arXiv subjects

Yige Hong

Publications and source records attributed to Yige Hong.

11 recordsLinked to original sources

arXiv2026

Optimality of a Threshold Policy for a Queueing System with One Fast Server and Two Identical Slow Servers

This paper studies the optimal control problem of a queueing system with three servers: one fast server and two identical slow servers. The two-server version of this problem, with one fast server and one slow server, was introduced by Lin and Kumar (1984), and the optimal policy has been shown to be of threshold type. However, generalizing this result beyond the two-server setting has been considered an open problem. In this paper, we resolve the first nontrivial case by proving that a threshold policy is optimal for the three-server system considered. The core technical ideas in this paper are generated by GPT-5.5 Pro. We have included a short report describing the authors' interactions with GPT-5.5 Pro. The authors verified the proofs and rewrote the paper for better rigor, clarity, and exposition. In addition, three key lemmas have also been verified in Lean 4.

math.OC↗

arXiv2025

An interpretable universal bound for multiserver queues via a leave-one-out technique

Bounding the steady-state queue length of a multiserver queue is a central challenge in queueing theory. Even for the classical $GI/GI/n$ queue with homogeneous servers, obtaining a simple, accurate bound that holds across all parameters is highly non-trivial. A recent breakthrough by Li and Goldberg (2025) establishes the first universal bound of order $O(1/(1-\rho))$, holding for every load $\rho<1$ and server count $n$ -- an order known to be tight in many regimes, including classical heavy-traffic, Halfin-Whitt, and Non-Degenerate Slowdown. However, their bounds carry astronomically large constants and rely on an intricate proof; they conjecture that a far simpler bound holds. We introduce a leave-one-out coupling technique that yields a new universal $O(1/(1-\rho))$ bound for the $GI/GI/n$ queue, with a simple and transparent proof. Moreover, for light-tailed service times, the leading constant in our bound is orders of magnitude smaller than that in prior work. For instance, we bound the $M/GI/n$ queue's mean queue length by simply $1/(1-\rho)$ for New-Better-than-Used-in-Expectation service times, with similarly clean bounds for gamma, phase-type, and bounded service times. Finally, our techniques extend to $GI/GI/n$ queues with fully heterogeneous service-time distributions, a setting not addressed by prior universal bounds.

math.PR↗

arXiv2025

Projection-based Lyapunov method for fully heterogeneous weakly-coupled MDPs

Heterogeneity poses a fundamental challenge for many real-world large-scale decision-making problems but remains largely understudied. In this paper, we study the fully heterogeneous setting of a prominent class of such problems, known as weakly-coupled Markov decision processes (WCMDPs). Each WCMDP consists of $N$ arms (or subproblems), which have distinct model parameters in the fully heterogeneous setting, leading to the curse of dimensionality when $N$ is large. We show that, under mild assumptions, an efficiently computable policy achieves an $O(1/\sqrt{N})$ optimality gap in the long-run average reward per arm for fully heterogeneous WCMDPs as $N$ becomes large. This is the first asymptotic optimality result for fully heterogeneous average-reward WCMDPs. Our main technical innovation is the construction of projection-based Lyapunov functions that certify the convergence of rewards and costs to an optimal region, even under full heterogeneity.

cs.LG↗

arXiv2024

Achieving Exponential Asymptotic Optimality in Average-Reward Restless Bandits without Global Attractor Assumption

We consider the infinite-horizon average-reward restless bandit problem. We propose a novel \emph{two-set policy} that maintains two dynamic subsets of arms: one subset of arms has a nearly optimal state distribution and takes actions according to an Optimal Local Control routine; the other subset of arms is driven towards the optimal state distribution and gradually merged into the first subset. We show that our two-set policy is asymptotically optimal with an $O(\exp(-C N))$ optimality gap for an $N$-armed problem, under the mild assumptions of aperiodic-unichain, non-degeneracy, and local stability. Our policy is the first to achieve \emph{exponential asymptotic optimality} under the above set of easy-to-verify assumptions, whereas prior work either requires a strong \emph{global attractor} assumption or only achieves an $O(1/\sqrt{N})$ optimality gap. We further discuss obstacles in weakening the assumptions by demonstrating examples where exponential asymptotic optimality is not achievable when any of the three assumptions is violated. Notably, we prove a lower bound for a large class of locally unstable restless bandits, showing that local stability is particularly fundamental for exponential asymptotic optimality. Finally, we use simulations to demonstrate that the two-set policy outperforms previous policies on certain RB problems and performs competitively overall.

cs.LG↗

arXiv2024

Analysis of Markovian Arrivals and Service with Applications to Intermittent Overload

In many important real-world queueing settings, arrival and service rates fluctuate over time. We consider the MAMS system, where the arrival and service rates each vary according to an arbitrary finite-state Markov chain, allowing intermittent overload to be modeled. This model has been extensively studied, and we derive results matching those found in the literature via a somewhat novel framework. We derive a characterization of mean queue length in the MAMS system, with explicit bounds for all arrival and service chains at all loads, using our new framework. Our bounds are tight in heavy traffic. We prove even stronger bounds for the important special case of two-level arrivals with intermittent overload. Our framework is based around the concepts of relative arrivals and relative completions, which have previously been used in studying the MAMS system, under different names. These quantities allow us to tractably capture the transient correlational effect of the arrival and service processes on the mean queue length.

cs.PF↗

arXiv2024

Unichain and Aperiodicity are Sufficient for Asymptotic Optimality of Average-Reward Restless Bandits

We consider the infinite-horizon, average-reward restless bandit problem in discrete time. We propose a new class of policies that are designed to drive a progressively larger subset of arms toward the optimal distribution. We show that our policies are asymptotically optimal with an $O(1/\sqrt{N})$ optimality gap for an $N$-armed problem, assuming only a unichain and aperiodicity assumption. Our approach departs from most existing work that focuses on index or priority policies, which rely on the Global Attractor Property (GAP) to guarantee convergence to the optimum, or a recently developed simulation-based policy, which requires a Synchronization Assumption (SA).

cs.LG↗

arXiv2023

The RESET and MARC Techniques, with Application to Multiserver-Job Analysis

Multiserver-job (MSJ) systems, where jobs need to run concurrently across many servers, are increasingly common in practice. The default service ordering in many settings is First-Come First-Served (FCFS) service. Virtually all theoretical work on MSJ FCFS models focuses on characterizing the stability region, with almost nothing known about mean response time. We derive the first explicit characterization of mean response time in the MSJ FCFS system. Our formula characterizes mean response time up to an additive constant, which becomes negligible as arrival rate approaches throughput, and allows for general phase-type job durations. We derive our result by utilizing two key techniques: REduction to Saturated for Expected Time (RESET) and MArkovian Relative Completions (MARC). Using our novel RESET technique, we reduce the problem of characterizing mean response time in the MSJ FCFS system to an M/M/1 with Markovian service rate (MMSR). The Markov chain controlling the service rate is based on the saturated system, a simpler closed system which is far more analytically tractable. Unfortunately, the MMSR has no explicit characterization of mean response time. We therefore use our novel MARC technique to give the first explicit characterization of mean response time in the MMSR, again up to constant additive error. We specifically introduce the concept of "relative completions," which is the cornerstone of our MARC technique.

cs.PF↗

arXiv2023

Restless Bandits with Average Reward: Breaking the Uniform Global Attractor Assumption

We study the infinite-horizon restless bandit problem with the average reward criterion, in both discrete-time and continuous-time settings. A fundamental goal is to efficiently compute policies that achieve a diminishing optimality gap as the number of arms, $N$, grows large. Existing results on asymptotic optimality all rely on the uniform global attractor property (UGAP), a complex and challenging-to-verify assumption. In this paper, we propose a general, simulation-based framework, Follow-the-Virtual-Advice, that converts any single-armed policy into a policy for the original $N$-armed problem. This is done by simulating the single-armed policy on each arm and carefully steering the real state towards the simulated state. Our framework can be instantiated to produce a policy with an $O(1/\sqrt{N})$ optimality gap. In the discrete-time setting, our result holds under a simpler synchronization assumption, which covers some problem instances that violate UGAP. More notably, in the continuous-time setting, we do not require \emph{any} additional assumptions beyond the standard unichain condition. In both settings, our work is the first asymptotic optimality result that does not require UGAP.

cs.LG↗

arXiv2023

Performance of the Gittins Policy in the G/G/1 and G/G/k, With and Without Setup Times

How should we schedule jobs to minimize mean queue length? In the preemptive M/G/1 queue, we know the optimal policy is the Gittins policy, which uses any available information about jobs' remaining service times to dynamically prioritize jobs. For models more complex than the M/G/1, optimal scheduling is generally intractable. This leads us to ask: beyond the M/G/1, does Gittins still perform well? Recent results show Gittins performs well in the M/G/k, meaning that its additive suboptimality gap is bounded by an expression which is negligible in heavy traffic. But allowing multiple servers is just one way to extend the M/G/1, and most other extensions remain open. Does Gittins still perform well with non-Poisson arrival processes? Or if servers require setup times when transitioning from idle to busy? In this paper, we give the first analysis of the Gittins policy that can handle any combination of (a) multiple servers, (b) non-Poisson arrivals, and (c) setup times. Our results thus cover the G/G/1 and G/G/k, with and without setup times, bounding Gittins's suboptimality gap in each case. Each of (a), (b), and (c) adds a term to our bound, but all the terms are negligible in heavy traffic, thus implying Gittins's heavy-traffic optimality in all the systems we consider. Another consequence of our results is that Gittins is optimal in the M/G/1 with setup times at all loads.

cs.PF↗

arXiv2022

Near-Optimal Stochastic Bin-Packing in Large Service Systems with Time-Varying Item Sizes

In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule jobs with time-varying resource requirements is limited. Motivated by this gap, we propose a \emph{new setting} of the stochastic bin-packing problem in service systems that allows for \emph{time-varying} job resource requirements, also referred to as `item sizes' in traditional bin-packing terms. In this setting, a job or `item' must be dispatched to a server or `bin' upon arrival. Its resource requirement may vary over time while in service, following a Markovian assumption. Once the job's service is complete, it departs from the system. Our goal is to minimize the expected number of active servers, or `non-empty bins', in steady state. Under our problem formulation, we develop a job dispatch policy, named Join-Reqesting-Server (JRS). Broadly, JRS lets each server independently evaluate its current job configuration and decide whether to accept additional jobs, balancing the competing objectives of maximizing throughput and minimizing the risk of resource capacity overruns. The JRS dispatcher then utilizes these individual evaluations to decide which server to dispatch each arriving job to. The theoretical performance guarantee of JRS is in the asymptotic regime where the job arrival rate scales large linearly with respect to a scaling factor $r$. We show that JRS achieves an additive optimality gap of $O(\sqrt{r})$ in the objective value, where the optimal objective value is $\Theta(r)$. When specialized to constant job resource requirements, our result improves upon the state-of-the-art $o(r)$ optimality gap. Our technical approach highlights a novel policy conversion framework that reduces the policy design problem into a single-server problem.

cs.PF↗

arXiv2021

Sharp Waiting-Time Bounds for Multiserver Jobs

Multiserver jobs, which are jobs that occupy multiple servers simultaneously during service, are prevalent in today's computing clusters. But little is known about the delay performance of systems with multiserver jobs. We consider queueing models for multiserver jobs in scaling regimes where the system load becomes heavy and meanwhile the total number of servers in the system and the number of servers that a job needs become large. Prior work has derived upper bounds on the queueing probability in this scaling regime. However, without proper lower bounds, the existing results cannot be used to differentiate between policies. In this paper, we study the delay performance by establishing sharp bounds on the mean waiting time of multiserver jobs, where the waiting time of a job is the time spent in queueing rather than in service. We first characterize the exact order of the mean waiting time under the First-Come-First-Serve (FCFS) policy. Then we prove a lower bound on the mean waiting time of all policies, which has an order gap with the mean waiting time under FCFS. Finally, we show that the lower bound is achievable under a priority policy that we call Smallest-Need-First (SNF).

cs.PF↗