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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.

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].

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.

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., Comment: 21 pages, 15 figures

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.