Insensitivity of Proportional Fairness in Critically Loaded Bandwidth Sharing Networks

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…

Critically loaded queueing models that are throughput suboptimal

This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and heterogenous, exponential servers. Servers are dynamically chosen to serve customers, and buffers are available for customers waiting to be served. The arrival rates and the number of servers are scaled up in such a way that the processes representing the number of class-$i$ customers in the system, $i\in\mathcal{I}$, fluctuate about a static fluid model, that…

Critically loaded k-limited polling systems

We consider a two-queue polling model with switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$) in each queue. The major benefit of the $k$-limited service discipline is that it - besides bounding the cycle time - effectuates prioritization by assigning different service limits to different queues. System performance is studied in the heavy-traffic regime, in which one of the queues becomes critically loaded with the other queue remaining stable. By using a singular-perturbation technique, we rigorously prove heavy-traffic limits for th…

临界负载队列的相变与离开统计：振荡累积量与广义BRAVO

Phase transitions and departure statistics of critically loaded queues: oscillating cumulants and generalized BRAVO

本研究以队列为非平衡统计力学最小模型，发现稳态队列相变时离开统计累积量偏离泊松分布并振荡，推广了BRAVO效应，该现象或存在于其他边界驱动非平衡系统。

Optimal scheduling of critically loaded multiclass GI/M/n+M queues in an alternating renewal environment

In this paper, we study optimal control problems for multiclass GI/M/n+M queues in an alternating renewal (up-down) random environment in the Halfin-Whitt regime. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, we show that the limits of the diffusion-scaled state processes under non-anticipative, preemptive, work-conserving scheduling policies, are controlled jump diffusions driven by a compound Poisson jump process. We establish the asymptotic optimality of the infinite-horizon discounted and long-run average (ergodic) problems for the q…

带弃权（不执行）的最短队列加入：临界负载与严重过载状态

Join-the-Shortest Queue with Abandonment: Critically Loaded and Heavily Overloaded Regimes

研究带弃权的 Join-the-Shortest Queue 负载均衡系统，通过 State Space Collapse 和 Lyapunov 函数刻画了在临界负载与严重过载等三种状态下稳态队列长度的极限分布。