is reasonable to expect that the higher flexibility associated with the dynamic plans can deliver better results. However, we reiterate that only a heuristic approach is used to search for solutions. In all of the computational experiments, DISCO was solved with the GA approach on a PIII-866 PC for 20 generations.


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The computational time per run amounted to around 6000' seconds. Within this computational time, it can happen that the GA algorithm finds a better performing FGFC plan. Comparing the performances between the VGFC and VGVC plans, the difference is found to be not substantial. Only in 1 out 12 scenarios (marked with "***in Table 2) did the VGVC plans outperform the VGFC plans. It appears that the VGFC strategy is sufficiently flexible to tackle the traffic. Comparing the performances of the different control strategies at different information resolutions, we observe that the dynamic plans worked best at the finest resolution. In fact, according to Table 2, in several instances marked with "**", when information was aggregated at the 5-min or 15-min resolutions, the performance of the dynamic plans such determined was worse than the FGFC plans. Apart from the heuristic solution procedure discussed above, this could be attributed to the dynamic plans over-adapting themselves to the imperfect information, which turned out to be quite different from the real traffic (see Figures 3 and 4). Moreover, Table 2 shows that the data resolution used and delay performance are not monotonically related. That is to say, the 1-min resolution does not necessarily outperform the 5-min resolution, which in turn does not necessarily outperform the 15-min resolution. In particular, the 5-min resolution in several instances produced the worst delay performance among the resolutions evaluated. The reasons behind this deserve more in-depth investigation and are beyond the limited computational experiments conducted within this study. Ignoring this anomaly for the moment, comparing the results of the 15-min resolution versus those of the 1-min resolution, there is no appreciable benefit for the FGFC plans by opting for the 1-min resolution. The dynamic VGFC and VGVC plans would benefit more with the 1-min resolution, up to a few percent; yet such benefit is not guaranteed - the dynamic plans performed slightly worse with the 1-min resolution for the scenario on October 18, 2001.

'

This long computational time is a result of using the GA approach indiscriminately. We have recently developed a hybrid approach by combing the gradient-based approach with the GA approach that reduces the solution time to 100's of seconds for a similar solution quality. The detail of this approach is beyond the scope here but will be reported in hture studies. In any case, the focus here is not on the speed of the algorithm, which can definitely be improved significantly in the near future.


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To gain further insight into the performance of the timing plans, we construct Figures 10 and 11. In each of these two figures, the occupancy results along Argyle Street over time are plotted. The legend on each figure shows the intensity of each shade - basically, darker shade; more traffic. Areas with heavy shades show where and when the congestion was heavy. Figure 10 (Figure 11) shows the effect of the VGFC timing plan determined with information at the 20s resolution (5-min resolution) for October 11,200 1. Table 2 shows a substantial difference in performance: 10.11 veh-hr for the 20s resolution versus 12.75 veh-hr for the Smin resolution. Figure 10 shows that the traffic on Argyle Street could proceed without much delay; the VGFC plan determined with information at 20s resolution allowed for good progression. On the contrary, as for the VGFC plan determined with information at 5 min resolution, Figure 11 shows that a queue was first formed at Junction 3 (Reclamation Street) - marked as A in Figure 11. The queue gradually spilled back to Junction 2 (Shanghai Street) - marked as B and eventually to Junction 1 (Portland Street) marked as C; traffic streams from these cross-streets were blocked, causing additional delays for the entire system. Table 3 confirms this

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Street Shangha

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Street

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0.1 1-2 2-3 3-4 4-5 5-6 6-7 7.8 I8-9 I 9-10 I 10-11 I 11 -12 I 12 13 I 13 - 14 I 14-15 I 15 16 I 16-17 I 17 18 I 18 19 I 19-20

-

time

Fig. 10 Simulation of the VGFC plan determined with information at 20s resolution

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Adaptive Trafic Control: Control Strategy ...

Portland

Street

-

1

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-

112-13 113-14 114-15 115-16 116-17 117.18

Fig. 11. Simulation of the VGFC plan determined with information at 5-min resolutions

Specific Segment Argyle Street Portland Street Shanghai Street Reclamation Street Total

Total Delay (veh-hr) Plan with info at 5min Plan with info at 20s 8.32 1.18 2.10 1.15 12.75

7.04 0.74 1.16 1.16 10.11

finding. Shanghai Street and Portland Street, as well as Argyle Street, all incurred substantially more delays for the VGFC plan determined with information at 5min resolution. The VGFC plans are shown in Table 4. At first glance, they do not differ greatly from each other; both share a similar cycle time. In fact, the plan determined with information at 5-min resolution allocated more green times for Argyle Street at Junctions 1 and 2. However, Table 3 shows that this strategy not only did not help Argyle Street, it hurt the cross streets. At Junction 3, the cross street Reclamation Street did

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Hong K.Lo and H.F: Chow

Table 4. The VGFC timing plans determined with information at 20s, 5-min resolutions

marginally better, but this was achieved with a substantial reduction in the green time for Argyle Street at the 4* and 7* cycle, which hurt Argyle Street (see Figure 11). This result shows that the coordination between junctions is important, in addition to the green allocations. The system needs information at a fine resolution to set up the coordination correctly. One may also notice that the VGFC plans determined with information at the 20-s resolution are rather steady (Table 4), in the sense that the green times are not changing substantially from cycle to cycle. A sizeable change in green time happens only once every few cycles. Although one cannot infer too much based on these alone, this pattern does appear to be similar to the store-forward and multi-band results as observed in other applications of DISCO (Lo, 2001). Figure 10 clearly shows the variable bandwidths for the first four cycles. But this can only be achieved with good information. Consider Junction 3 in Table 4 as an example, the better timing plan extended the green time for Argyle Street to 90s in the 4* cycle, whereas the timing plan determined with the coarser information shortened it to 58s in the same cycle, which initiated a queue as marked by “A” in Figure 11. To summarize, there are benefits to be gained with the dynamic plans, if information is available at least at 1-min resolution. Moreover, the VGFC strategy is sufficient. One gains very little by opting for the most flexible VGVC strategy. Nevertheless, to save computational and

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communication costs, even the FGFC plans determined at the 15-min resolution is a reasonable option. Relationshiu between Control Strategv and Prediction Accuracy Table 5 shows the performance of the FGFC timing plans determined with predictions with different error rates. Entries in columns 2 - 6 show the statistics obtained from 30 realizations of each of the different predictions, according to the procedure depicted in Figure 8. The timing plans, determined with different predictions, were all evaluated by simulating in the same set of real traffic. For brevity, we only determine and present the results for the FGFC plans only. One can draw similar conclusions for the VGFC and VGVC strategies given that the performance differences between the FGFC and dynamic plans (as shown in Table 2) are within only a few percent. Table 5 shows that the mean delays of all the plans determined with prediction errors are higher than the one determined with perfect information, as expected. Theoretically, the delay in the last column should be the best given that perfect information or forecast is used. Nevertheless, the minimum delay achieved within each error rate (in the last row) was lower than 8.59 veh-hr. This indicates the limitation of the solution heuristic in association with the nature o f the problem. Even with perfect information, the solution found was only a local minimum. Table 5. Performance of the FGFC plans determined with predictions Total Delay (Veh-hr)

Std Dev

Plans determined with predictions with error rate Plan determined with perfect +lo% info 0% +5% -10% -5% 8.59 9.22 9.15 9.00 9.37 9.18 1.34 14.30 8.01

0.88 11.76 8.08

0.57 10.94 7.99

0.50 10.23 8.24

0.78 12.15 8.14

Another consistent trend observed in Table 5 is that plans determined with overestimated predictions (+5%; +lo%) on average outperformed plans determined with the corresponding underestimated predictions (-%;

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-10%). Using overestimated predictions, the timing plans such determined typically have longer cycle times and longer green times, as compared with plans determined with underestimated predictions. With the arrivals not perfectly forecasted, these extra green times and cycle times provide a buffer to hedge against the occurrence of overflow. Of course, these extra green times must be prudently determined, as they are not filly utilized all the time, causing some delay to the competing approaches. Elsewhere in Lo (2002), we showed that these green buffers, if appropriately determined, could lead to lower average delays. On the other hand, the result here reflects that it is detrimental to set the buffer to be too large. When the error is set at +lo%, Table 5 shows that its performance is worse than plans with the +5% error. The standard deviation of the delay performance of overestimated predictions is also smaller than that of underestimated predictions. The reason can again be attributed to the creation of green buffers with overestimated predictions, which reduces the chance of overflow. The occurrence of an overflow triggers a vicious cycle that leads to further overflows. Therefore, the total delay differs sharply in the presence or absence of an overflow. For underestimated predictions, the lack of green buffers increases the chance of overflow, leading to a higher variability in delay performance. In the event when the real traffic is actually low, the timing plans determined with underestimated predictions (with shorter cycle and green times) would result in lower delays. However, if the opposite occurs, the timing plans would not be able to clear the traffic, leading to substantial increases in overflow delays. Without the protection of a green buffer, it is expected that the performance of the timing plan will be subject to larger variations. In summary, overestimated predictions, if prudently chosen, can lead to both lower mean delays and tighter performance variations. In this sense, this prediction error can be put to use as an advantage. Nevertheless, as contended in Lo (2002), we reiterate the importance of striking a good balance in this overestimation, and that such results are only substantiated for the control strategy determined with DISCO. Relationship between Control Stratep. Data Resolution. and Prediction Accuracy Table 6 shows the numerical results. Each case represents the summary statistics for 30 realizations, following the procedures in Figure

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9. Overall, the control plans determined with information at the finest resolution of 1 minute performed the best, for each of the FGFC, VGFC, and VGVC strategies, in spite of a substantially larger prediction error of *lo%. Table 6. Performance of different control plans determined with different prec tions Total Delay (veh-hr; Mean Std Dev Max Min

Control Plans FGFC VGFC VGVC I-min predictions with + 10% error

Mean Std Dev Max

Min

-min predictions with -10% error

9.23

9.02

9.03

9.37

9.85

9.94

0.78

0.67

0.69

1.34

1.63

1.68

12.15

10.43

10.43

14.3

13.94

14.4

8.14

7.88

7.88

8.01

7.81

7.8 1

5-min predictions with +5% errors

Mean Std Dev Ma Min

Control Plans FGFC VGFC VGVC

5-min predictions with -5% errors

10.72

10.37

10.38

10.87

10.6 1

10.62

1.25

1.81

1.8

2.16

2.54

2.54

14.24

15.08

15.08

19.2

18.98

18.98

8.05 8.3 8.3 15-minpredictions with +2.5%

8.4 8.05 8.05 15-min predictions with -2.5%

errors

errors

11.65

11.32

11.36

11.79

11.38

11.43

3.24

3.27

3.25

2.99

3.07

2.98

23.76

23.76

23.76

23.14

23.47

23.47

8.28

8.33

8.33

8.56

8.55

8.57

Similarly, the control plans determined with information at the Smin resolution outperformed the ones determined with information at the 15min resolution. This trend indicates that the effect of resolution outweighs its associated effect of prediction error. The results also echo the trend observed in Section 4.2, namely, overestimated predictions produce better results or lower total delays than underestimated predictions. This is true for all types of control plans, FGFC, VGFC, and VGVC, and under all the error rates studied. Though most of the differences are bounded by a few percent, there are cases


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wherein the difference is substantial. For example, in the case of the VGVC plan at 1-min resolution, the delay changed from 9.94 veh-hr (associated with the prediction error of -10%) to 9.03 veh-hr (associated with the prediction error of + 1O%), or a 9% difference. Examining the performance standard deviations in Table 6, in general, those obtained with +lo% errors are smaller than those obtained with -10% errors. The same can be said about the case of +5% errors versus -5% errors. This can be attributed to the creation of sufficiently large green buffers that reduced the chance of overflow, as explained earlier. When the green buffers are not sufficiently established with lower overestimations, as in the case of +2.5% errors, the benefit of small standard deviations is absent. In fact, Table 6 shows that the performance standard deviations of the +2.5% errors were slightly larger than those of the -2.5% errors. This could be due to that the short green buffers thus created were not big enough to reduce the occurrence of overflow. Comparing the control plans, under almost all the error rateshesolutions studied , the dynamic (VGFC or VGVC) plans outperformed the FGFC plans, whereas the difference among the VGFC and VGVC plans was not substantial. In fact, in a number of scenarios, Table 6 shows that the VGFC plans performed slightly better than the VGVC plans. Although theoretically the VGVC plans are more flexible than the VGFC plans, in the presence of prediction errors, it appears that over-adapting the control plans to the imperfect information may actually hurt. Finally, Table 7 shows the performance degradations for each control strategy as a result of using imperfect predictions. These degradations are determined as the following. First, we find the best control plan for each control strategy (FGFC, VGFC, VGVC) assuming perfect forecasts at the finest resolution are available. The “ideal” delays of these best plans then form the base of determining the degradations. Table 7 shows the percentage difference of the actual delays, as a result of using imperfect predictions, as compared with the ideal delays. The results reiterate the same trends. The system would degrade substantially by using coarse predictions. More flexible control strategies would degrade more with coarse predictions. Overestimated predictions tend to produce smaller degradations as compared with underestimated predictions.

’

* The only exception is when the information underestimatesthe traffic by -10%.

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Table 7. Performance comparisons between the control plans determined with different predictions % delay increase as compared Control Plans with the "best" Ian 9.9% 10.0% 7.4% fo @ 1-min, +10% error 26.4% 26.5% 24.8% fo @5-min, +5% error fo ls-min, +2.5% error 35.7%

I

I

E , fo @ 1-min, - 10% error fo @5-min, -5% error

9.1% 26.6% 37.3%

20.1% 29.3% 38.7%

2 1.2% 29.4% 39.3%

Concluding Remarks In this paper, we engaged a recently developed dynamic signal control model, DISCO, to investigate the relationship between Control strategy, data Resolution, and prediction Accuracy (or the CRA relationship), which is crucial to the development of adaptive traffic control systems. Based on the results of this extensive simulation study, these trends emerge: The system would benefit more if predictions were produced at fine resolutions, such as 1 minute. The system is more sensitive to data resolution than prediction errors. The system would benefit more from predictions of 1-min resolution, 10% random errors than from predictions of 15-min resolution, 2.5% random errors. Overestimated predictions lead to lower delays as compared with underestimated predictions. However, the extent of this overestimation for improved performance needs to be prudently traded and needs further study. 0 The dynamic plans (VGFC or VGVC) perform better than the static plans (FGFC) for a good range of resolutions and error levels. 0 In the presence of prediction errors, the most flexible VGVC plans are not as effective as the less flexible VGFC plans. This may be attributed to the VGVC plans over-adapting

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themselves to the imperfect information. As the VGFC plans are also easier to calculate than the VGVC plans, VGFC seems to be a well-balanced strategy for adaptive traffic control systems.

Acknowledgement This research is sponsored by the Hong Kong Research Grant Council's direct allocation grant RGC-DAG97/98.EG03 and Competitive Earmarked Research Grant HKUST6105/99E and Sino Software Research Institute Awards, SSRI98/99.EG02 and SSRI99/00.EG02. We are gratehl for the helphl and constructive comments of the two anonymous referees.

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