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Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…

Analysis of PDEs · Mathematics 2023-09-28 Jonathan R. Potts , Kevin J. Painter

We study $n$ parallel queues in an extreme heavy-traffic regime: each server works at rate $n$, while jobs arrive to a dispatcher at rate $n^2-(a-b)\sqrt{n}$, with fixed $a>b>0$. Arrivals are routed by a marginal join-the-shortest-queue…

Probability · Mathematics 2026-05-19 Sayan Banerjee , Amarjit Budhiraja , Eva Loeser

We consider the processor sharing $M/M/1$-PS queue which also models balking. A customer that arrives and sees $n$ others in the system "balks" (i.e., decides not to enter) with probability $1-b_n$. If $b_n$ is inversely proportional to…

Probability · Mathematics 2011-04-26 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl

We study an optimal-control problem of polling systems with large switchover times, when a holding cost is incurred on the queues. In particular, we consider a stochastic network with a single server that switches between several buffers…

Probability · Mathematics 2020-09-01 Yue Hu , Jing Dong , Ohad Perry

We study the generic non-equilibrium steady states in asymmetric exclusion processes on a closed network with bottlenecks. To this end we proposes and study closed simple networks with multiply-connected non-identical junctions. Depending…

Statistical Mechanics · Physics 2015-01-13 Rakesh Chatterjee , Anjan Kumar Chandra , Abhik Basu

A new approach to the steady state detection in the uniformization method of solving continuous time Markov chains is introduced. The method is particularly useful in solving inhomogenous CTMC's in multiple steps, where the desired error…

Performance · Computer Science 2014-10-14 Maciej Burak

The Join-the-Shortest Queue (JSQ) policy is a classical benchmark for the performance of many-server queueing systems due to its strong optimality properties. While the exact analysis of the JSQ policy is an open question to date, even…

Probability · Mathematics 2025-05-27 Zhisheng Zhao , Sayan Banerjee , Debankur Mukherjee

We study infinite-horizon asymptotic average optimality for parallel server network with multiple classes of jobs and multiple server pools in the Halfin-Whitt regime. Three control formulations are considered: 1) minimizing the queueing…

Optimization and Control · Mathematics 2019-03-20 Ari Arapostathis , Guodong Pang

Steady-state solutions for a variety of relevant queueing systems are known today, e.g., from queueing theory, effective bandwidths, and network calculus. The behavior during transient phases, on the other hand, is understood to a much…

Networking and Internet Architecture · Computer Science 2015-06-16 Nico Becker , Markus Fidler

We consider a multi-class G/G/1 queue with a finite shared buffer. There is task admission and server scheduling control which aims to minimize the cost which consists of holding and rejection components. We construct a policy that is…

Performance · Computer Science 2015-08-31 Mark Shifrin

Explicit results are derived using simple and exact methods for the joint and marginal queue-length distributions for the M/M/c queue with two non-preemptive priority levels. Equal service rates are assumed. Two approaches are considered.…

Probability · Mathematics 2023-09-19 Josef Zuk , David Kirszenblat

The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…

Optimization and Control · Mathematics 2012-10-09 Moussa Balde , Philippe Jouan

We study optimal scheduling in multi-class queueing systems with reentrance, where jobs may return for additional service after completion. Such reentrance creates feedback loops that fundamentally alter congestion dynamics and challenge…

Optimization and Control · Mathematics 2025-09-16 Lin Franklin Feng , Yue Hu , Xu Kuang

This paper studies the sensitivity (or insensitivity) of a class of load balancing algorithms that achieve asymptotic zero-waiting in the sub-Halfin-Whitt regime, named LB-zero. Most existing results on zero-waiting load balancing…

Probability · Mathematics 2022-02-17 Xin Liu , Kang Gong , Lei Ying

In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…

Optimization and Control · Mathematics 2021-12-01 Andrea Zanelli , Quoc Tran Dinh , Moritz Diehl

We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…

Probability · Mathematics 2017-01-02 Carlo Lancia , Gianluca Guadagni , Sokol Ndreca , Benedetto Scoppola

Multiuser Multi-Packet Transmission (MPT) from an Access Point (AP) equipped with multiple antennas to multiple single-antenna nodes can be achieved by exploiting the spatial dimension of the channel. In this paper we present a queueing…

Networking and Internet Architecture · Computer Science 2013-10-22 Boris Bellalta , Azadeh Faridi , Jaume Barcelo , Vanesa Daza , Miquel Oliver

We develop a switched predictor-feedback law, which achieves global asymptotic stabilization of linear systems with input delay and with the plant and actuator states available only in (almost) quantized form. The control design relies on a…

Optimization and Control · Mathematics 2024-09-06 Florent Koudohode , Nikolaos Bekiaris-Liberis

This paper studies the heavy-traffic asymptotics for the multiclass FIFO M${}^X$/G/1 queue. We first derive the probability generating function of the joint queue length distribution. Using the probability generating function, we then…

Probability · Mathematics 2014-04-25 Hiroshi Miyawaki , Hiroyuki Masuyama , Yutaka Takahashi

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service…

Classical Analysis and ODEs · Mathematics 2013-09-13 Qiang Zhen , Charles Knessl