Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Friday, February 21, 2014 - 04:00
GLK 115

Speaker Info

OSU Civil & Construction Engineering

Mobility is one of the greatest freedoms that people desire to enjoy, but congestion across all of our transportation modes continues to limit predictable, reliable movement of people and goods, and poses a serious threat to the economic growth. Americans are experiencing longer delays, longer periods of congestion not only on roads in larger urban areas, but also in suburban and rural areas. Transportation decision-makers
and researchers are striving to reduce trac congestion and increase system capacity, but this requires a better understanding of how congestion forms and dissipates on our highways. To unveil the underlying mechanism, transportation researchers and practitioners generally start with the fundamental diagram of traffic flow.

This talk focuses on modeling the fundamental diagram of traffic flow in
stochastic ways (fundamental diagram is a graphical representation of the relation among traffic
flow, speed, and density) which has
been the foundation of traffic flow theory and transportation engineering
analysis. For example, the analysis
of traffic dynamics relies on input from this fundamental diagram to find
when and where congestion builds
up and how it dissipates; traffic engineers use a fundamental diagram to
determine how well a highway
facility serves its users (i.e., level of service) and how to plan for new
facilities in case of capacity expansion
(i.e., highway capacity analysis). Underlying a fundamental diagram is the
relation between traffic speed
and density which roughly corresponds to drivers' speed choices under
varying car-following distances.
First rigorously documented by Dr. Bruce D. Greenshields in 1935, such a
relation has been explored
in many follow-up studies, but these attempts are dominantly deterministic
in nature, i.e., they model traffic
speed solely as a function of traffic density. Though these functional
speed-density models are able to
coarsely explain how traffic slows down as more vehicles are crowded on
highways, empirical observations
show a wide-scattering of traffic speeds around the values predicted by
these models. In addition, functional
speed-density models lead to deterministic prediction of traffic dynamics,
which lack the power to address the
uncertainty brought about by random factors (i.e., driver
perception-reaction differences, driver and vehicle
heterogeneity) in traffic flow. Therefore, it appears more appropriate to
view the speed-density relation as
a stochastic process, in which a certain density level gives rise not only
to an average value of traffic speed
but also to its variation because of the randomness of drivers' speed
choices. Therefore, a stochastic speed-
density model is developed to better represent empirical observations and
provide a basis for a probabilistic
prediction of traffic dynamics. Following the results, a stochastic
fundamental diagram of traffic flow is
established. On the application side, the stochastic speed-density
relationship model can potentially be used
for real-time on-line prediction and to explain phenomenons (i.e.,
capacity drop, spontaneous congestion, and
traffic hysteresis) in a similar manner. This enables dynamic control and
management systems to anticipate
problems before they occur rather than simply reacting to existing