arXiv subjects

Seung Min Baik

Publications and source records attributed to Seung Min Baik.

4 recordsLinked to original sources

arXiv2025

Lifetime Analysis of Circular $k$-out-of-$n$: G Balanced Systems in a Shock Environment

This paper examines the lifetime distributions of circular $k$-out-of-$n$: G balanced systems operating in a shock environment, providing a unified framework for both discrete- and continuous-time perspectives. The system remains functioning only if at least $k$ operating units satisfy a predefined balance condition (BC). Building on this concept, we demonstrate that the shock numbers to failure (SNTF) follow a discrete phase-type distribution by modeling the system's stochastic dynamics with a finite Markov chain and applying BC-based state space consolidation. Additionally, we develop a computationally efficient method for directly computing multi-step transition probabilities of the underlying Markov chain. Next, assuming the inter-arrival times between shocks follow a phase-type distribution, we establish that the continuous-time system lifetime, or the time to system failure (TTF), also follows a phase-type distribution with different parameters. Extensive numerical studies illustrate the impact of key parameters-such as the number of units, minimum requirement of the number of operating units, individual unit reliability, choice of balance condition, and inter-shock time distribution-on the SNTF, TTF, and their variability.

eess.SY↗

arXiv2023

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↗

arXiv2023

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↗

arXiv2023

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↗