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We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit…

Probability · Mathematics 2010-01-14 Anatolii A. Puhalskii , Josh E. Reed

This paper considers a novel travel-delay-based Max Pressure algorithm for control of arbitrary transportation networks with signalized intersections. The traditional number-of-vehicle-based Max Pressure (Original-MP) algorithm has received…

Optimization and Control · Mathematics 2022-10-14 Hao Liu , Vikash V. Gayah

We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation…

Probability · Mathematics 2013-02-14 Niek Bouman , Sem C. Borst , Onno J. Boxma , Johan S. H. van Leeuwaarden

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers…

Probability · Mathematics 2014-01-22 Xin Liu , Qi Gong , Vidyadhar G. Kulkarni

This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…

Probability · Mathematics 2024-09-05 B. R. Vinay Kumar , Lasse Leskelä

Lyapunov drift and Lyapunov optimization are powerful techniques for optimizing time averages in stochastic queueing networks subject to stability. However, there are various definitions of queue stability in the literature, and the most…

Optimization and Control · Mathematics 2010-10-28 Michael J. Neely

The Markovian arrival process (MAP) has proven a versatile model for fitting dependent and non-exponential interarrival times, with a number of applications to queueing, teletraffic, reliability or finance. Despite theoretical properties of…

Computation · Statistics 2014-01-15 Emilio Carrizosa , Pepa Ramírez-Cobo

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…

Probability · Mathematics 2025-08-26 Zhen-Qing Chen , J. G. Dai , Jin Guang

Consideration is given to the three different analytical methods for the computation of upper bounds for the rate of convergence to the limiting regime of one specific class of (in)homogeneous continuous-time Markov chains. This class is…

The Foster-Lyapunov theorem and its variants serve as the primary tools for studying the stability of queueing systems. In addition, it is well known that setting the drift of the Lyapunov function equal to zero in steady-state provides…

Probability · Mathematics 2015-03-19 Atilla Eryilmaz , R. Srikant

Focusing on stochastic systems arising in mean-field models, the systems under consideration belong to the class of switching diffusions, in which continuous dynamics and discrete events coexist and interact. The discrete events are modeled…

Probability · Mathematics 2019-01-18 Son L. Nguyen , George Yin , Tuan A. Hoang

Considering a Manhattan mobility model in vehicle-to-vehicle networks, this work studies a power minimization problem subject to second-order statistical constraints on latency and reliability, captured by a network-wide maximal data queue…

Networking and Internet Architecture · Computer Science 2018-10-30 Chen-Feng Liu , Mehdi Bennis

We study the steady-state delay performance of load balancing in large-scale systems with heterogeneous servers in the heavy-traffic regimes. The system consists of $N$ servers, each with a local buffer of size $b-1$, serving jobs in the…

Probability · Mathematics 2026-02-27 Xin Liu , Lei Ying

We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…

Probability · Mathematics 2008-03-19 David Gamarnik , Petar Momcilovic

This paper considers a wireless link with randomly arriving data that is queued and served over a time-varying channel. It is known that any algorithm that comes within $\epsilon$ of the minimum average power required for queue stability…

Optimization and Control · Mathematics 2014-11-19 Michael J. Neely

In this paper, motivated by considerations of server utilization and energy consumptions in cloud computing, we investigate a homogeneous queueing system with a threshold-based workload control scheme. In this system, a virtual machine will…

Probability · Mathematics 2018-07-18 Qihui Bu , Liwei Liuand Yiqiang Q. Zhao

In this article, we consider a continuous review (s, S) inventory system with failures of demand fulfillment (service) modeled as a Markov-modulated retrial queueing system. The inventory system features a single product that experiences…

Probability · Mathematics 2023-07-18 James Cordeiro , Ying-Ju Chen , Andres Larrain-Hubach , Mark Abramson

Service systems like data centers and ride-hailing are popularly modeled as queueing systems in the literature. Such systems are primarily studied in the steady state due to their analytical tractability. However, almost all applications in…

Probability · Mathematics 2025-08-28 Hoang Huy Nguyen , Sushil Mahavir Varma , Siva Theja Maguluri

We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies…

Probability · Mathematics 2012-03-07 Devavrat Shah , Damon Wischik

Max weighted queue (MWQ) control policy is a widely used cross-layer control policy that achieves queue stability and a reasonable delay performance. In most of the existing literature, it is assumed that optimal MWQ policy can be obtained…

Systems and Control · Computer Science 2013-11-20 Junting Chen , Vincent K. N. Lau