} Summation Transfer
7.2 Recommendations
7.2.1 Recommendation for Neural-Kalman filter
The numerical analyses indicated the potential of the NKF in estimating dynamic O-D travel time and flow. The NKF especially showed its capabilities in describing non-linearity of dynamic O-D flows. However, the results found here should not be over-estimated. This study mainly focused on the development of the new model for estimating dynamic O-D travel time and flow on a long freeway. The numerical analyses demonstrated in this study may not be sufficient to fully investigate the new model. Also, the NKF tends to estimate dynamic O-D travel time and flow with some sensitive fluctuations especially when traffic conditions drastically change. They sometimes made the RMS errors by the NKF higher than those from the RKF. Sensitivity of the NKF are mainly caused by:
• Parameter tuning problems of an ANN model.
141
• Insufficient traffic data for training ANN models, which cover extensive traffic situations
It was found that three parameters of the ANN model, θj,θk and u0. were quite sensitive to the estimates of O-D travel time and flow. They should be carefully adjusted on a trial and error basis through many experiments of the calibration process.
If traffic conditions on freeways were not predicted in advance, even the NKF models brought sensitive fluctuations as shown in a numerical analysis in Chapter V. However, the advance predictions helped to reduce the sensitive estimates for any case. This implies that ANN models require training data sets to cover extensive traffic situations to yield more accurate estimates of dynamic O-D travel time and flow.
The number of time steps m in Eqs. 3.28 and 3.29 is also an important parameter, which denotes how many time steps the state variables should be considered in a Kalman filter model. The numerical analyses used the fix values for m such as three or five. However, the parameter should be also carefully adjusted depending on the travel times and traffic conditions on long freeways. It should be numerically investigated how many previous time steps are influential for the current state variables.
As mentioned above, ANN models require large field data sets to identify the satisfactory connection weights. However, it is extremely difficult to collect such numerous data from real world. The traffic data used in this study are coming from virtual assumptions and a simulation software package for both free flow and congested situations. Also, the freeway network is still small from actual implementation. More field data sets, which cover various traffic situations, should be used to fully train the ANN models. Further research should be directed to investigate the capability of the NKF for real congested situations on large road networks.
7.2.2 Another approach for O-D travel time and flow estimations
(a) Use of probe vehicles or AVI (Automatic Vehicle Identification) camera
Probe vehicles and AVI cameras are useful techniques to directly measure the O-D travel time and flow. In these techniques, however, the variables are measured at the "end" of the trips.
What the drivers want to know is the expected O-D travel time and flow at the "beginning" of their trips. Even if the probe vehicles or AVI cameras measure those variables, they are already "old" information for the drivers, which depart their origins because traffic conditions dynamically change in real-time. This difference between the "measured" and "expected" O-D travel time / flow is significant when the freeway is long. The actual O-D travel time and flow measured by probe vehicles or AVI cameras can be used as the data to update some parameters of NKF in real-time. As introduced in Chapter II, the ADVANCE project developed by Dillenburg et al. (1995) uses up to 3,000 probe vehicles for the direct measurement of actual O-D travel times. The actual measurement data may be quite efficient for more accurate O-D travel time estimations.
(b) Application of dynamic traffic states estimation models
DYNASMART-X (The University of Texas at Austin, 2000) and PARAMICS (Quadstone Limited, 2000) introduced in the literature survey, have the system to predict the traffic conditions some time steps ahead, and then estimate O-D travel times. This system is preferable to estimate and update the O-D travel times because the travel time estimates are based on accurate prediction of traffic states.
Nakatsuji et al. (1995; 1997) have used Kalman filter and NKF techniques for estimating dynamic traffic states on freeways. Since state and measurement equations are clearly defined in analytical equations by macroscopic model (Papageorgiou et al., 1989), traffic states such as link density and space mean speed can be estimated with more accuracy.
As shown in Figure 2.3, O-D travel time is computed by summing up link travel times along the O-D pairs. Link travel time is solely the function of link length and space mean speed.
Therefore, the application of the traffic states estimation technique will lead to another method of estimating O-D travel time and flow. Since this method allows Kalman filter or NKF to be formulated by explicit and analytical state / measurement equations, better estimates of O-D travel time and flow may be expected.
Some interview surveys (e.g. Kyattak et al.; 1996 and Ben-Akiva et al., 1991) have revealed that drivers need frequently updated travel time information for their route choice behavior.
The Kalman filter technique fully meets this requirement, and has the ability of estimating and updating the travel time in real-time. Further studies should be addressed to develop more sophisticated Kalman filter models for estimating O-D travel time and flow with more accuracy.
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151 Appendix
Link Traffic Volumes and Spot Speeds
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Link traffic volume (vph)
Lane 1 Vol Lane 2 Vol Lane 3 Vol
Figure A.1: Link traffic volume at HP (Tuesday, 22/December/1998)
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Figure A.2: Spot speed at HP (Tuesday, 22/December/1998)
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Figure A.3: Link traffic volume at EP (Tuesday, 22/December/1998)
0 10 20 30 40 50 60 70 80
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Figure A.4: Spot speed at EP (Tuesday, 22/December/1998)
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Figure A.5: Link traffic volume at SSP (Tuesday, 22/December/1998)
0 20 40 60 80 100 120
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Lane 2 Spd Lane 3 Spd Lane 4 Spd Lane 5 Spd
Figure A.6: Spot speed at SSP (Tuesday, 22/December/1998)
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Figure A.7: Link traffic volume at HP (Wednesday, 23/December/1998)
0 20 40 60 80 100 120
7:30 7:35
7:40 7:45
7:50 7:55
8:00 8:05
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Figure A.8: Spot speed at HP (Wednesday, 23/December/1998)
0 500 1000 1500 2000 2500
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Figure A.9: Link traffic volume at EP (Wednesday, 23/December/1998)
0 10 20 30 40 50 60 70 80 90
7:30 7:35
7:40 7:45
7:50 7:55
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Figure A.10: Spot speed at EP (Wednesday, 23/December/1998)