arXiv subjects

Jin Guang

Publications and source records attributed to Jin Guang.

8 recordsLinked to original sources

arXiv2026

Diffusion-Based Policies for Dynamic Control of Stochastic Processing Networks

We consider a processing network model with $m$ job classes or buffers, exogenous input flows into some classes, $n$ processing activities, and $p$ servers. Each activity is either a specified server processing jobs of a specified class, or a fictional input server delivering jobs of a specified class; jobs change class in Markovian fashion after completing service. A standard multiclass queueing network, with its one-to-one correspondence between job classes and activities, is a special case, but our general model allows two or more ways to process a given class, and some or all input flows may be turned away at the system manager's discretion. Costs are linear: a holding cost per time unit for each class $i$ job in the system, and a rejection penalty for each class $i$ arrival denied access $(i=1,\ldots,m)$. The system manager makes input control, job routing, and order-of-service decisions to minimize expected discounted costs over an infinite horizon. We formulate an approximating Brownian control problem (BCP) whose state space is the $m$-dimensional nonnegative orthant; control is a drift vector chosen from a bounded polyhedral set, based on dynamic state observations. Using recently developed computational methods, the BCP can be solved numerically in dimensions up to at least $m=50$, and we explain how the numerical solution is translated into an implementable control policy for the queueing system of original interest. Previous work on heavy traffic diffusion approximations suggests that this policy is nearly optimal in the heavy traffic parameter regime, and numerical examples support that conjecture. We also discuss its advantage over an alternative approach, featured in our previous work, where the BCP is replaced by a lower-dimensional "equivalent workload formulation" that is computationally efficient but difficult to interpret in the network of original interest.

math.OC↗

arXiv2025

Functional Limits of Generalized Jackson Networks in Multi-scale Heavy Traffic

We investigate the functional limits of generalized Jackson networks in a multi-scale heavy traffic regime where stations approach full utilization at distinct, separated rates. Our main result shows that the appropriately scaled queue length processes converge weakly to a limit process whose coordinates are mutually independent. This finding reveals the underlying dynamic mechanism that explains the asymptotic independence previously observed only in stationary distributions. The specific form of the limit process is shown to depend on the initial conditions. In this paper, we consider the matching-rate and the lowest-rate initial conditions. Although the corresponding limit processes have different laws, they have the same product-form exponential limiting distribution on the positive orthant as $t\to\infty$. Moreover, we introduce and analyze a blockwise multi-scale heavy traffic regime. In this regime, the network's stations are partitioned into blocks, where stations in different blocks approach the heavy traffic at different rates, while stations within the same block share a common rate. We obtain the functional limits in this regime as well, showing that the limit process exhibits blockwise independence.

math.PR↗

arXiv2025

Asymptotic Product-form Steady-state Distribution for Semimartingale Reflecting Brownian Motion in Multi-scaling Regime

Inspired by Dai et al. [2023], we develop a novel multi-scaling asymptotic regime for semimartingale reflecting Brownian motion (SRBM). In this regime, we establish the steady-state convergence of SRBM to a product-form limit with exponentially distributed components by assuming the P-reflection matrix and a uniform moment bound condition. We further demonstrate that the uniform moment bound condition holds in several subclasses of P-matrices. Our proof approach is rooted in the basic adjoint relationship (BAR) for SRBM proposed by Harrison and Williams [1987a].

math.PR↗

arXiv2024

Steady-State Convergence of the Continuous-Time Routing System with General Distributions in Heavy Traffic

This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those commonly found in the literature, we prove that the scaled steady-state queue length at each station converges weakly to an identical exponential random variable in heavy traffic. Specifically, our results hold under the assumption of the $(2 + \delta_0)$th moment for the interarrival and service distributions with some $\delta_0 > 0$. The proof leverages the Palm version of the basic adjoint relationship (BAR) as a key technique.

math.PR↗

arXiv2024

Uniform Moment Bounds for Generalized Jackson Networks in Multi-scale Heavy Traffic

We establish uniform moment bounds for steady-state queue lengths of generalized Jackson networks (GJNs) in multi-scale heavy traffic as recently proposed by Dai et al. [2023]. Uniform moment bounds lay the foundation for further analysis of the limit stationary distribution. Our result can be used to verify the crucial moment state space collapse (SSC) assumption in Dai et al. [2023] to establish a product-form limit of GJN in the multi-scale heavy traffic regime. Our proof critically utilizes the Palm version of the basic adjoint relationship (BAR) as developed in Braverman et al. [2023].

math.PR↗

arXiv2022

Tail Quantile Estimation for Non-preemptive Priority Queues

Motivated by applications in computing and telecommunication systems, we investigate the problem of estimating p-quantile of steady-state sojourn times in a single-server multi-class queueing system with non-preemptive priorities for p close to 1. The main challenge in this problem lies in efficient sampling from the tail event. To address this issue, we develop a regenerative simulation algorithm with importance sampling. In addition, we establish a central limit theorem for the estimator to construct the confidence interval. Numerical experiments show that our algorithm outperforms benchmark simulation methods. Our result contributes to the literature on rare event simulation for queueing systems.

math.PR↗

arXiv2021

A High-fidelity, Machine-learning Enhanced Queueing Network Simulation Model for Hospital Ultrasound Operations

We collaborate with a large teaching hospital in Shenzhen, China and build a high-fidelity simulation model for its ultrasound center to predict key performance metrics, including the distributions of queue length, waiting time and sojourn time, with high accuracy. The key challenge to build an accurate simulation model is to understanding the complicated patient routing at the ultrasound center. To address the issue, we propose a novel two-level routing component to the queueing network model. We apply machine learning tools to calibrate the key components of the queueing model from data with enhanced accuracy.

cs.LG↗

arXiv2013

Finding overlapping communities in networks using evolutionary method

Community structure is a typical property of many real-world networks, and has become a key to understand the dynamics of the networked systems. In these networks most nodes apparently lie in a community while there often exists a few nodes straddling several communities. An ideal algorithm for community detection is preferable which can identify the overlapping communities in such networks. To represent an overlapping division we develop a encoding schema composed of two segments, the first one represents a disjoint partition and the second one represents a extension of the partition that allows of multiple memberships. We give a measure for the informativeness of a node, and present an evolutionary method for detecting the overlapping communities in a network.

cs.SI↗