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This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed…

Probability · Mathematics 2026-02-11 Michel Mandjes , Daniël Rutgers , Werner Scheinhardt

We consider an automatic overload control for two large service systems modeled as multi-server queues, such as call centers. We assume that the two systems are designed to operate independently, but want to help each other respond to…

Probability · Mathematics 2014-07-30 Ohad Perry , Ward Whitt

Probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account.…

Systems and Control · Electrical Eng. & Systems 2022-03-02 Mengshuo Jia , Qianni Cao , Chen Shen , Gabriela Hug

The ability to predict traffic flow over time for crowded areas during rush hours is increasingly important as it can help authorities make informed decisions for congestion mitigation or scheduling of infrastructure development in an area.…

Machine Learning · Computer Science 2023-04-03 Zann Koh , Yan Qin , Yong Liang Guan , Chau Yuen

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…

Probability · Mathematics 2009-09-29 H. Christian Gromoll , Łukasz Kruk

In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic…

Probability · Mathematics 2010-07-13 Guodong Pang , Ward Whitt

We prove a many-server heavy-traffic fluid limit for an overloaded Markovian queueing system having two customer classes and two service pools, known in the call-center literature as the X model. The system uses the…

Probability · Mathematics 2013-01-24 Ohad Perry , Ward Whitt

We consider a queueing network operating under a strictly upper-triangular routing matrix with per column at most one non-negative entry. The root node is fed by a Gaussian process with stationary increments. Our aim is to characterize the…

Probability · Mathematics 2025-03-24 Nikolai Kriukov , Krzysztof Dȩbicki , Michel Mandjes

We study large-scale systems operating under the JSQ$(d)$ policy in the presence of stringent task-server compatibility constraints. Consider a system with $N$ identical single-server queues and $M(N)$ task types, where each server is able…

Probability · Mathematics 2020-08-25 Daan Rutten , Debankur Mukherjee

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

The fast growing scale and heterogeneity of current communication networks necessitate the design of distributed cross-layer optimization algorithms. So far, the standard approach of distributed cross-layer design is based on dual…

Networking and Internet Architecture · Computer Science 2011-08-11 Jia Liu , Hanif D. Sherali

The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…

Optimization and Control · Mathematics 2021-08-03 Raina Raj , Vidyottama Jain

A parallel server system is a stochastic processing network with applications in manufacturing, supply chain, ride-hailing, call centers, etc. Heterogeneous customers arrive in the system, and only a subset of servers can serve any customer…

Networking and Internet Architecture · Computer Science 2023-01-10 Sushil Mahavir Varma , Siva Theja Maguluri

This paper explores a deep reinforcement learning approach applied to the packet routing problem with high-dimensional constraints instigated by dynamic and autonomous communication networks. Our approach is motivated by the fact that…

Networking and Internet Architecture · Computer Science 2020-03-05 Ramy E. Ali , Bilgehan Erman , Ejder Baştuğ , Bruce Cilli

In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We study load balancing under the Batch Sampling routing scheme for a network of $n$ servers storing a set of files using the…

Probability · Mathematics 2017-07-10 Amarjit Budhiraja , Eric Friedlander

The Join-the-Shortest-Queue (JSQ) load balancing scheme is known to minimise the average response time of jobs in homogeneous systems with identical servers. However, for {\em heterogeneous} systems with servers having different processing…

Probability · Mathematics 2024-10-22 Sanidhay Bhambay , Burak Büke , Arpan Mukhopadhyay

We consider the so-called GI/GI/N queueing network in which a stream of jobs with independent and identically distributed service times arrive according to a renewal process to a common queue served by $N$ identical servers in a…

Probability · Mathematics 2017-12-06 Reza Aghajani , Kavita Ramanan

We consider a two-node tandem queueing network in which the upstream queue is M/G/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. We investigate…

Probability · Mathematics 2017-02-08 H. Christian Gromoll , Bryce Terwilliger , Bert Zwart

In this paper, we consider a load balancing system under a general pull-based policy. In particular, each arrival is randomly dispatched to one of the servers whose queue lengths are below a threshold, if there are any; otherwise, this…

Performance · Computer Science 2018-08-22 Xingyu Zhou , Jian Tan , Ness Shroff

In Internet environment, traffic flow to a link is typically modeled by superposition of ON/OFF based sources. During each ON-period for a particular source, packets arrive according to a Poisson process and packet sizes (hence service…

Probability · Mathematics 2015-08-28 Wanyang Dai