Robust Line Planning under Unknown Incentives and Elasticity of Frequencies

Abstract

The problem of robust line planning requests for a set of
origin-destination paths (lines) along with their traffic rates (frequencies)
in an underlying railway network infrastructure, which are robust to
fluctuations of real-time parameters of the solution.
In this work, we investigate a variant of robust line planning stemming
from recent regulations in the railway sector that introduce competition
and free railway markets, and set up a new application scenario: there is
a (potentially large) number of line operators that have their lines fixed
and operate as competing entities struggling to exploit the underlying
network infrastructure via frequency requests, while the management of
the infrastructure itself remains the responsibility of a single (typically
governmental) entity, the network operator.
The line operators are typically unwilling to reveal their true incentives.
Nevertheless, the network operator would like to ensure a fair (or, socially
optimal) usage of the infrastructure, e.g., by maximizing the (unknown to
him) aggregate incentives of the line operators. We show that this can be
accomplished in certain situations via a (possibly anonymous) incentive-
compatible pricing scheme for the usage of the shared resources, that is
robust against the unknown incentives and the changes in the demands
of the entities. This brings up a new notion of robustness, which we
call incentive-compatible robustness, that considers as robustness of the
system its tolerance to the entities' unknown incentives and elasticity
of demands, aiming at an eventual stabilization to an equilibrium point
that is as close as possible to the social optimum.