694 research outputs found
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
Non-expected utility vs. expected utility theory in consumption/savings decisions over the life cycle
Diese Dissertation beschäftigt sich mit der Frage, ob die Rank-Dependent Utility Theorie oder die Cumulative Prospect Theorie, welche zu den sogenannten Nicht-Erwartungsnutzen Theorien gehören, reale Daten über Konsum- und
Sparentscheidungen besser abbilden können als die Erwartungsnutzentheorie.
Wir verwenden ein Konsum/Spar Modell and die Methode der Simulierten Momente um zwei Parameter zu schätzen, welche in unserem Aufbau die Rank-Dependent Utility Theory, die Cumulative Prospect Theorie und die Erwartungsnutzentheorie
unterscheiden. Wir schlagen für das Auflösen des Modells
eine Methode vor, für welche die Kritik hinsichtlich dem Gebrauch von Nicht-Erwartungsnutzen Theorien in dynamischen Modellen nicht zutreffend
ist. Das Endergebnis ist, dass die Rank-Dependent Utility Theorie die Daten am besten abbilden kann.This thesis deals with the question if Rank-Dependent Utility or Cumulative Prospect Theory, belonging to the so called Non-Expected Utility models, are better in explaining real life data on consumption and savings decisions than Expected Utility Theory. We use a consumption/savings model and the Method
of Simulated Moments to estimate two parameters, which distinguish Expected Utility, Rank-Dependent Utility and Cumulative Prospect Theory in our setting.
For the solution of the model we propose a method to which the conventional critique on Non-Expected Utility in dynamic settings does not apply. Our main finding is that Rank-Dependent Utility Theory is the theory which
fits the data best
Stochastic analysis of nonlinear dynamics and feedback control for gene regulatory networks with applications to synthetic biology
The focus of the thesis is the investigation of the generalized repressilator model
(repressing genes ordered in a ring structure). Using nonlinear bifurcation analysis
stable and quasi-stable periodic orbits in this genetic network are characterized
and a design for a switchable and controllable genetic oscillator is proposed. The
oscillator operates around a quasi-stable periodic orbit using the classical engineering
idea of read-out based control. Previous genetic oscillators have been
designed around stable periodic orbits, however we explore the possibility of
quasi-stable periodic orbit expecting better controllability.
The ring topology of the generalized repressilator model has spatio-temporal
symmetries that can be understood as propagating perturbations in discrete lattices.
Network topology is a universal cross-discipline transferable concept and
based on it analytical conditions for the emergence of stable and quasi-stable
periodic orbits are derived. Also the length and distribution of quasi-stable oscillations
are obtained. The findings suggest that long-lived transient dynamics
due to feedback loops can dominate gene network dynamics.
Taking the stochastic nature of gene expression into account a master equation
for the generalized repressilator is derived. The stochasticity is shown to influence
the onset of bifurcations and quality of oscillations. Internal noise is shown to
have an overall stabilizing effect on the oscillating transients emerging from the
quasi-stable periodic orbits.
The insights from the read-out based control scheme for the genetic oscillator
lead us to the idea to implement an algorithmic controller, which would direct
any genetic circuit to a desired state. The algorithm operates model-free, i.e. in
principle it is applicable to any genetic network and the input information is a
data matrix of measured time series from the network dynamics. The application
areas for readout-based control in genetic networks range from classical tissue
engineering to stem cells specification, whenever a quantitatively and temporarily
targeted intervention is required
A Queueing Model to Study Ambulance Offload Delays
The ambulance offload delay problem is a well-known result of overcrowding and congestion in emergency departments. Offload delay refers to the situation where area hospitals are unable to accept patients from regional ambulances in a timely manner due to lack of staff and bed capacity. The problem of offload delays is not a simple issue to resolve and has caused severe problems to the emergency medical services (EMS) providers, emergency department (ED) staff, and most importantly patients that are transferred to hospitals by ambulance. Except for several reports on the problem, not much research has been done on the subject. Almost all research to date has focused on either EMS or ED planning and operation and as far as we are aware there are no models which have considered the coordination of these units. We propose an analytical model which will allow us to analyze and explore the ambulance offload delay problem. We use queuing theory to construct a system representing the interaction of EMS and ED, and model the behavior of the system as a continuous time Markov chain. The matrix geometric method will be used to numerically compute various system performance measures under different conditions.
We analyze the effect of adding more emergency beds in the ED, adding more ambulances, and reducing the ED patient length of stay, on various system performance measures such as the average number of ambulances in offload delay, average time in offload delay, and ambulance and bed utilization. We will show that adding more beds to the ED or reducing ED patient length of stay will have a positive impact on system performance and in particular will decrease the average number of ambulances experiencing offload delay and the average time in offload delay. Also, it will be shown that increasing the number of ambulances will have a negative impact on offload delays and increases the average number of ambulances in offload delay. However, other system performance measures are improved by adding more ambulances to the system. Finally, we will show the tradeoffs between adding more emergency beds, adding more ambulances, and reducing ED patient length of stay. We conclude that the hospital is the bottleneck in the system and in order to reduce ambulance offload delays, either hospital capacity has to be increased or ED patient length of stay is to be reduced
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Nearly reducible finite Markov chains: theory and algorithms
Finite Markov chains are probabilistic network models that are commonly used as representations of dynamical processes in the physical sciences, biological sciences, economics, and elsewhere. Markov chains that appear in realistic modelling tasks are frequently observed to be nearly reducible, incorporating a mixture of fast and slow processes that leads to ill-conditioning of the underlying matrix of probabilities for transitions between states. Hence, the wealth of established theoretical results that makes Markov chains attractive and convenient models often cannot be used straightforwardly in practice, owing to numerical instability associated with the standard computational procedures to evaluate the expressions. This work is concerned with the development of theory, algorithms, and simulation methods for the efficient and numerically stable analysis of finite Markov chains, with a primary focus on exact approaches that are robust and therefore applicable to nearly reducible networks. New methodologies are presented to determine representative paths, identify the dominant transition mechanisms for a particular process of interest, and analyze the local states that have a strong influence on the characteristics of the global dynamics. The novel approaches yield new insights into the behaviour of Markovian networks, addressing and overcoming numerical challenges. The methodology is applied to example models that are relevant to current problems in chemical physics, including Markov chains representing a protein folding transition, and a configurational transition in an atomic cluster.
Relevant classical theory of finite Markov chains and a description of existing robust algorithms for their numerical analysis is given in Chapter 1. The remainder of this thesis considers the problem of investigating a transition from an initial set of states in a Markovian network to an absorbing (target) macrostate.
A formal approach to determine a finite set of representative transition paths is proposed in Chapter 2, based on exact pathwise decomposition of the total productive flux. This analysis allows for the importance of competing dynamical processes to be rigorously quantified. A robust state reduction algorithm to compute the expectation of any path property for a transition between two endpoint states is also described in Chapter 2.
Chapter 3 reports further numerically stable state reduction algorithms to compute quantities that characterize the features of a transition at a statewise level of detail, allowing for identification of the local states that play a key role in modulating the slow dynamics. An expression is derived for the probability that a state is visited on a path that proceeds directly to the absorbing state without revisiting the initial state, which characterizes the dynamical relevance of an individual state to the overall transition process.
In Chapter 4, an unsupervised strategy is proposed to utilize a highly efficient simulation algorithm for sampling paths on a Markov chain. The framework employs a scalable community detection algorithm to obtain an initial clustering of the network into metastable sets of states, which is subsequently refined by a variational optimization procedure. The optimized clustering is then used as the basis for simulating trajectory segments that necessarily escape from the metastable macrostates.
The thesis is concluded with an overview of recent related advances that are beyond the scope of the current work (Chapter 5), and a discussion of potential applications where the novel methodology reported herein may be applied to perform insightful analyses that were previously intractable.Cambridge Commonwealth, European and International Trust
Engineering and Physical Sciences Research Counci
Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]
An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u
Proceedings, MSVSCC 2013
Proceedings of the 7th Annual Modeling, Simulation & Visualization Student Capstone Conference held on April 11, 2013 at VMASC in Suffolk, Virginia
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