Related papers: Scheduling parallel servers in the nondegenerate s…
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…
Multi-server queueing systems are widely used models for job scheduling in machine learning, wireless networks, crowdsourcing, and healthcare systems. This paper considers a multi-server system with multiple servers and multiple types of…
Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times…
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…
Modern data centers serve workloads which are capable of exploiting parallelism. When a job parallelizes across multiple servers it will complete more quickly, but jobs receive diminishing returns from being allocated additional servers.…
We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded…
We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any,…
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…
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…
We consider Markovian multiclass multi-pool networks with heterogeneous server pools, each consisting of many statistically identical parallel servers, where the bipartite graph of customer classes and server pools forms a tree. Customers…
Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to…
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-scale parallel-server system, where each server independently adjusts its processing speed in a decentralized manner. The objective is to minimize the overall cost, which comprises the average cost of maintaining the…
The model is motivated by the problem of load distribution in large-scale cloud-based data processing systems. We consider a heterogeneous service system, consisting of multiple large server pools. The pools are different in that their…
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…
Given a random variable $N$ with values in ${\mathbb{N}}$, and $N$ i.i.d. positive random variables $\{\mu_k\}$, we consider a queue with renewal arrivals and $N$ exponential servers, where server $k$ serves at rate $\mu_k$, under two work…
We are interested in a large queue in a $GI/G/k$ queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a…
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…
This paper studies the limiting behavior of a closed queueing network with multiple single-server and infinite-server stations. Under a heavy traffic asymptotic regime$\unicode{x2014}$where the number of jobs and single-server service rates…
This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…