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Young Myoung Ko

Publications and source records attributed to Young Myoung Ko.

9 recordsLinked to original sources

Patch-based Memory Gate Model in Time Series Foundation Model

Recently reconstruction-based deep models have been widely used for time series anomaly detection, but as their capacity and generalization capability increase, these models tend to over-generalize, often reconstructing unseen anomalies accurately. Prior works have attempted to mitigate this by incorporating a memory architecture that stores prototypes of normal patterns. Nevertheless, these approaches suffer from high training costs and have yet to be effectively integrated with time series foundation models (TSFMs). To address these challenges, we propose MOMEMTO, an improved TSFM variant for anomaly detection, enhanced with a patch-based memory module to mitigate over-generalization. The memory module is designed to capture representative normal patterns from multiple domains and enables a single model to be jointly fine-tuned across these domains through a multi-domain training strategy. MOMEMTO initializes memory items with latent representations from a pre-trained encoder, organizes them into patch-level units, and updates them via an attention mechanism. We evaluate our method using 23 univariate benchmark datasets. Experimental results demonstrate that MOMEMTO, as a single model, achieves higher scores on AUC and VUS metrics compared to baseline methods, and further enhances the performance of its backbone TSFM, particularly in few-shot learning scenarios.

cs.LG↗

The Number of Overlapping Customers in Erlang-A Queues: An Asymptotic Approach

In this paper, we investigate the number of customers that overlap or coincide with a virtual customer in an Erlang-A queue. Our study provides a novel approach that exploits fluid and diffusion limits for the queue to approximate the mean and variance of the number of overlapping customers. We conduct a detailed analysis of the fluid and diffusion limit differential equations to derive these approximations. We also construct new accurate approximations for the mean and variance of the waiting time in the Erlang-A queue by combining fluid limits with the polygamma function. Our findings have important implications for queueing theory and evaluating the overlap risk of more complicated service systems.

math.PR↗

Distributionally Robust Stratified Sampling for Stochastic Simulations with Multiple Uncertain Input Models

This paper presents a robust version of the stratified sampling method when multiple uncertain input models are considered for stochastic simulation. Various variance reduction techniques have demonstrated their superior performance in accelerating simulation processes. Nevertheless, they often use a single input model and further assume that the input model is exactly known and fixed. We consider more general cases in which it is necessary to assess a simulation's response to a variety of input models, such as when evaluating the reliability of wind turbines under nonstationary wind conditions or the operation of a service system when the distribution of customer inter-arrival time is heterogeneous at different times. Moreover, the estimation variance may be considerably impacted by uncertainty in input models. To address such nonstationary and uncertain input models, we offer a distributionally robust (DR) stratified sampling approach with the goal of minimizing the maximum of worst-case estimator variances among plausible but uncertain input models. Specifically, we devise a bi-level optimization framework for formulating DR stochastic problems with different ambiguity set designs, based on the $L_2$-norm, 1-Wasserstein distance, parametric family of distributions, and distribution moments. In order to cope with the non-convexity of objective function, we present a solution approach that uses Bayesian optimization. Numerical experiments and the wind turbine case study demonstrate the robustness of the proposed approach.

math.OC↗

Reliability Improvement of Circular k-out-of-n: G Balanced Systems through Center of Gravity

This paper considers a circular k-out-of-n: G balance system equipped with homogeneous and stationary units. Building on previous research by Endharta et al. (Reliability Engineering & System Safety, 2018), we propose a new balance definition in circular k-out-of-n: G balance systems based on the concept of center of gravity. According to this condition, a circular k-out-of-n: G balance system is considered balanced if its center of gravity is located at the origin. This new balance condition is not only simple but also advantageous as it covers the previous two balance conditions of symmetry and proportionality. To evaluate the system's reliability, we consider the minimum tie-sets, and extensive numerical studies verify the enhancement of system reliability resulting from the proposed balance definition.

eess.SY↗

QoS-aware energy-efficient workload routing and server speed control policy in data centers: a robust queueing theoretic approach

Operating cloud service infrastructures requires high energy efficiency while ensuring a satisfactory service level. Motivated by data centers, we consider a workload routing and server speed control policy applicable to the system operating under fluctuating demands. Dynamic control algorithms are generally more energy-efficient than static ones. However, they often require frequent information exchanges between routers and servers, making the data centers' management hesitate to deploy these algorithms. This study presents a static routing and server speed control policy that could achieve energy efficiency similar to a dynamic algorithm and eliminate the necessity of frequent communication among resources. We take a robust queueing theoretic approach to response time constraints for the quality of service (QoS) conditions. Each server is modeled as a G/G/1 processor sharing queue, and the concept of uncertainty sets defines the domain of stochastic primitives. We derive an approximative upper bound of sojourn times from uncertainty sets and develop an approximative sojourn time quantile estimation method for QoS. Numerical experiments confirm the proposed static policy offers competitive solutions compared with the dynamic algorithm.

cs.PF↗

Overlapping time of a virtual customer in time-varying many-server queues

Motivated by the ongoing COVID-19 pandemic, this paper investigates customers' infection risk by evaluating the overlapping time of a virtual customer with others in queueing systems. Most of the current methodologies focus on characterizing the risk in stationary systems, which may not apply to the more practical time-varying systems. As such, we propose an approximation framework that relies on the fluid limit to compute the expected overlapping time in time-varying queueing systems. Simulation experiments verify the accuracy of our approach.

math.PR↗

Stabilizing the virtual response time in single-server processor sharing queues with slowly time-varying arrival rates

Motivated by the work of Whitt, who studied stabilization of the mean virtual waiting time (excluding service time) in a $GI_t/GI_t/1/FCFS$ queue, this paper investigates the stabilization of the mean virtual response time in a single-server processor sharing (PS) queueing system with a time-varying arrival rate and a service rate control (a $GI_t/GI_t/1/PS$ queue). We propose and compare a modified square-root (SR) control and a difference-matching (DM) control to stabilize the mean virtual response time of a $GI_t/GI_t/1/PS$ queue. Extensive simulation studies with various settings of arrival processes and service times show that the DM control outperforms the SR control for heavy-traffic conditions, and that the SR control performs better for light-traffic conditions.

cs.PF↗

Critically loaded multi-server queues with abandonments, retrials, and time-varying parameters

In this paper, we consider modeling time-dependent multi-server queues that include abandonments and retrials. For the performance analysis of those, fluid and diffusion models called "strong approximations" have been widely used in the literature. Although they are proven to be asymptotically exact, their effectiveness as approximations in critically loaded regimes needs to be investigated. To that end, we find that existing fluid and diffusion approximations might be either inaccurate under simplifying assumptions or computationally intractable. To address that concern, this paper focuses on developing a methodology by adjusting the fluid and diffusion models so that they significantly improve the estimation accuracy. We illustrate the accuracy of our adjusted models by performing a number of numerical experiments.

math.PR↗

Effectively tailoring fluid and diffusion models for non-stationary state-dependent queueing systems

In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be asymptotically exact, their effectiveness as approximations in the non-asymptotic regime needs to be investigated. We find that existing fluid and diffusion approximations might be either inaccurate under simplifying assumptions or computationally intractable. To address this concern, this paper focuses on developing a methodology based on adjusting the fluid model so that it provides exact mean queue lengths. Further, we provide a computationally tractable algorithm that exploits Gaussian density in order to obtain performance measures of the system. We illustrate the accuracy of our algorithm using a wide variety of numerical experiments.

math.PR↗