日時： 2018年11月28日(水) 16:00～17:00
場所： 東京大学工学部 14号館 5階 534号室
https://www.u-tokyo.ac.jp/camp
講演者： Laura Vargas Koch (RWTH Aachen University)
講演題目：Nash Flows over Time with Spillback
講演概要：
Modeling traffic in road networks is a widely studied but
challenging problem, especially under the assumption that
drivers act selfishly. A common approach used in simulation
software is the deterministic queuing model, for which the
structure of dynamic equilibria has been studied extensively
in the last couple of years. The basic idea is to model traffic
by a continuous flow that travels over time from a source to
a sink through a network, in which the arcs are endowed with
transit times and capacities. Whenever the flow rate exceeds
the capacity a queue builds up and the infinitesimally small
flow particles wait in line in front of the bottleneck.
Since the queues have no physical dimension, it was not possible,
until now, to represent spillback in this model. This was
a big drawback, since spillback can be regularly observed
in real traffic situations and has a huge impact on travel
times in highly congested regions. We extend the deterministic
queuing model by introducing a storage capacity that bounds
the total amount of flow on each arc. If an arc gets full,
the inflow capacity is reduced to the current outflow rate,
which can cause queues on previous arcs and blockages of
intersections, i.e., spillback. We carry over the main
results of the original model to our generalization and
characterize dynamic equilibria, called Nash flows over time,
by sequences of particular static flows, we call spillback
thin flows. Furthermore, we give a constructive proof for
the existence of dynamic equilibria, which suggests an algorithm
for their computation.
This is joint work with Leon Sering from TU Berlin.