arXiv subjects

Christos G. Cassandras

Publications and source records attributed to Christos G. Cassandras.

At least 109 records · Page 6Linked to original sources

arXiv2018

The Price of Anarchy in Transportation Networks: Data-Driven Evaluation and Reduction Strategies

Among the many functions a Smart City must support, transportation dominates in terms of resource consumption, strain on the environment, and frustration of its citizens. We study transportation networks under two different routing policies, the commonly assumed selfish user-centric routing policy and a socially-optimal system-centric one. We consider a performance metric of efficiency - the Price of Anarchy (PoA) - defined as the ratio of the total travel latency cost under selfish routing over the corresponding quantity under socially-optimal routing. We develop a data-driven approach to estimate the PoA, which we subsequently use to conduct a case study using extensive actual traffic data from the Eastern Massachusetts road network. To estimate the PoA, our approach learns from data a complete model of the transportation network, including origin-destination demand and user preferences. We leverage this model to propose possible strategies to reduce the PoA and increase efficiency.

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arXiv2017

Stochastic Flow Models with Delays and Applications to Multi-Intersection Traffic Light Control

We extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movement. We apply this framework to the multi-intersection traffic light control problem by including transit delays for vehicles moving from one intersection to the next. Using Infinitesimal Perturbation Analysis (IPA) for this SFM with delays, we derive new on-line gradient estimates of several congestion cost metrics with respect to the controllable green and red cycle lengths. The IPA estimators are used to iteratively adjust light cycle lengths to improve performance and, in conjunction with a standard gradient-based algorithm, to obtain optimal values which adapt to changing traffic conditions. We introduce two new cost metrics to better capture congestion and show that the inclusion of delays in our analysis leads to improved performance relative to models that ignore delays.

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arXiv2017

Decentralized Optimal Control for Connected Automated Vehicles at Intersections Including Left and Right Turns

In prior work, we addressed the problem of optimally controlling on line connected and automated vehicles crossing two adjacent intersections in an urban area to minimize fuel consumption while achieving maximal throughput without any explicit traffic signaling and without considering left and right turns. In this paper, we extend the solution of this problem to account for left and right turns under hard safety constraints. Furthermore, we formulate and solve another optimization problem to minimize a measure of passenger discomfort while the vehicle turns at the intersection and we investigate the associated tradeoff between minimizing fuel consumption and passenger discomfort.

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arXiv2017

Decentralized Event-Driven Algorithms for Multi-Agent Persistent Monitoring

We address the issue of identifying conditions under which the centralized solution to the optimal multi-agent persistent monitoring problem can be recovered in a decentralized event-driven manner. In this problem, multiple agents interact with a finite number of targets and the objective is to control their movement in order to minimize an uncertainty metric associated with the targets. In a one-dimensional setting, it has been shown that the optimal solution can be reduced to a simpler parametric optimization problem and that the behavior of agents under optimal control is described by a hybrid system. This hybrid system can be analyzed using Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven centralized gradient-based algorithm. We show that the IPA gradient can be recovered in a distributed manner in which each agent optimizes its trajectory based on local information, except for one event requiring communication from a non-neighbor agent. Simulation examples are included to illustrate the effectiveness of this "almost decentralized" algorithm and its fully decentralized counterpart where the aforementioned non-local event is ignored.

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arXiv2017

A Submodularity-Based Approach for Multi-Agent Optimal Coverage Problems

We consider the optimal coverage problem where a multi-agent network is deployed in an environment with obstacles to maximize a joint event detection probability. The objective function of this problem is non-convex and no global optimum is guaranteed by gradient-based algorithms developed to date. We first show that the objective function is monotone submodular, a class of functions for which a simple greedy algorithm is known to be within 0.63 of the optimal solution. We then derive two tighter lower bounds by exploiting the curvature information (total curvature and elemental curvature) of the objective function. We further show that the tightness of these lower bounds is complementary with respect to the sensing capabilities of the agents. The greedy algorithm solution can be subsequently used as an initial point for a gradient-based algorithm to obtain solutions even closer to the global optimum. Simulation results show that this approach leads to significantly better performance relative to previously used algorithms.

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arXiv2017

Optimal Control and Coordination of Connected and Automated Vehicles at Urban Traffic Intersections

We address the problem of coordinating online a continuous flow of connected and automated vehicles (CAVs) crossing two adjacent intersections in an urban area. We present a decentralized optimal control framework whose solution yields for each vehicle the optimal acceleration/deceleration at any time in the sense of minimizing fuel consumption. The solu- tion, when it exists, allows the vehicles to cross the intersections without the use of traffic lights, without creating congestion on the connecting road, and under the hard safety constraint of collision avoidance. The effectiveness of the proposed solution is validated through simulation considering two intersections located in downtown Boston, and it is shown that coordination of CAVs can reduce significantly both fuel consumption and travel time.

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arXiv2017

City-Scale Intelligent Systems and Platforms

As of 2014, 54% of the earth's population resides in urban areas, and it is steadily increasing, expecting to reach 66% by 2050. Urban areas range from small cities with tens of thousands of people to megacities with greater than 10 million people. Roughly 12% of the global population today lives in 28 megacities, and at least 40 are projected by 2030. At these scales, the urban infrastructure such as roads, buildings, and utility networks will cover areas as large as New England. This steady urbanization and the resulting expansion of infrastructure, combined with renewal of aging urban infrastructure, represent tens of trillion of dollars in new urban infrastructure investment over the coming decades. These investments must balance factors including impact on clean air and water, energy and maintenance costs, and the productivity and health of city dwellers. Moreover, cost-effective management and sustainability of these growing urban areas will be one of the most critical challenges to our society, motivating the concept of science- and data-driven urban design, retrofit, and operation-that is, "Smart Cities".

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arXiv2017

Optimal Control of Connected Automated Vehicles at Urban Traffic Intersections: A Feasibility Enforcement Analysis

Earlier work has established a decentralized optimal control framework for coordinating online a continuous flow of connected automated vehicles (CAVs) entering a control zone and crossing two adjacent intersections in an urban area. A solution, when it exists, allows the vehicles to cross the intersections without the use of traffic lights, without creating congestion on the connecting road, and under the hard safety constraint of collision avoidance. We establish the conditions under which such solutions exist and show that they can be enforced through an appropriately designed feasibility enforcement zone that precedes the control zone. The proposed solution and overall control architecture are illustrated through simulation.

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arXiv2016

Data-driven Estimation of Origin-Destination Demand and User Cost Functions for the Optimization of Transportation Networks

In earlier work (Zhang et al., 2016) we used actual traffic data from the Eastern Massachusetts transportation network in the form of spatial average speeds and road segment flow capacities in order to estimate Origin-Destination (OD) flow demand matrices for the network. Based on a Traffic Assignment Problem (TAP) formulation (termed "forward problem"), in this paper we use a scheme similar to our earlier work to estimate initial OD demand matrices and then propose a new inverse problem formulation in order to estimate user cost functions. This new formulation allows us to efficiently overcome numerical difficulties that limited our prior work to relatively small subnetworks and, assuming the travel latency cost functions are available, to adjust the values of the OD demands accordingly so that the flow observations are as close as possible to the solutions of the forward problem. We also derive sensitivity analysis results for the total user latency cost with respect to important parameters such as road capacities and minimum travel times. Finally, using the same actual traffic data from the Eastern Massachusetts transportation network, we quantify the Price of Anarchy (POA) for a much larger network than that in Zhang et al. (2016).

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arXiv2016

Event-driven Trajectory Optimization for Data Harvesting in Multi-Agent Systems

We propose a new event-driven method for on-line trajectory optimization to solve the data harvesting problem: in a two-dimensional mission space, N mobile agents are tasked with the collection of data generated at M stationary sources and delivery to a base with the goal of minimizing expected collection and delivery delays. We define a new performance measure that addresses the event excitation problem in event-driven controllers and formulate an optimal control problem. The solution of this problem provides some insights on its structure, but it is computationally intractable, especially in the case where the data generating processes are stochastic. We propose an agent trajectory parameterization in terms of general function families which can be subsequently optimized on line through the use of Infinitesimal Perturbation Analysis (IPA). Properties of the solutions are identified, including robustness with respect to the stochastic data generation process and scalability in the size of the event set characterizing the underlying hybrid dynamical system. Explicit results are provided for the case of elliptical and Fourier series trajectories and comparisons with a state-of-the-art graph-based algorithm are given.

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arXiv2016

Optimal control for a robotic exploration, pick-up and delivery problem

This paper addresses an optimal control problem for a robot that has to find and collect a finite number of objects and move them to a depot in minimum time. The robot has fourth-order dynamics that change instantaneously at any pick-up or drop-off of an object. The objects are modeled by point masses with a-priori unknown locations in a bounded two-dimensional space that may contain unknown obstacles. For this hybrid system, an Optimal Control Problem (OCP) is approximately solved by a receding horizon scheme, where the derived lower bound for the cost-to-go is evaluated for the worst and for a probabilistic case, assuming a uniform distribution of the objects. First, a time-driven approximate solution based on time and position space discretization and mixed integer programming is presented. Due to the high computational cost of this solution, an alternative event-driven approximate approach based on a suitable motion parameterization and gradient-based optimization is proposed. The solutions are compared in a numerical example, suggesting that the latter approach offers a significant computational advantage while yielding similar qualitative results compared to the former. The methods are particularly relevant for various robotic applications like automated cleaning, search and rescue, harvesting or manufacturing.

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arXiv2016

Event excitation for event-driven control and optimization of multi-agent systems

We consider event-driven methods in a general framework for the control and optimization of multi-agent systems, viewing them as stochastic hybrid systems. Such systems often have feasible realizations in which the events needed to excite an on-line event-driven controller cannot occur, rendering the use of such controllers ineffective. We show that this commonly happens in environments which contain discrete points of interest which the agents must visit. To address this problem in event-driven gradient-based optimization problems, we propose a new metric for the objective function which creates a potential field guaranteeing that gradient values are non-zero when no events are present and which results in eventual event excitation. We apply this approach to the class of cooperative multi-agent data collection problems using the event-driven Infinitesimal Perturbation Analysis (IPA) methodology and include numerical examples illustrating its effectiveness.

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arXiv2016

Optimal Energy-Efficient Downlink Transmission Scheduling for Real-Time Wireless Networks

It has been shown that using appropriate channel coding schemes in wireless environments, transmission energy can be significantly reduced by controlling the packet transmission rate. This paper seeks optimal solutions for downlink transmission control problems, motivated by this observation and by the need to minimize energy consumption in real-time wireless networks. Our problem formulation deals with a more general setting than the paper authored by Gamal et. al., in which the MoveRight algorithm is proposed. The MoveRight algorithm is an iterative algorithm that converges to the optimal solution. We show that even under the more general setting, the optimal solution can be efficiently obtained through an approach decomposing the optimal sample path through certain "critical tasks" which in turn can be efficiently identified. We include simulation results showing that our algorithm is significantly faster than the MoveRight algorithm. We also discuss how to utilize our results and receding horizon control to perform on-line transmission scheduling where future task information is unknown.

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arXiv2016

Optimal Event-Driven Multi-Agent Persistent Monitoring of a Finite Set of Targets

We consider the problem of controlling the movement of multiple cooperating agents so as to minimize an uncertainty metric associated with a finite number of targets. In a one-dimensional mission space, we adopt an optimal control framework and show that the solution is reduced to a simpler parametric optimization problem: determining a sequence of locations where each agent may dwell for a finite amount of time and then switch direction. This amounts to a hybrid system which we analyze using Infinitesimal Perturbation Analysis (IPA) to obtain a complete on-line solution through an event-driven gradient-based algorithm which is also robust with respect to the uncertainty model used. The resulting controller depends on observing the events required to excite the gradient-based algorithm, which cannot be guaranteed. We solve this problem by proposing a new metric for the objective function which creates a potential field guaranteeing that gradient values are non-zero. This approach is compared to an alternative graph-based task scheduling algorithm for determining an optimal sequence of target visits. Simulation examples are included to demonstrate the proposed methods.

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arXiv2016

Personalized Cancer Therapy Design: Robustness vs. Optimality

Intermittent Androgen Suppression (IAS) is a treatment strategy for delaying or even preventing time to relapse of advanced prostate cancer. IAS consists of alternating cycles of therapy (in the form of androgen suppression) and off-treatment periods. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. In spite of extensive recent clinical experience with IAS, the design of an ideal protocol for any given patient remains one of the main challenges associated with effectively implementing this therapy. We use a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We apply Infinitesimal Perturbation Analysis (IPA) to a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and derive unbiased estimators of the cost metric gradient with respect to various model and therapy parameters. These estimators are subsequently used for system analysis. By evaluating sensitivity estimates with respect to several model parameters, we identify critical parameters and demonstrate that relaxing the optimality condition in favor of increased robustness to modeling errors provides an alternative objective to therapy design for at least some patients.

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arXiv2016

Solving A Class of Discrete Event Simulation-based Optimization Problems Using "Optimality in Probability"

We approach a class of discrete event simulation-based optimization problems using optimality in probability, an approach which yields what is termed a "champion solution". Compared to the traditional optimality in expectation, this approach favors the solution whose actual performance is more likely better than that of any other solution; this is an effective alternative to the traditional optimality sense, especially when facing a dynamic and nonstationary environment. Moreover, using optimality in probability is computationally promising for a class of discrete event simulation-based optimization problems, since it can reduce computational complexity by orders of magnitude compared to general simulation-based optimization methods using optimality in expectation. Accordingly, we have developed an "Omega Median Algorithm" in order to effectively obtain the champion solution and to fully utilize the efficiency of well-developed off-line algorithms to further facilitate timely decision making. An inventory control problem with nonstationary demand is included to illustrate and interpret the use of the Omega Median Algorithm, whose performance is tested using simulations.

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arXiv2015

An Optimal Control Approach for the Data Harvesting Problem

We propose a new method for trajectory planning to solve the data harvesting problem. In a two-dimensional mission space, $N$ mobile agents are tasked with the collection of data generated at $M$ stationary sources and delivery to a base aiming at minimizing expected delays. An optimal control formulation of this problem provides some initial insights regarding its solution, but it is computationally intractable, especially in the case where the data generating processes are stochastic. We propose an agent trajectory parameterization in terms of general function families which can be subsequently optimized on line through the use of Infinitesimal Perturbation Analysis (IPA). Explicit results are provided for the case of elliptical and Fourier series trajectories and some properties of the solution are identified, including robustness with respect to the data generation processes and scalability in the size of an event set characterizing the underlying hybrid dynamic system.

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arXiv2015

Lifetime Maximization of Wireless Sensor Networks with a Mobile Source Node

We study the problem of routing in sensor networks where the goal is to maximize the network's lifetime. Previous work has considered this problem for fixed-topology networks. Here, we add mobility to the source node, which requires a new definition of the network lifetime. In particular, we redefine lifetime to be the time until the source node depletes its energy. When the mobile node's trajectory is unknown in advance, we formulate three versions of an optimal control problem aiming at this lifetime maximization. We show that in all cases, the solution can be reduced to a sequence of Non- Linear Programming (NLP) problems solved on line as the source node trajectory evolves.

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