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

A comprehensive literature classification of simulation optimisation methods

Simulation Optimization (SO) provides a structured approach to the system design and configuration when analytical expressions for input/output relationships are unavailable. Several excellent surveys have been written on this topic. Each survey concentrates on only few classification criteria. This paper presents a literature survey with all classification criteria on techniques for SO according to the problem of characteristics such as shape of the response surface (global as compared to local optimization), objective functions (single or multiple objectives) and parameter spaces (discrete or continuous parameters). The survey focuses specifically on the SO problem that involves single per-formance measureSimulation Optimization, classification methods, literature survey

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

Flow Level QoE of Video Streaming in Wireless Networks

The Quality of Experience (QoE) of streaming service is often degraded by frequent playback interruptions. To mitigate the interruptions, the media player prefetches streaming contents before starting playback, at a cost of delay. We study the QoE of streaming from the perspective of flow dynamics. First, a framework is developed for QoE when streaming users join the network randomly and leave after downloading completion. We compute the distribution of prefetching delay using partial differential equations (PDEs), and the probability generating function of playout buffer starvations using ordinary differential equations (ODEs) for CBR streaming. Second, we extend our framework to characterize the throughput variation caused by opportunistic scheduling at the base station, and the playback variation of VBR streaming. Our study reveals that the flow dynamics is the fundamental reason of playback starvation. The QoE of streaming service is dominated by the first moments such as the average throughput of opportunistic scheduling and the mean playback rate. While the variances of throughput and playback rate have very limited impact on starvation behavior.Comment: 14 page

Structural Properties of the Stability of Jamitons

It is known that inhomogeneous second-order macroscopic traffic models can reproduce the phantom traffic jam phenomenon: whenever the sub-characteristic condition is violated, uniform traffic flow is unstable, and small perturbations grow into nonlinear traveling waves, called jamitons. In contrast, what is essentially unstudied is the question: which jamiton solutions are dynamically stable? To understand which stop-and-go traffic waves can arise through the dynamics of the model, this question is critical. This paper first presents a computational study demonstrating which types of jamitons do arise dynamically, and which do not. Then, a procedure is presented that characterizes the stability of jamitons. The study reveals that a critical component of this analysis is the proper treatment of the perturbations to the shocks, and of the neighborhood of the sonic points.Comment: 22 page, 6 figure