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.