679 research outputs found
Congestion management in traffic-light intersections via Infinitesimal Perturbation Analysis
We present a flow-control technique in traffic-light intersections, aiming at
regulating queue lengths to given reference setpoints. The technique is based
on multivariable integrators with adaptive gains, computed at each control
cycle by assessing the IPA gradients of the plant functions. Moreover, the IPA
gradients are computable on-line despite the absence of detailed models of the
traffic flows. The technique is applied to a two-intersection system where it
exhibits robustness with respect to modeling uncertainties and computing
errors, thereby permitting us to simplify the on-line computations perhaps at
the expense of accuracy while achieving the desired tracking. We compare, by
simulation, the performance of a centralized, joint two-intersection control
with distributed control of each intersection separately, and show similar
performance of the two control schemes for a range of parameters
Topics in perturbation analysis for stochastic hybrid systems
Control and optimization of Stochastic Hybrid Systems (SHS) constitute
increasingly active fields of research. However, the size and complexity of
SHS frequently render the use of exhaustive verification techniques
prohibitive. In this context, Perturbation Analysis techniques, and in
particular Infinitesimal Perturbation Analysis (IPA), have proven to be
particularly useful for this class of systems. This work focuses on applying
IPA to two different problems: Traffic Light Control (TLC) and control of
cancer progression, both of which are viewed as dynamic optimization
problems in an SHS environment.
The first part of this thesis addresses the TLC problem for a single
intersection modeled as a SHS. A quasi-dynamic control policy is proposed
based on partial state information defined by detecting whether vehicle
backlogs are above or below certain controllable threshold values. At first,
the threshold parameters are controlled while assuming fixed cycle lengths
and online gradient estimates of a cost metric with respect to these
controllable parameters are derived using IPA techniques. These estimators
are subsequently used to iteratively adjust the threshold values so as to
improve overall system performance. This quasi-dynamic analysis of the TLC\
problem is subsequently extended to parameterize the control policy by green
and red cycle lengths as well as queue content thresholds. IPA estimators
necessary to simultaneously control the light cycles and thresholds
are rederived and thereafter incorporated into a standard gradient based
scheme in order to further ameliorate system performance.
In the second part of this thesis, the problem of controlling cancer
progression is formulated within a Stochastic Hybrid Automaton (SHA)
framework. Leveraging the fact that cell-biologic changes necessary for cancer development may be schematized as a series of discrete steps, an integrative closed-loop framework is proposed for describing the progressive development of cancer and determining optimal personalized therapies. First, the problem of cancer heterogeneity is addressed through a novel Mixed Integer Linear Programming (MILP) formulation that integrates somatic mutation and gene expression data to infer the temporal sequence of events from cross-sectional data. This formulation is tested using both simulated data and real breast cancer data with matched somatic mutation and gene expression measurements from The Cancer Genome Atlas (TCGA). Second, the use of basic IPA techniques for optimal personalized cancer therapy design is introduced and a methodology applicable to stochastic models of cancer progression is developed. A case study of optimal therapy design for advanced prostate cancer is performed. Given the importance of accurate modeling in conjunction with optimal therapy design, an ensuing analysis is performed in which sensitivity estimates with respect to several model parameters are evaluated and critical parameters are identified. Finally, the tradeoff between system optimality and robustness (or, equivalently, fragility) is explored so as to generate valuable insights on modeling and control of cancer progression
Control and optimization methods for problems in intelligent transportation systems
This thesis aims to address three research topics in intelligent transportation systems
which include multi-intersection traffic light control based on stochastic flow models with
delays and blocking, optimization of mobility-on-demand systems using event-driven receding
horizon control and the optimal control of lane change maneuvers in highways for
connected and automated vehicles.
First, for the traffic light control work, 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 movements, as well as blocking effects due to space constraints. 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 and possible blocking
between two intersections. Using Infinitesimal Perturbation Analysis (IPA) for this SFM
with delays and possible blocking, 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.
The second problem relates to developing an event-driven Receding Horizon Control
(RHC) scheme for a Mobility-on-Demand System (MoDS) in a transportation network
where vehicles may be shared to pick up and drop off passengers so as to minimize a
weighted sum of passenger waiting and traveling times. Viewed as a discrete event system,
the event-driven nature of the controller significantly reduces the complexity of the vehicle
assignment problem, thus enabling its real-time implementation.
Finally, optimal control policies are derived for a Connected Automated Vehicle (CAV)
cooperating with neighboring CAVs in order to implement a lane change maneuver consisting
of a longitudinal phase where the CAV properly positions itself relative to the cooperating
neighbors and a lateral phase where it safely changes lanes. For the first phase, the maneuver time subject to safety constraints and subsequently the associated energy consumption of all cooperating vehicles in this maneuver are optimized. For the second phase, time and energy are jointly optimized based on three different solution methods including a real-time approach based on Control Barrier Functions (CBFs). Structural properties of the optimal policies which simplify the solution derivations are provided in the case of the longitudinal maneuver, leading to analytical optimal control expressions. The solutions, when they exist, are guaranteed to satisfy safety constraints for all vehicles involved in the maneuver
Aggregate matrix-analytic techniques and their applications
The complexity of computer systems affects the complexity of modeling techniques that can be used for their performance analysis. In this dissertation, we develop a set of techniques that are based on tractable analytic models and enable efficient performance analysis of computer systems. Our approach is three pronged: first, we propose new techniques to parameterize measurement data with Markovian-based stochastic processes that can be further used as input into queueing systems; second, we propose new methods to efficiently solve complex queueing models; and third, we use the proposed methods to evaluate the performance of clustered Web servers and propose new load balancing policies based on this analysis.;We devise two new techniques for fitting measurement data that exhibit high variability into Phase-type (PH) distributions. These techniques apply known fitting algorithms in a divide-and-conquer fashion. We evaluate the accuracy of our methods from both the statistics and the queueing systems perspective. In addition, we propose a new methodology for fitting measurement data that exhibit long-range dependence into Markovian Arrival Processes (MAPs).;We propose a new methodology, ETAQA, for the exact solution of M/G/1-type processes, (GI/M/1-type processes, and their intersection, i.e., quasi birth-death (QBD) processes. ETAQA computes an aggregate steady state probability distribution and a set of measures of interest. E TAQA is numerically stable and computationally superior to alternative solution methods. Apart from ETAQA, we propose a new methodology for the exact solution of a class of GI/G/1-type processes based on aggregation/decomposition.;Finally, we demonstrate the applicability of the proposed techniques by evaluating load balancing policies in clustered Web servers. We address the high variability in the service process of Web servers by dedicating the servers of a cluster to requests of similar sizes and propose new, content-aware load balancing policies. Detailed analysis shows that the proposed policies achieve high user-perceived performance and, by continuously adapting their scheduling parameters to the current workload characteristics, provide good performance under conditions of transient overload
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