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Transportation Engineering

KSCE Journal of Civil Engineering Vol. 12, No. 2/March 2008/pp. 129~140 DOI: 10.1007/s12205-008-0129-6

Online Implementation of DynaMIT: A Prototype Traffic Estimation and Prediction Program By Byungkyu (Brian) Park*, Joyoung Lee**, Devi M. Pampati***, and Brian L. Smith**** ···································································································································································································································

Abstract This paper presents a pilot study of conducting an online implementation of DynaMIT, one of traffic estimation and prediction (TrEP) programs developed by an MIT research team with the support from the U.S. Federal Highway Administration, in Hampton Roads, VA, U.S.A. As a first step, a test-bed network was coded and DynaMIT’s supply and demand parameters were calibrated before evaluating the performance of the online implementation of DynaMIT. Based on the online implementation of DynaMIT for three days, it was found that DynaMIT showed fairly good performance on the estimation and prediction of the sensor counts with the root mean square normalized (RMSN) error ranges between 0.15 and 0.25 for estimations, and 0.25 and 0.4 for predictions. Even though speed and travel times showed some discrepancies, further investigations indicated that the performance of DynaMIT can be significantly improved with adequately calibrated supply parameters. Keywords: TrEP, DynaMIT, calibration, estimation, prediction, online implementation ···································································································································································································································

1. Introduction In order to manage the increasing demands placed on the surface transportation system, intelligent transportation systems (ITS) are being deployed to improve the efficiency, safety, and predictability of travel. A significant limitation of current ITS deployments is that they operate in a reactive mode. It is widely believed that a predictive capability must be developed in order to fully realize the promise of ITS. The Federal Highway Administration (FHWA) recognized this and initiated the traffic estimation and prediction (TrEP) program in 1994. TrEP programs provide predictive traffic information to ITS sub-systems to help generate proactive, network-wide, coordinated guidance and control strategies. They also generate travel information for pre-trip planning (i.e., travel mode, departure time, and route) and other traffic information and guidance to travelers for en-route diversion. To date, two DTA systems have been developed in the FHWA program, DYNASMART by the University of Texas (Mahmassani et al., 1994), and DynaMIT by the Massachusetts Institute of Technology (Ben-Akiva et al., 1995). In recent years, two remarkable tests on DTA have been successfully performed on a test-bed network in Irvine, CA by

DYNASMART-X of the University of Maryland (Mahmassani et al., 2004) and DynaMIT (Antoniou, 2004). TrEP programs integrate a detailed network traffic model with models of traveler behavior. Through combining information from historical databases with real-time inputs from field installations (e.g., surveillance data and control logic of traffic signals, ramp meters, toll booths, etc.), TrEP programs generate estimates of future traffic conditions. Before proceeding with wide-scale field implementation of TrEP programs, it is necessary to conduct a pilot study to assess its performance of predicting traffic conditions. The purpose of this paper is to implement such a pilot study that implements DynaMIT, one of two TrEP programs, in Hampton Roads, VA, identifies such potential challenges as DynaMIT is not able to consider physical constraints of link capacity during OD estimation process because of the fixed assignment matrix and addresses ad hoc solutions to such challenges. In addition, the performance of DynaMIT’s prediction capability was evaluated using traffic sensor counts, speed, and field measured travel times. The remainder of this paper discusses the study network, calibration of DynaMIT, and field evaluation results.

*Assistant Prof., Dept. of Civil and Environmental Engineering, Univ. of Virginia, Charlottesville, VA 22904, USA (Corresponding Author, E-mail: [email protected]) **Graduate Research Assistant, Dept. of Civil and Environmental Engineering, Univ. of Virginia, Charlottesville, VA 22904, USA (E-mail: [email protected]) ***Data Analyst/Project Manager, Deccan International, Salinas, CA 93901, USA (E-mail: [email protected]) ****Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Virginia, Charlottesville, VA 22904, USA (E-mail: [email protected]) Vol. 12, No. 2 / March 2008

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Byungkyu (Brian) Park, Joyoung Lee, Devi M. Pampati, and Brian L. Smith

2. The DynaMIT and Study Network DynaMIT, in which stands for Dynamic Network Assignment for the Management of Information to Travelers, is a simulation based system, which integrates a detailed network traffic model with models of traveler behavior. DynaMIT has two main functions: state estimation and prediction based guidance generation. State estimation provides information about the current state of network in terms of current segment based flows, queues, speeds, densities and OD flows. Prediction-based guidance depends on the expected future traffic conditions, which depend on the drivers’ route choice decisions, which in turn depends on the guidance provided to the drivers (Balakrishna, 2002). As shown in Fig. 1, the pilot study network composed of three freeways segments: I-64 between Bay Avenue and the Virginia Beach - Chesapeake City Limits, I-564 between Terminal Boulevard and I-64, and I-264 between Broad Creek and Rosemont Road. This 19-mile segment contains 12 interchanges. In order to provide an alternative route to the travelers, the network has been extended. Hence, the original study network, which mainly

comprised of three freeway sections, mentioned above, has been extended by the adding entire I-664 and I-64 segments, which forms the outer loop. In addition, reversible high occupancy vehicle (RHOV) freeway mainline is coded as bi-directional such that the network can handle for both morning and afternoon peak periods.

3. DynaMIT Calibration 3.1 Supply Parameter Calibration A general procedure of supply parameter calibration includes segment classification, determination of key parameters (i.e., capacity, free flow speed (FFS) and maximum density under FFS) and curve fittings. Segments of the network were classified into several groups based on corridors and roadway geometric characteristics and number of lanes. Roadway geometric characteristics included basic freeway section, merging roadway, diverging roadway, weaving roadway and ramps (Park et al., 2004). The capacities of each segment groups were determined from (i) speed-flow plots where double loop detector data are available and/or (ii) the Highway Capacity Manual (TRB, 2000). Free flow speed of each group was also determined on the basis of field data and the HCM. Maximum densities under free flow conditions were determined using the HCM level of services A and B densities. While speeds and flows are relatively accurate as they are directly measured from double loop detectors, densities could be less reliable mainly because they are estimated from occupancies. Thus, instead of calibrating a speed-density function, flow-speed function was calibrated. It is noted that the calibrated parameters under speed-density function and flowspeed function should be identical. The speed-density function was converted into a flow-speed function as shown below. q = qobv , u = uf

if qobv/uobv d k0

q = uobv ^ kjam > 1 – uobv e u f 1 / D @ 1 / E + k0 `

if qobv/uobv > k0

Where, qobv uobv q u uf k0 DE

(1)

: Field flow (vph) : Field speed (kph) : Estimated flow(vph) : Estimated speed(kph) : Free flow speed(kph) : Free flow speed density(veh/km/lane) : Parameters

Table 1 shows the final version of estimated parameters for selected groups. 3.2 Demand Calibration

Fig. 1. Snapshot of Hampton Roads Network for DynaMIT and Its Detailed Snapshot at an Interchange

3.2.1 Initial OD Estimation A double-constrained gravity model was used to obtain the initial OD matrix. The principle of this model was that the gross domestic imports and exports of a given commodity for all states are equal. When applied in traffic OD flow estimations, this

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KSCE Journal of Civil Engineering

Online Implementation of DynaMIT: A Prototype Traffic Estimation and Prediction Program Table 1. Hampton Roads Supply Parameters uf

D

E

k0

kjam

2 lane basic freeway

65

1.176

0.555

15

210

3 and 3+ lane basic freeway

70

1.383

0.651

15

210

2 lane merging area

65

1.102

0.543

15

210

3 and 3+ lane merging area

68

1.443

0.698

15

210

Segment Type

2 lane diverging area

63

1.111

0.54

15

210

3 ,3+ lane diverging area (I-64, I-564)

65

1.350

0.689

15

210

3 ,3+ lane diverging area (I-264)

60

1.475

0.796

15

210

Weaving area (I-64 and I-564)

65

1.62

0.755

15

210

Weaving area (I-264)

60

1.577

0.764

15

210

Ramp

50

1.81

1.53

15

150

model can make the total attraction trips equal to the total production trips for all zones. As the Hampton Roads network is a well-bounded freeway system in which all on ramps are considered as origins and off ramps as destinations, the total trips entering and exiting the freeway system should be close to equality. Hence, the double-constrained gravity model was chosen for estimating the initial OD matrix from the station data (Park et al., 2004). 3.2.2 Historical OD Estimation Three normal days in 2004 were used for demand calibration. Demand calibration process of DynaMIT involved the estimation of both historical OD flows and a Varcov (i.e., variance-covariance) matrix. The Varcov matrix represents the reliability of both traffic sensor counts and OD flows (Balakrishna, 2002). However, as the relative importance of traffic sensor and OD pair demands is unknown, demand calibration process needs to make an assumption. It was decided that relatively higher weights (i.e., Varcov values) were assigned to the OD pairs having low counts, while proportional weights (e.g., 1:1, 1:10 or 10:1) were given to both sensor counts and OD flows with higher counts. One of reasons that relatively higher weights were given to the OD pairs with low counts was to prevent OD flows with low counts being overadjusted. This obviously ensures that OD flows with high counts are being adjusted to match sensor counts. Once OD flows show an indication of convergence and no significant changes in error estimates, the estimated OD flows can be considered as historical OD. The following steps summarize the procedure followed in the demand calibration process. • Step 1: DynaMIT was run with traffic counts from a normal day using the initial OD matrix obtained from the gravity model • Step 2: By replacing the initial OD with the OD obtained at the end of Step 1, DynaMIT was run for the second day • Step 3: Using the new OD matrix at the end of Step 2, DynaMIT was again run with the first and second days by following the same procedure as in the Steps 1 and 2. An updated OD was obtained. Vol. 12, No. 2 / March 2008

• Step 4: Using the updated OD matrix obtained at the end of Step 3, DynaMIT is run for the third day. 3.2.3 OD Estimation Challenges and Ad Hoc Solutions During the historical OD estimation and online implementation (in which also estimates OD) it was observed that a severe congestion continuously occurred. Through an extensive investigation, it was found that this congestion came from the result of OD estimation. One of inherent issues in the current DynaMIT OD estimation method is that an optimization uses fixed assignment matrix that is obtained from an existing OD matrix. As such, when a new OD matrix is updated on the basis of the fixed assignment matrix and sensor counts, the new assignment matrix from newly updated OD matrix often show significant discrepancies with the fixed assignment matrix. This often results in unrealistic OD flows that exceed some link flow capacities. As evidenced in Table 2, in which shows a total OD flows to a destination node by hour from 2 PM to 6 PM, two of the newly estimated OD flows exceeded destination link capacity. When DynaMIT simulates the newly estimated OD flows to estimate sensor counts, congestion occurs near the destination link and it is propagated to other segments resulting in huge discrepancies on certain segments. Obviously, this was due to the use of an assignment matrix in which dose not consider physical link capacity constraints. An ad-hoc solution to this issue was to increase Varcov values (i.e., weights) associated with those OD pairs. This ensured OD flows of such OD pairs were not changed

131

Table 2. Total OD Flow to a Destination Node Period

Initial OD

Estimated OD

Segment Capacity

14:00~15:00

1258

2752

2350

15:00~16:00

1869

3140

2350

16:00~17:00

1754

1922

2350

17:00~18:00

1668

2203

2350

18:00~19:00

1469

2048

2350


too much. However, during online implementations adjusting Varcov weights is not feasible due to time constraints. Thus, an ad-hoc solution that simply simulates DynaMIT with a newly estimated OD, evaluates its performance, and determines whether to accept a newly estimated OD or retain historical OD, was implemented. Ideally, this challenge should be addressed by considering link capacity during OD estimation. Another challenge with the Varcov was updating it in real-time to reflect the reliability and/or the data quality of the traffic

sensor counts. At this point there are no good set of rules for such an update. Therefore, an ad-hoc solution adopted for this challenge was to maintain an initial Varcov that was used at the start of the calibration process. As such, the higher weights (weight of 10) on a scale of 1 to 10 were given for OD pairs with low OD flows. This has resolved the challenge of updating Varcov. In addition, the data quality of traffic sensor counts was applied to Varcov value as a multiplier. For example, a data quality of 0.8 (indicating 80% of sensor data passed screening test) can be multiplied to the Varcov value associated to that station. 3.3 Estimated OD With the challenges and ad hoc solutions discussed above, OD estimation procedure was implemented. As shown in Fig. 2, the estimated ODs were converged after the second day iteration. As the entire OD matrix for 24 hour periods were converged, the OD estimation was considered to be completed. In addition to the hourly total OD flow comparisons, correlation between observed and estimated sensor counts was calculated. Higher correlation values indicate better matches between observed and simulated sensor counts. It is noted that only sensor counts with data quality of 50% or above were used in the comparisons and correlation calculations. As shown in Fig. 3, correlation coefficients of both day 1 and day 2 are well above 0.92 indicating that the estimated OD matrix is acceptable.

Fig. 3. Comparisons between Observed and Simulated Counts

Fig. 2. Hourly OD Flow Variation by Each Run (for 24 hrs) 132


Online Implementation of DynaMIT: A Prototype Traffic Estimation and Prediction Program

4. Online Evaluation 4.1 Online Evaluation Methodology Online evaluation was conducted for almost three days from June 15 to 17, 2005. All required data for the online evaluation were provided in real-time by various sources such as detectors, CCTV cameras, and operators who insert incident information into the database. In addition to these real time data, online evaluation needs to predict origin-destination (OD) demand that is often based on time series modeling. An extensive research conducted by Park et al. (2004) on this test-bed network indicated that the use of autoregressive moving average model produced severe fluctuations in OD flows and recommended not to use time series based model. Thus, this online evaluation was conducted by using the most recent updated OD demands instead of the one updated by the timer series model. In the previous studies, the primary performance measure used for assessing the accuracy of DynaMIT’s estimation and pre-

diction capabilities was traffic counts. However, it is generally understood that traffic counts are not sensitive, especially in distinguishing congestion levels. For example, different speeds can be observed while same number of vehicles is processed at a given segment. Thus, this study considers speed and travel times in addition to traffic counts. Speed data was obtained from double-loop stations, and travel times were collected using a probe vehicle that was being operated for the first 2 days on a few selected key routes. During the online evaluation runs, several incidents were observed from the incident management subsystem. Only the major incidents which led to lane closures (i.e., significant reduction in capacity) were considered. 4.2 Online Evaluation Results 4.2.1 Comparison of Estimated Traffic Counts Fig. 4 shows the plots of variation of root mean square

Fig. 4. RMSN Errors of Estimated Traffic Counts foR Three Days (5 minute interval) Vol. 12, No. 2 / March 2008

133


normalized (RMSN) errors observed in the estimation of traffic counts by time of day for each of the three days. The first observation that can be made from these plots is that the range of RMSN error values excluding the spikes are comparable to those observed during the calibration process and does not vary significantly by different time of day. Furthermore, the range of RMSN errors is similar for all three days indicating that the historical OD obtained from the calibration is adequate for normal weekdays. It is noted that the spikes in the RMSN errors for all three days came from the fact that the DynaMIT version used in this online evaluation did not correctly consider unfinished trips when DynaMIT restarts. As shown in Fig. 5, the comparison of both estimated and actual traffic counts under incident conditions was conducted at each individual station where an incident was reported. The dotted boxes shown in Fig. 5 highlight the comparison between estimated and observed traffic counts during incident

periods. In general, estimated traffic counts during incident periods were as good as those estimated during non-incident periods. Among these three incidents, the incident occurred near the station 195 was the most severe one. Consequently, it is likely to make an error in the estimation of incident input parameters such as start and end times of incident, incident location, and incident capacity reduction factor. Thus discrepancies shown at the beginning or even before the incident start time could be due to inaccurate information on such incident parameter. However, the other two incidents near stations 147 and 21 were relatively minor in terms of duration and severity. As expected, the DynaMIT’s estimated traffic counts matched quite well with observed traffic counts for relatively minor incident cases. Based on these results, it can be concluded that DynaMIT’s traffic count estimation capability under incident condition is acceptable. 4.2.2 Comparison of Predicted Traffic Counts Fig. 6 shows the RMSN errors of the predicted traffic counts

Fig. 5. Comparison of Estimated and Actual Traffic Counts during Incidents 134



Fig. 6. RMSN Errors of Predicted Traffic Counts for Three Days (30 min intervals)

from DynaMIT for three days. From these plots, it can be observed that the errors in predicted counts are higher than those of estimated counts. Since the prediction interval used for the online evaluation was 30 minutes, the output of the traffic counts from DynaMIT as well as observed traffic counts were aggregated into 30 minute intervals. As such, the RMSN errors were calculated for 30 minute intervals. From these plots shown in Fig. 6, it can be observed that the errors in predicted counts are higher than those of estimated counts. The results are a bit worse than what was observed during the off-line evaluations (Park et al., 2004). In addition, the predicted and actual counts from those stations where incidents were occurred are plotted in Fig. 7. It is noted that the accuracy of predicted results was not as good as that of Vol. 12, No. 2 / March 2008

estimated results. One interesting observation is that the predicted counts at station 147 were very low compared to actual counts, while estimated counts at the same station showed fairly good matches. On the contrary, prediction results at station 21 are quite promising. They were better than those of estimation results. As such, the results of estimations and predictions under incident conditions were not consistent. This could be, in part, due to a lack of knowledge in incident condition (i.e., exact location, starting and ending time, and capacity reduction factor), errors in predicted OD flows, and/or inaccurate supply parameters. However, it appears that no method can pin point the cause of such discrepancies.

135


Fig. 7. Comparison of Predicted Traffic Counts during Incidents

4.2.3 Comparison of Speeds Since the estimated speeds from single-loop stations were not accurate, it was decided to use speed data obtained from doubleloop stations with 50% or better data quality. Plots shown in Fig. 8 provide comparison results for day 2 at a few selected stations. At station 56, most of time DynaMIT’s estimated speeds match well with those of actual speeds. However, for a few time periods, there exist some discrepancies. Interestingly, both underestimation and overestimation were observed. Similar conditions were observed at station 71. Given that plots shown on these stations were normal and uncongested conditions, it can be concluded that DynaMIT can estimate speeds pretty well for those conditions. The estimated and actual speed plots at station 91, representing normal congested conditions, exhibit discrepancies. In addition,

although actual speeds never dropped below 20 mph, DynaMIT’s estimated speeds dropped to 10 mph, the minimum speed given in the supply parameter. Given that there was no incident near this station and traffic counts between actual and estimated were similar, the discrepancies were likely caused due to inaccurate supply parameters (i.e., speed-density relationship). Thus, these discrepancies can be improved by adjusting supply parameters as long as actual traffic data are available. However, as noted earlier, one of the challenges in the supply parameter estimation was lack of available actual data. The comparison result at station 195 is of interest. As shown in Figs. 5 and 7, traffic counts during the incident period were fairly accurate. However, the estimated and observed speed measurements showed significant discrepancies. This certainly indicates that traffic counts may not be a sensitive measure especially for

136



Fig. 8. Comparison Plots of Estimated Speeds vs. Actual Speeds

uncongested conditions. This could be, in part, due to the use of an inaccurate incident capacity reduction factor. Previous research proved that DynaMIT can adequately estimate and predict incident conditions as long as accurate incident related information is used in the evaluation (Park and Cao, 2005). Vol. 12, No. 2 / March 2008

4.2.4 Comparison of Estimated Travel Times DynaMIT’s estimated travel times and field measured travel times matched quite well except for a few segments. Fig. 9 shows comparison results of two selected routes representing both normal (i.e., uncongested) and congested conditions. These

137


Fig. 9. Comparison Results : Estimated Travel Times between DynaMIT and Field

results came from an individual simulation run and other runs showed similar results. Further investigation indicates that the segments where travel times matched well were mostly free flow conditions as shown on westbound AM off period in Fig. 9(a), while the segments showing discrepancies were experienced congestions as shown on eastbound (I-264 to I-64) AM peak in Fig. 9(b). Given that traffic sensor counts matched quite well, it seems that these discrepancies were in part due to inadequate supply parameters. Further calibration on supply parameters could have improved DynaMIT’s travel time estimation capabilities. 4.2.5 Comparison of Predicted Travel Times As shown in Tables 3, a total of sixteen OD pairs were used for

predicted travel time comparisons. As traffic on eastbound in the morning peak is not usually congested, the predicted travel times match very well. However, predicted travel times during PM peak showed discrepancies. This also suggests that predicted travel times become less accurate during congested conditions. It is noted that both congested and normal (i.e., uncongested) conditions, traffic counts matched reasonably well. It is believed that better calibration of supply parameters with actual traffic data could help improve prediction capability of the DynaMIT program. 4.3 Diagnosis of Discrepancies and Supply Parameter Adjustment In general, three possible factors can contribute discrepancies

138


Online Implementation of DynaMIT: A Prototype Traffic Estimation and Prediction Program Table 3. Comparison of Actual and Predicted Travel Times (I-64 to I-264)

HR Bridge Tunnel

N. Hampton Blvd.

Witchduck Road

Independ. Blvd

Rosemont

AM Peak

Observed

19:25

21:07

22:02

24:14

Predicted

17:26

19:06

20:26

23:02

PM Peak

Observed

23:34

27:24

28:46

29:41

Predicted

19:26

21:08

22:35

25:25

AM Peak

Observed

8:24

9:06

10:01

12:13

Predicted

8:12

9:49

11:14

13:57

PM Peak

Observed

12:02

15:52

17:14

19:09

Predicted

9:16

11:08

12:41

15:29

AM Peak

Observed

7:23

8:05

9:00

11:12

Predicted

7:07

8:44

10:09

12:52

PM Peak

Observed

11:10

15:00

16:22

18:17

Predicted

8:11

9:53

11:25

14:11

AM Peak

Observed

3:39

4:22

5:17

7:29

Predicted

3:06

4:45

6:10

8:01

PM Peak

Observed

5:39

9:29

10:51

12:46

Predicted

3:43

5:24

6:52

9:40

Tidewater Dr.

Chesapeake Blvd.

Newton Road

Fig. 10. Adjustment of Supply Parameters

in DynaMIT output. They are OD flows, path finding algorithm, and supply parameters. Assume a single segment is considered. If traffic counts match quite well (i.e., estimated OD flows are good), it is likely that travel time (or speed) discrepancy was due to supply parameters. This is because path selection would not have much effect on travel times over a single segment. However, when key routes, instead of single segment, are considered, all three factors could contribute to discrepancies. In the case of the Hampton Roads network used in this study, path finding algorithm can be ruled out as the network does not provide viable alternative routes. Given that most of sensor counts provided good matches, the discrepancies in travel times were likely due to supply parameters. An experiment that supports the adjustment of supply parameters can significantly improve DynaMIT’s estimation and prediction capability was performed. Although the adjusted supply Vol. 12, No. 2 / March 2008

parameters should be verified with field data, if data becomes available, the adjustments were made within a reasonable boundary. Fig. 10 shows the estimated travel times on a small corridor with three consecutive segments in which are consisted of a diverging segment (ID: 59) and two basic mainline segments (ID: 171 and 64). The estimated travel times obtained from supply parameters that are calibrated by aggregated groups (labeled as Estimated supply parameters) show significant discrepancies, while travel times from adjusted supply parameters were close to those from field measured. The results imply that adequately calibrated supply parameters would improve the estimation and prediction of DynaMIT.

5. Conclusions and Recommendations

139

This study conducted an online implementation of DynaMIT


in Hampton Roads, VA. During the online implementation, several challenges were encountered especially for OD estimations. The proposed ad-hoc solutions were found to be effective to such challenges. DynaMIT showed good performance with the RMSN errors of between 0.15 and 0.25 in the estimation of traffic sensor counts, while those of predicted traffic sensor counts ranged from 0.25 to 0.4. These errors were fairly consistent regardless of network congestion levels. The performance of traffic counts estimation during incidents was as good as those shown during normal conditions, except for a case with sever incident condition where the estimation of incident parameters could not be done accurately. As such, it is concluded that DynaMIT can adequately model incident conditions as long as incident parameters are properly determined. When speeds and travel times were used in the evaluation of DynaMIT’s estimation and prediction capabilities during online evaluation, it was observed that both estimation and prediction show some discrepancies during congested conditions even though traffic counts matched quite well. This clearly indicates that the traffic count is not a very sensitive measure in the evaluation of DynaMIT’s estimation and prediction capabilities. In addition, it suggests that supply parameters may not be optimal for all the segments. Obviously, this was not a limitation of DynaMIT, but it is due to lack of actual field traffic data. As traffic data is not available for each segment of the network, supply parameters of those segments were obtained from similar segments. Based on the results of the online evaluation of DynaMIT in Hampton Roads, the following recommendations were made: • Performance of the DynaMIT’s estimation and prediction capability should be evaluated using speed and/or travel times instead of traffic sensor counts. • DynaMIT’s OD estimation module should consider the physical capacity of exit link. In addition, better guidelines on how to initialize/update the Varcov weights should be

developed. • Supply parameters of each segment should be carefully calibrated with actual traffic data, if possible. If such parameters were approximated with the HCM or those of similar segments, the results should be used with caution. • Implementation of time-variant parameter estimation, if possible, especially vehicle mix and/or weather conditions significantly changes over time.

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