The BAR approach for multiclass queueing networks with SBP service policies
The basic adjoint relationship (BAR) approach is an analysis technique based on the
stationary equation of a Markov process. This approach was introduced to study heavy …
stationary equation of a Markov process. This approach was introduced to study heavy …
Transform methods for heavy-traffic analysis
D Hurtado-Lange, ST Maguluri - Stochastic Systems, 2020 - pubsonline.informs.org
The drift method was recently developed to study queuing systems in steady state. It was
used successfully to obtain bounds on the moments of the scaled queue lengths that are …
used successfully to obtain bounds on the moments of the scaled queue lengths that are …
Performance of the Gittins policy in the G/G/1 and G/G/k, with and without setup times
We consider the classic problem of preemptively scheduling jobs of unknown size (aka
service time) in a queue to minimize mean number-in-system, or equivalently mean …
service time) in a queue to minimize mean number-in-system, or equivalently mean …
A load balancing system in the many-server heavy-traffic asymptotics
D Hurtado-Lange, ST Maguluri - Queueing Systems, 2022 - Springer
We study a load balancing system in the many-server heavy-traffic regime. We consider a
system with N servers, where jobs arrive to the system according to a Poisson process and …
system with N servers, where jobs arrive to the system according to a Poisson process and …
Heavy traffic distribution of queueing systems without resource pooling
P Jhunjhunwala, ST Maguluri - arXiv preprint arXiv:2206.06504, 2022 - arxiv.org
This paper studies the heavy-traffic joint distribution of queue lengths in two stochastic
processing networks (SPN), viz., an input-queued switch operating under the MaxWeight …
processing networks (SPN), viz., an input-queued switch operating under the MaxWeight …
[PDF][PDF] Asymptotic product-form steady-state for generalized Jackson networks in multi-scale heavy traffic
We prove that under a multi-scale heavy traffic condition, the stationary distribution of the
scaled queue length vector process in any generalized Jackson network has a product-form …
scaled queue length vector process in any generalized Jackson network has a product-form …
Stein's method for the single server queue in heavy traffic
Following recent developments in the application of Stein's method in queueing theory, this
paper is intended to be a short treatment showing how Stein's method can be developed …
paper is intended to be a short treatment showing how Stein's method can be developed …
On uniform exponential ergodicity of Markovian multiclass many-server queues in the Halfin–Whitt regime
A Arapostathis, H Hmedi… - Mathematics of Operations …, 2021 - pubsonline.informs.org
We study ergodic properties of Markovian multiclass many-server queues that are uniform
over scheduling policies and the size of the system. The system is heavily loaded in the …
over scheduling policies and the size of the system. The system is heavily loaded in the …
Steady-state convergence of the continuous-time JSQ system with general distributions in heavy traffic
Steady-State Convergence of the Continuous-Time JSQ System with General Distributions in
Heavy Traffic Page 1 Steady-State Convergence of the Continuous-Time JSQ System with …
Heavy Traffic Page 1 Steady-State Convergence of the Continuous-Time JSQ System with …
Uniform moment bounds for generalized Jackson networks in multi-scale heavy traffic
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 …
Jackson networks (GJNs) in multi-scale heavy traffic as recently proposed by Dai et …