Related papers: Systems with large flexible server pools: Instabil…
In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…
We consider a large queueing system that consists of many strategic servers that are weakly interacting. Each server processes jobs from its unique critically loaded buffer and controls the rate of arrivals and departures associated with…
Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…
This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded $G/Ph/n+GI$ queues, where the…
In previous papers we developed a deterministic fluid approximation 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…
This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…
The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs…
We introduce a "system-wide safety staffing" (SWSS) parameter for multiclass multi-pool networks of any tree topology, Markovian or non-Markovian, in the Halfin-Whitt regime. This parameter can be regarded as the optimal reallocation of the…
We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…
We study a many-server queueing model with server vacations, where the population size dynamics of servers and customers are coupled: a server may leave for vacation only when no customers await, and the capacity available to customers is…
This paper considers a parallel system of queues fed by independent arrival streams, where the service rate of each queue depends on the number of customers in all of the queues. Necessary and sufficient conditions for the stability of the…
In geographically-distributed systems, communication latencies are non-negligible. The perceived processing time of a request is thus composed of the time needed to route the request to the server and the true processing time. Once a…
Let $Q_{\lambda}(t,y) $ be the number of people present at time $t$ with $y$ units of remaining service time in an infinite server system with arrival rate equal to $\lambda>0$. In the presence of a non-lattice renewal arrival process and…
Heterogeneity is becoming increasingly ubiquitous in modern large-scale computer systems. Developing good load balancing policies for systems whose resources have varying speeds is crucial in achieving low response times. Indeed, how best…
In this paper we study coordinated multipath routing at the flow-level in networks with routes of length one. As a first step the static case is considered, in which the number of flows is fixed. A clustering pattern in the rate allocation…
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…
We study the steady-state performance of parallel-server systems under an immediate routing architecture with two sources of heterogeneity: servers and job classes, subject to compatibility constraints. We focus on the…
We consider a multihop wireless system. There are multiple source-destination pairs. The data from a source may have to pass through multiple nodes. We obtain a channel scheduling policy which can guarantee end-to-end mean delay for the…
We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient scalable…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…