47 research outputs found
Complexity and Approximation of the Continuous Network Design Problem
We revisit a classical problem in transportation, known as the continuous
(bilevel) network design problem, CNDP for short. We are given a graph for
which the latency of each edge depends on the ratio of the edge flow and the
capacity installed. The goal is to find an optimal investment in edge
capacities so as to minimize the sum of the routing cost of the induced Wardrop
equilibrium and the investment cost. While this problem is considered as
challenging in the literature, its complexity status was still unknown. We
close this gap showing that CNDP is strongly NP-complete and APX-hard, both on
directed and undirected networks and even for instances with affine latencies.
As for the approximation of the problem, we first provide a detailed analysis
for a heuristic studied by Marcotte for the special case of monomial latency
functions (Mathematical Programming, Vol.~34, 1986). Specifically, we derive a
closed form expression of its approximation guarantee for arbitrary sets S of
allowed latency functions. Second, we propose a different approximation
algorithm and show that it has the same approximation guarantee. As our final
-- and arguably most interesting -- result regarding approximation, we show
that using the better of the two approximation algorithms results in a strictly
improved approximation guarantee for which we give a closed form expression.
For affine latencies, e.g., this algorithm achieves a 1.195-approximation which
improves on the 5/4 that has been shown before by Marcotte. We finally discuss
the case of hard budget constraints on the capacity investment.Comment: 27 page
On the Resilience of Traffic Networks under Non-Equilibrium Learning
We investigate the resilience of learning-based \textit{Intelligent
Navigation Systems} (INS) to informational flow attacks, which exploit the
vulnerabilities of IT infrastructure and manipulate traffic condition data. To
this end, we propose the notion of \textit{Wardrop Non-Equilibrium Solution}
(WANES), which captures the finite-time behavior of dynamic traffic flow
adaptation under a learning process. The proposed non-equilibrium solution,
characterized by target sets and measurement functions, evaluates the outcome
of learning under a bounded number of rounds of interactions, and it pertains
to and generalizes the concept of approximate equilibrium. Leveraging
finite-time analysis methods, we discover that under the mirror descent (MD)
online-learning framework, the traffic flow trajectory is capable of restoring
to the Wardrop non-equilibrium solution after a bounded INS attack. The
resulting performance loss is of order
(), with a constant dependent on the size of the
traffic network, indicating the resilience of the MD-based INS. We corroborate
the results using an evacuation case study on a Sioux-Fall transportation
network.Comment: 8 pages, 3 figures, with a technical appendi
Capacity Allocation and Pricing of High Occupancy Toll Lane Systems with Heterogeneous Travelers
In this article, we study the optimal design of High Occupancy Toll (HOT)
lanes. In our setup, the traffic authority determines the road capacity
allocation between HOT lanes and ordinary lanes, as well as the toll price
charged for travelers who use the HOT lanes but do not meet the high-occupancy
eligibility criteria. We build a game-theoretic model to analyze the decisions
made by travelers with heterogeneous values of time and carpool disutilities,
who choose between paying or forming carpools to take the HOT lanes, or taking
the ordinary lanes. Travelers' payoffs depend on the congestion cost of the
lane that they take, the payment and the carpool disutilities. We provide a
complete characterization of travelers' equilibrium strategies and resulting
travel times for any capacity allocation and toll price. We also calibrate our
model on the California Interstate highway 880 and compute the optimal capacity
allocation and toll design
Joint Estimation of OD Demands and Cost Functions in Transportation Networks from Data
Existing work has tackled the problem of estimating Origin-Destination (OD)
demands and recovering travel latency functions in transportation networks
under the Wardropian assumption. The ultimate objective is to derive an
accurate predictive model of the network to enable optimization and control.
However, these two problems are typically treated separately and estimation is
based on parametric models. In this paper, we propose a method to jointly
recover nonparametric travel latency cost functions and estimate OD demands
using traffic flow data. We formulate the problem as a bilevel optimization
problem and develop an iterative first-order optimization algorithm to solve
it. A numerical example using the Braess Network is presented to demonstrate
the effectiveness of our method.Comment: To appear at the Proceedings of the 58th IEEE Conference on Decision
and Contro
Demand-Independent Optimal Tolls
3sìWardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium. The classical approach to find such tolls is marginal cost pricing which requires the exact knowledge of the demand on the network. In this paper, we investigate under which conditions demand-independent optimum tolls exist that induce the system optimum flow for any travel demand in the network. We give several characterizations for the existence of such tolls both in terms of the cost structure and the network structure of the game. Specifically we show that demand-independent optimum tolls exist if and only if the edge cost functions are shifted monomials as used by the Bureau of Public Roads. Moreover, non-negative demand-independent optimum tolls exist when the network is a directed acyclic multi-graph. Finally, we show that any network with a single origin-destination pair admits demand-independent optimum tolls that, although not necessarily non-negative, satisfy a budget constraint.openopenRiccardo Colini-Baldeschi; Max Klimm; Marco ScarsiniCOLINI BALDESCHI, Riccardo; Klimm, Max; Scarsini, Marc
Detection and optimization problems with applications in smart cities
This dissertation proposes solutions to a selected set of detection and optimization problems, whose applications are focused on transportation systems. The goal is to help build smarter and more efficient transportation systems, hence smarter cities.
Problems with dynamics evolving in two different time-scales are considered:
(1) In a fast time-scale, the dissertation considers the problem of detection, especially statistical anomaly detection in real-time. From a theoretical perspective and under Markovian assumptions, novel threshold estimators are derived for the widely used Hoeffding test. This results in a test with a much better ability to control false alarms while maintaining a high detection rate. From a practical perspective, the improved test is applied to detecting non-typical traffic jams in the Boston road network using real traffic data reported by the Waze smartphone navigation application. The detection results can alert the drivers to reroute so as to avoid the corresponding areas and provide the most urgent "targets" to the Transportation department and/or emergency services to intervene and remedy the underlying cause resulting in these jams, thus, improving transportation systems and contributing to the smart city agenda.
(2) In a slower time-scale, the dissertation investigates a host of optimization problems, including estimation and adjustment of Origin-Destination (OD) demand, traffic assignment, recovery of travel cost functions, and joint recovery of travel cost functions and OD demand (joint problem). Integrating these problems leads to a data-driven predictive model which serves to diagnose/control/optimize the transportation network. To ensure good accuracy of the predictive model and increase its robustness and consistency, several novel formulations for the travel cost function recovery problem and the joint problem are proposed. A data-driven framework is proposed to evaluate the Price-of-Anarchy (PoA; a metric assessing the degree of congestion under selfish user-centric routing vs. socially-optimal system-centric routing). For the case where the PoA is larger than expected, three viable strategies are proposed to reduce it. To demonstrate the effectiveness and efficiency of the proposed approaches, case-studies are conducted on three benchmark transportation networks using synthetic data and an actual road network (from Eastern Massachusetts (EMA)) using real traffic data. Moreover, to facilitate research in the transportation community, the largest highway subnetwork of EMA has been released as a new benchmark network