University of Waterloo
http://hdl.handle.net/10012/1
The University of Waterloo institution-wide UWSpace community.2023-12-10T14:48:20ZTopics in Modeling and Analysis of Low-Latency Systems
http://hdl.handle.net/10012/20145
Topics in Modeling and Analysis of Low-Latency Systems
Ghanbarian, Samira
Cloud-based architectures have become integral elements of modern networking infrastructure and are characterized by a large number of servers operating in parallel. Optimizing performance in these systems, with a particular focus on specific metrics such as system response time and the probability of loss, is critical to ensure user satisfaction. To address this challenge, this thesis analyzes load balancing policies that are designed to efficiently assign incoming user requests to the servers such that the system performance is optimized. In particular, the thesis focuses on a specialized category known as "randomized dynamic load balancing policies". These policies optimize system performance by dynamically adapting assignment decisions based on the current state of the system while interacting with a randomly selected subset of servers. Given the complex interdependencies among servers and the large size of these systems, an exact analysis of these systems is intractable. Consequently, the thesis studies these systems in the system size limit. It employs relevant limit theorems, including mean-field techniques and Stein's approach, as crucial mathematical tools. Furthermore, the thesis evaluates the accuracy of these limits when applied to systems of finite size, providing valuable insights into the practical applicability of the proposed load balancing policies.
Motivated by different types of user requests or jobs, the thesis focuses on two main job categories: single-server jobs which can only run on a single server to represent non-parallelizable requests, and multiserver jobs, which can run on multiple servers simultaneously modeling parallelizable requests.
The first part of the thesis studies single-server jobs in a system comprising a large number of processor sharing servers operating in parallel, where servers have different processing speeds and unlimited queueing buffers. The objective is to design randomized load balancing policies that minimize the average response time of jobs. A novel policy is introduced that allocates incoming jobs to servers based on predefined thresholds, state information from a randomly sampled subset of servers, and their processing speeds. The policy subsumes a broad class of other load balancing policies by adjusting the threshold levels, offering a unified framework for concurrent analysis of multiple load balancing policies. It is shown that under this policy, the system achieves the maximal stability region. Moreover, it is shown that as the system size approaches infinity, the transient and stationary stochastic occupancy measure of the system converges to a deterministic mean-field limit and the unique fixed point of this mean-field limit, respectively. As a result, the study of the asymptotic average response time of jobs becomes feasible through the fixed point of the mean-field limit. The analysis continues by studying error estimation related to asymptotic values in finite-sized systems. It is shown that when the mean delay of the finite-size system is approximated by its asymptotic value, the error is proportional to the inverse square root of the system size.
Subsequently, the thesis analyzes adaptive multiserver jobs in loss systems, where they can be parallelized across a variable number of servers, up to a maximum degree of parallelization. In loss systems, each server can process only a finite number of jobs simultaneously and blocks any additional jobs beyond this capacity. Therefore, the goal is to devise randomized job assignment schemes that optimize the average response time of accepted jobs and the blocking probability while interacting with a sampled subset of servers. A load balancing policy is proposed, where the number of allocated servers for processing each job depends on the state information of a randomly sampled subset of servers and the maximum degree of parallelization. Employing Stein's method, it is shown that, provided that the sampling size grows at an appropriate rate, the difference between the steady-state system and a suitable deterministic system that exhibits optimality, decreases to zero as the system size increases. Thus, as the system size approaches infinity, the steady-state system achieves a zero blocking probability and optimal average response time for accepted jobs. Additionally, the thesis analyzes error estimation for these asymptotic values in finite-sized systems and establishes the error bounds as a function of the number of servers in the system.
2023-12-08T00:00:00ZHydride Generation as a Sample Introduction Technique for Detection of Arsenic by Microplasma
http://hdl.handle.net/10012/20144
Hydride Generation as a Sample Introduction Technique for Detection of Arsenic by Microplasma
Qadeer, Laiba
Microplasma can be used as a portable analytical instrument for elemental analysis of samples due to their small size, low power consumption, low carrier gas consumption, and low cost. This is specifically important for areas where contamination of water by arsenic is prevalent (e.g., because arsenic is indigenous to the soil). Due to the volatility of arsenic and its organic compounds, it is only chemical vapor generation (CVG) that can be used to introduce the sample into the microplasma. In this project, equipment for hydride generation (a type of CVG) was designed and used to test this sample introduction technique for microplasma. It was found that response of microplasma towards water vapors and hydrogen released from the hydride generation reaction was different when it was operated in each of three different carrier gases, namely helium, argon, and mixture of argon with 1000 ppm hydrogen. Similarly, the best observation position for arsenic over the microplasma tube was also different for helium microplasma and argon microplasma (0.84 cm and 1.34 cm away from the front electrode where carrier gas and analyte are introduced, respectively). Arsenic signals were also found to be more intense in helium microplasma, as compared to that in argon microplasma and argon – 1000 ppm hydrogen microplasma. Afterwards, the arsenic peaks at 197.3 nm and 228.8 nm were used to estimate the detection limit for arsenic in helium microplasma and argon microplasma, respectively. The detection limit for arsenic in helium and argon microplasma were estimated to be 31 ppb and 40 ppb, respectively. Although this project proved the feasibility of microplasma for detecting arsenic in liquid samples, it was concluded that more research is needed in this field to improve the reproducibility in the measurement of emission signal and the detection limit for arsenic, by making changes in the equipment and the design of gas-liquid separator.
2023-12-08T00:00:00ZAnalyzing Issues of Privacy and Offline Transactions In Central Bank Digital Currencies
http://hdl.handle.net/10012/20143
Analyzing Issues of Privacy and Offline Transactions In Central Bank Digital Currencies
Lee, Michael
With the popularity of cryptocurrencies like bitcoin and Ethereum, many central banks have begun to look into issuing their own digital currency. For many central banks, the goal of a central bank digital currency (CBDC) is to provide a user experience similar to paper money, but fully digital. The central bank also plays an important role in the system, namely acting as a source of trust. This source of trust is an important differentiator, as it incentivizes the use of alternative technologies to confirm transactions, rather than using inefficient consensus protocols such as a proof-of-work blockchain.
In order to act as a true paper money alternative, two of the biggest hurdles that need to be overcome are privacy and offline transactions. In this thesis, we will examine these issues in more detail, discussing what problems they pose and what (if any) solutions have been presented in the existing literature. Additionally, we will be offering our own solutions, using hash chains to provide user privacy, and presenting a prototype CBDC system for offline transactions.
2023-12-08T00:00:00ZExpanding the Scope of Random Feature Models: Theory and Applications
http://hdl.handle.net/10012/20142
Expanding the Scope of Random Feature Models: Theory and Applications
Saha, Esha
Data, defined as facts and statistics collected together for analysis is at the core of every inference or decision made by any living organism. Right from the time we are born, our brain collects data from everything that is happening around us and helps us to make decisions based on past experiences. With the advent of technology, humans have been trying to develop methods that can learn from data and generalize well based on past information. While this attempt has been greatly successful with the development of the machine learning community, one parallel field that also developed along with it is the need to have a theoretical understanding of these methods. It is important to understand the workings of the algorithms to be able to quantify the cause and nature of the error they can make so that informed decisions can be made using these results, especially for sensitive applications such as in the medical field.
At the heart of these methods lies the mathematical formulation and analysis of such learning algorithms. One such method that particularly caught the attention of researchers recently is the random feature model (RFM), introduced for reducing the complexity and faster computation of kernel methods in large-scale machine learning algorithms. These classes of methods can provide theoretical interpretations and have the potential to perform well numerically, thus being more reliable than black box methods such as deep neural networks.
This thesis aims to explore RFMs by expanding their theory and applications in the machine-learning community. We begin our exploration by developing a fast algorithm for high dimensional function approximation using a random feature-based surrogate model. Assuming the target function is a lower-order additive function, we incorporate sparsity as a side information within our model to get numerical results that are better (or comparable) to other well-known methods and also provide risk and error bounds for our model. Extending the idea of learning functions, we build a model to learn and predict the dynamics of an epidemic from incomplete and scarce data. This model combines the idea of random feature approximation with the use of Takens' delay embedding theorem on the given input data. RFMs have majorly been explored in a form that resembles a shallow neural network with fixed hidden parameters.
In our third project, motivated to work on the idea of multiple layers in an RFM, we propose an interpretable RFM whose architecture is inspired by diffusion models. We make the model interpretable by providing error bounds on the sampled data from its true distribution and show numerically that the proposed model is capable of generating images from data as well as denoising it.
2023-12-07T00:00:00Z