Jack Reilly

Mobile Phones as Seismologic Sensors: Automating Data Extraction for the iShake System

There are a variety of approaches to seismic sensing, which range from collecting sparse measurements with high-fidelity seismic stations to non-quantitative, post-earthquake surveys. The sparse nature of the high-fidelity stations and the inaccuracy of the surveys create the need for a high-density, semi-quantitative approach to seismic sensing. To fill this void, the UC Berkeley iShake project designed a mobile client-backend server architecture that uses sensor-equipped mobile devices to measure earthquake ground shaking. iShake provides the general public with a service to more easily contribute more quantitatively significant data to earthquake research by automating the data collection and reporting mechanisms via the iShake mobile application. The devices act as distributed sensors that enable measurements to be taken and transmitted with a cellular network connection. Shaking table testing was used to assess the quality of the measurements obtained from the iPhones and iPods on a benchmark of 150 ground motions. Once triggered by a shaking event, the devices transmit sensor data to a backend server for further processing. After a seismic event is verified by high-fidelity stations, filtering algorithms are used to detect falling phones, as well as device-specific responses to the event. A method was developed to determine the absolute orientation of a device to estimate the direction of first motion of a seismic event. A “virtual earthquake” pilot test was conducted on the UC Berkeley campus to verify the operation of the iShake system. By designing and fully implementing a system architecture, developing signal processing techniques unique to mobile sensing, and conducting shaking table tests to confirm the validity of the sensing platform, the iShake project serves as foundational work for further studies in seismic sensing on mobile devices.

A PDE-ODE Model for a Junction with Ramp Buffer

We consider the Lighthill--Whitham--Richards traffic flow model on a junction composed by one mainline, an onramp, and an offramp, which are connected by a node. The onramp dynamics is modeled using an ordinary differential equation describing the evolution of the queue length. The definition of the solution of the Riemann problem at the junction is based on an optimization problem and the use of a right-of-way parameter. The numerical approximation is carried out using a Godunov scheme, modified to take into account the effects of the onramp buffer. We present the result of some simulations and numerically check the convergence of the method.

Adjoint-Based Optimization on a Network of Discretized Scalar Conservation Laws with Applications to Coordinated Ramp Metering

The adjoint method provides a computationally efficient means of calculating the gradient for applications in constrained optimization. In this article, we consider a network of scalar conservation laws with general topology, whose behavior is modified by a set of control parameters in order to minimize a given objective function. After discretizing the corresponding partial differential equation models via the Godunov scheme, we detail the computation of the gradient of the discretized system with respect to the control parameters and show that the complexity of its computation scales linearly with the number of discrete state variables for networks of small vertex degree. The method is applied to the problem of coordinated ramp metering on freeway networks. Numerical simulations on the I15 freeway in California demonstrate an improvement in performance and running time compared with existing methods. In the context of model predictive control, the algorithm is shown to be robust to noise in the initial data and boundary conditions.

On the characterization and computation of Nash equilibria on parallel networks with horizontal queues

We study inefficiencies in parallel networks with horizontal queues due to the selfish behavior of players, by comparing social optima to Nash equilibria. The article expands studies on routing games which traditionally model congestion with latency functions that increase with the flow on a particular link. This type of latency function cannot capture congestion effects on horizontal queues. Latencies on horizontal queues increase as a function of density, and flow can decrease with increasing latencies. This class of latency functions arises in transportation networks. For static analysis of horizontal queues on parallel-link networks, we show that there may exist multiple Nash equilibria with different total costs, which contrasts with results for increasing latency functions. We present a novel algorithm, quadratic in the number of links, for computing the Nash equilibrium that minimizes total cost (best Nash equilibrium). The relative inefficiencies of best Nash equilibria are evaluated through analysis of the price of stability, and analytical results are presented for two-link networks. Price of stability is shown to be sensitive to changes in demand when links are near capacity, and congestion mitigation strategies are discussed, motivated by our results.

Stackelberg Routing on Parallel Networks With Horizontal Queues

In order to address inefficiencies of Nash equilibria for congestion networks with horizontal queues, we study the Stackelberg routing game on parallel networks: assuming a coordinator has control over a fraction of the flow, and that the remaining players respond selfishly, what is an optimal Stackelberg strategy of the coordinator, i.e. a strategy that minimizes the cost of the induced equilibrium? We study Stackelberg routing for a new class of latency functions, which models congestion on horizontal queues. We introduce a candidate strategy, the non-compliant first strategy, and prove it to be optimal. Then we apply these results by modeling a transportation network in which a coordinator can choose the routes of a subset of the drivers, while the rest of the drivers choose their routes selfishly.

Evaluating the Reliability of Phones as Seismic Monitoring Instruments

Emergency responders must “see” the effects of an earthquake clearly and rapidly for effective response. This paper presents a novel use of cell phone and information technology to measure ground motion intensity parameters. The phone sensor is an imperfect device and has a limited operational range. Thus, shake table tests were performed to evaluate their reliability as seismic monitoring instruments. Representative handheld devices, either rigidly connected to the table or free to move, measured shaking intensity parameters well. Bias in 5%-damped spectral accelerations measured by phones was less than 0.05 and 0.2 [log(g)] during one-dimensional (1-D) and three-dimensional (3-D) shaking in frequencies ranging from 1 Hz to 10 Hz. They did tend to overestimate the Arias Intensity, but this error declined for stronger motions with larger signal-to-noise ratios. With these ubiquitous measurement devices, a more accurate and rapid portrayal of the damage distribution during an earthquake can be provided.

On Stackelberg routing on parallel networks with horizontal queues

This paper presents a game theoretic framework for studying Stackelberg routing games on parallel networks with horizontal queues, such as transportation networks. First, we introduce a new class of latency functions that models congestion due to the formation of physical queues. For this new class, some results from the classical congestion games literature (in which latency is assumed to be a non-decreasing function of the flow) do not hold. In particular, we find that there may exist multiple Nash equilibria that have different total costs. We provide a simple polynomial-time algorithm for computing the best Nash equilibrium, i.e., the one which achieves minimal total cost. Then we study the Stackelberg routing game: assuming a central authority has control over a fraction of the flow on the network (compliant flow), and that the remaining flow (non-compliant) responds selfishly, what is the best way to route the compliant flow in order to minimize the total cost? We propose a simple Stackelberg strategy, the Non-Compliant First (NCF) strategy, that can be computed in polynomial time. We show that it is optimal for this new class of latency on parallel networks. This work is applied to modeling and simulating congestion relief on transportation networks, in which a coordinator (traffic management agency) can choose to route a fraction of compliant drivers, while the rest of the drivers choose their routes selfishly.

Distributed Optimization for Shared State Systems: Applications to Decentralized Freeway Control via Subnetwork Splitting

Optimal control problems on dynamical systems are concerned with finding a control policy, which minimizes a desired objective, where the objective value depends on the future evolution of the system (the state of the system), which, in turn, depends on the control policy. For systems which contain subsystems that are disjoint across the state variables, distributed optimization techniques exist, which iteratively update subsystems concurrently and then exchange information between subsystems with shared control variables. This article presents a method, based on the asynchronous alternating directions method of multiplier algorithm, which extends these techniques to subsystems with shared control and state variables, while maintaining similar communication structure. The method is used as the basis for splitting network flow control problems into many subnetwork control problems with shared boundary conditions. The decentralized and parallel nature of the method permits high scalability with respect to the size of the network. For highly nonconvex applications, an efficient method, based on adjoint gradient computations, is presented for solving subproblems with shared state. The method is applied to decentralized, coordinated ramp metering and variable speed limit control on a realistic freeway network model using distributed model predictive control.

Discrete-time system optimal dynamic traffic assignment (SO-DTA) with partial control for horizontal queuing networks

We consider the System Optimal Dynamic Traffic Assignment problem with Partial Control (SO-DTA-PC) for general networks with horizontal queuing. The goal of which is to optimally control any subset of the networks agents to minimize the total congestion of all agents in the network. We adopt a flow dynamics model that is a Godunov discretization of the Lighthill-Williams-Richards (LWR) partial differential equation with a triangular flux function and a corresponding multi-commodity junction solver. Full Lagrangian paths are assumed to be known for the controllable agents, while we only assume knowledge of the aggregate split ratios for the non-controllable (selfish) agents. We solve the resulting finite horizon non-linear optimal control problem using the discrete adjoint method.

Discrete-Time System Optimal Dynamic Traffic Assignment (SO-DTA) with Partial Control for Physical Queuing Networks

We consider the System Optimal Dynamic Traffic Assignment (SO-DTA) problem with Partial Control for general networks with physical queuing. Our goal is to optimally control any subset of the networks agents to minimize the total congestion of all agents in the network. We adopt a flow dynamics model that is a Godunov discretization of the Lighthill–Williams–Richards partial differential equation with a triangular flux function and a corresponding multicommodity junction solver. The partial control formulation generalizes the SO-DTA problem to consider cases where only a fraction of the total flow can be controlled, as may arise in the context of certain incentive schemes. This leads to a nonconvex multicommodity optimization problem. We define a multicommodity junction model that only requires full Lagrangian paths for the controllable agents, and aggregate turn ratios for the noncontrollable (selfish) agents. We show how the resulting finite horizon nonlinear optimal control problem can be efficiently so...