This paper has presented a quantum mechanics-based approach to modeling the dynamic driving maneuvers in the process of passing by a lane-blocking incident via the adjacent lane.
Considering the potential effects of drivers’ psychological factors on the aforementioned incident-induced driving behavior, a quantum mechanics-based methodology is proposed by incorporating several psychological factors, including the stimulus oriented from the variations of optical flows, curiosity, and internal pressure into the model formulation. Then, a microscopic traffic behavior module, which consists of three sequential phases, including (1) initial stimulus, (2)
glancing-around car-following, and (3) incident-induced driving maneuvers, is formulated for characterizing the dynamic driver behavior in the entire process of passing by an incident site, followed by the development of a microscopic simulation model to test the validity of the proposed method.
Our preliminary test results have implied that the proposed microscopic driver behavior models permit reproducing the dynamics of incident-induced driving maneuvers using quantum mechanics-based methodology. Particularly, it appears feasible to reformulate the corresponding car-following models based on the concepts of quantum mechanics-based optic flow variations, as claimed in Baker (1999). Moreover, the proposed method exhibited its potential advantages for the application of analyzing microscopic traffic maneuvers under the conditions of freeway lane-blocking incidents in comparison with the existing microscopic traffic simulators.
Nevertheless, more elaborate experimental design involving the utilization of advanced devices for data collection and model testing is apparently needed. For instance, we are presently testing the model under various traffic flow scenarios, where a variety of traffic arrivals as well as the effects of lane-changing and queuing effects of the blocked lane is considered. Furthermore, we attempt to further test the proposed methodology in a multi-lane mainline segment such that the embedded incident-induced lane-changing model can also be examined. In addition, elaborate examinations of the postulated assumptions may be needed in future research. The applications of the quantum mechanics-based approach to the formulation of dynamic driving maneuvers may also warrant more research. These include the use of the proposed approach in reproducing incident-free car-following and lane-changing maneuvers on either freeways or surface streets.
More importantly, it is expected that this study can not only provide the feasible access to a better understanding of the influence of human psychological and physical factors in driving maneuvers to improve road safety, but also stimulate more researchers devoted to exploring more
related issues and solutions to add more value to the literature of applied physics and related areas.
Acknowledgments
This work was supported by the National Science Council of Taiwan under Grant NSC 96-2416-H-009-011-MY3.
References
Baker, R.G.V., 1999. On the quantum mechanics of optic flow and its application to driving in uncertain environments. Transportation Research Part F 2, 27-53.
Beiser, A., 1969. Perspectives of modern physics. New York: McGraw-Hill.
Bartmann, D., Spijkers, W., and Hess, M., 1991. Street environment, driving speed and field of version. In A.G. Gale, I.D. Brown, C.M. Haslegrave, I. Moorhead, and S.P. Taylor, Version in Vehicles III. Amsterdam: Elsevier.
Brackstone, M, McDonald, M., 1999. Car-following: a historical review. Transportation Research Part F 2, 181-196.
Cavallo, V. and Laurent, M., 1988. Visual information and skill level in time-to-collision estimation. Perception 17, 623-632.
Chakroborty, P. and Kikuchi, S., 1999. Evaluation of the general motors based car-following models and a proposed fuzzy inference model. Transportation Research C, 7C (4), pp. 209-235.
Chou, Y.-H., and Sheu, J.-B., 1992. A simulation model of mixed traffic flow in roundabouts.
Transportation Planning Journal, 21(3), 301-333.
Daganzo, C. F. and Laval, J. A., 2005. Moving bottlenecks: a numerical method that converges in flows. Transportation Research Part B 39(9), 855-863.
Fodor, J. A., 1983. The Modularity of Mind. Cambridge, MA: The MIT Press.
Gibson, J. J., 1966. The senses considered as a perceptual system. Boston: Houghton Mifflin.
Hall, R. W., 2002. Incident dispatching, clearance and delay. Transportation Research Part A 36(1), 1-16.
Holland, E. N., 1998. A generalized stability criterion for motorway traffic. Transportation Research B, 32(2), 141-154.
Kayser, H.J., and Hess, M., 1991. The dependency of drivers’ viewing behavior on speed and street environment structure. In A.G. Gale, I.D. Brown, C.M. Haslegrave, I. Moorhead, and S.P. Taylor, Version in Vehicles III. Amsterdam: Elsevier.
Kikuchi, S. and Chakroborty, P., 1992. Car-following model based on fuzzy inference system.
Transportation Research Record 1365, pp.82-91, 1992.
Lee, D. N., 1980. The optic flow field: the foundation of vision. Philosophical Transactions of the Royal Society 290, 169-179.
MacLeod, R. W. and Ross, H. E., 1983. Optic flow and cognitive factors in time-to-collision estimates. Perception 12, 417-423.
May, A.D., 1990. Traffic Flow Fundamentals. Prentice-Hall, Englewood Cliffs, NJ.
Messer, C. J., Dudek, C. L. and Friebele, J. D., 1973. Method for predicting travel time and other operational measures in real-time during freeway incident conditions. Highway Research Record 461, 1-16.
Miura, T., 1987. Behavior oriented version: functional field of view and processing resources. In J.K.
O’Regan and A. Levy-Schoen, Eye Movements: From Physiology to Cognition. Amsterdam:
Elsevier.
Mossison, M. A., 1990. Understanding quantum physics: a user manual. New Jersey: Printice-Hall.
Newell, G. F., 1999. Flows upstream of a highway bottleneck. In: Ceder, A. (Ed.), Transportation and Traffic Theory. Pergamon, Amsterdam, NL, pp. 125-146.
Newell, G. F., 1993. A simplified theory of kinematic waves in highway traffic, part II: queuing at freeway bottlenecks. Transportation Research part B, 27B, 4, 289-303.
Osaka, N., 1988. Speed estimation through restricted visual field. In A.G. Gale, M.H. Freeman, C.M.
Haslegrave, P. Smith and S.P. Taylor, Version in Vehicles II. Amsterdam: Elsevier.
Ranney, T. A., 1999. Psychological factors that influence car-following and car-following model development. Transportation Research Part F 2, 213-219.
Sheu, J.-B., 2006. A composite traffic flow modeling approach for incident-responsive network traffic assignment. Physica A 367, 461-478.
Sheu, J.-B., Chou, Y.-H. and Chen, A., 2004. Stochastic modeling and real-time prediction of incident effects on surface street traffic congestion. Applied Mathematical Modelling 28(5), 445-468.
Sheu, J.-B., 2003. A stochastic modeling approach to real-time prediction of queue overflows, Transportation Science 37(1), 97-119.
Sheu, .J.-B., Chou, Y.-H., and Shen, L.-J., 2001a. A stochastic estimation approach to real-time prediction of incident effects on freeway traffic congestion. Transportation Research-Part B, 35B(6), pp.575-592.
Sheu, J.-B. and Ritchie, S. G., 2001b. Stochastic modeling and real-time prediction of vehicular lane-changing behavior. Transportation Research-Part B 35B(7), pp. 695-716.
Zhang, H. M. and Kim, T., 2005. A car-following theory for multiphase vehicular traffic flow.
Transportation Research Part B 39(5), 385-399.
Initialization:
vehicle approaching from a given adjacent lane
Phase 1:
Initial stimulus
Phase 2:
Glancing-around car-following behavior
Phase 3:
Incident-induced driving maneuvers
Termination:
Passing by the incidnet site
dynamics of driving maneuvers in the process of approaching
the incidet site through the adjacent lanes
Fig. 1. Conceptual framework of the proposed model
∆ y
∆ x
Fig. 2. Definition of a peripheral visual field
i i-1
) (t
∆x ′
incident
moving vehicle
) (t
∆y ′
lane
lane
li
l
lane lΛ
Fig. 3. Illustration of the perceived lane changes to the farther adjacent lane l
i
incident
moving vehicle lane
lane
li
l
lane lΛ
i-1
i
)
i(t′′
θ )
i(t′′
θ
Fig. 4. Illustration of the turning angle restriction
2.1 km 0.9 km
Fig. 5. Scheme of the study site
Fig. 6. Illustration of the simulated-vehicle manipulation function
Process of vehicle movements
Select a target vehicle
Return perceiving anomalous tarffic
flows Vehicle generation
no
yes
Mode-5 Incident-induced traffic
model in the blocked lane
Mode-3 Glancing-around
car-following model no
yes
Mode-4 Incident-induced driving behavior model
in the adjacent lane Mode-1
General car-following behavior
Initial stimulus
Incident is perceived
yes
no
moving in the blocked lane
yes
no
passing by the incident
no
yes
Mode-2 Initial stimulus
Removing the vehicle from
simulation
Fig. 7. Framework of the proposed microscopic traffic simulation program
[ ( )] 1 ( )
Fig. 8. Primary procedures for examining simulated headway distributions
Table 1. Summary of the static characteristics of vehicles and calibrated traffic parameters
vehicle Light goods
Testing with respect to the arrival rate (assumed to follow a negative binomial distribution) Samples Mean value
(veh/10sec.)
Standard deviation (veh/10sec.)
Chi-square estimate Critical value Result
316 3.58 1.19 9.74 11.07 accepted
Testing with respect to the arrival speed (assumed to follow a normal distribution) Type of
vehicle
Sample Mean value (m/s) Other key parameters
the average reaction time (sec.) the minimum acceptable headway (sec.)
0.78 0.85
Table 2. Summary of the comparison results (arrival volume) Aggregate arrival volume
(veh/5 min.)
Aggregate arrival volume (veh/15 min.) Sampling interval
Data source
Light vehicle
Heavy vehicle
Total Light vehicle
Heavy vehicle
Total
Video-based data 164 51 215 498 148 646
Proposed model 159 49 208 479 156 635
Paramics 157 45 202 471 139 610
Relative error associated with the proposed model (%)
-3.0 -3.9 -3.3 -3.8 5.4 -1.7
Relative error associated with Paramics (%)
-4.3 -11.8 -6.0 -5.4 -6.1 -5.6
Table 3. Summary of the comparison results (departure volume) Aggregate arrival volume
(veh/5 min.)
Aggregate arrival volume (veh/15 min.) Sampling interval
Data source
Light vehicle
Heavy vehicle
Total Light vehicle
Heavy vehicle
Total
Video-based data 125 39 164 378 115 493
Proposed model 117 40 157 365 110 475
Paramics 110 32 142 329 99 428
Relative error associated with the proposed model (%)
-6.4 2.6 -4.3 -6.1 -4.3 -3.7
Relative error associated with Paramics (%)
-12.0 -17.9 -13.4 -13.0 -13.9 -13.2
Table 4. Summary of the comparison results (average link travel time) Criteria
Data source
Average link travel time (sec.)
Relative error (%)
Video-based data 125.4
Proposed model 118.2 -5.7%
Paramics 149.3 19.1%
Table 5. Summary of the comparison results (lane usage) Criteria
Data source
Lane usage (%) adjacent lane blocked lane
Relative error (%) adjacent lane blocked lane
Video-based data 68.3 31.7
Proposed model 66.5 33.5 2.6 5.7
Paramics 56.6 43.4 17.3 36.9
Table 6. Test results of simulated headway distributions Simulated
data group
Collection location upstream
from the incident site
(km)
Chi-square value
Critical point with significance level α =0.1
Degrees of freedom
Test result
1 2.4 5.7 10.64 6 Accepted
2 2.1 4.2 10.64 6 Accepted
3 1.9 6.5 10.64 6 Accepted
4 1.5 7.9 10.64 6 Accepted
5 1.3 8.9 10.64 6 Accepted
6 1.0 8.6 10.64 6 Accepted
7 0.6 9.7 10.64 6 Accepted
8 0.4 10.4 10.64 6 Accepted
9 0.1 23.1 10.64 6 Not accepted
10 0.0 8.2 10.64 6 Accepted