Related papers: Multiserver-job Response Time under Multilevel Sca…
We consider a system with $N$ parallel servers where incoming jobs are immediately replicated to, say, $d$ servers. Each of the $N$ servers has its own queue and follows a FCFS discipline. As soon as the first job replica is completed, the…
This paper addresses the analysis of the queue-length process of single-server queues under overdispersion, i.e., queues fed by an arrival process for which the variance of the number of arrivals in a given time window exceeds the…
We present an analysis of large-scale load balancing systems, where the processing time distribution of tasks depends on both the task and server types. Our study focuses on the asymptotic regime, where the number of servers and task types…
Our interest lies in load balancing jobs in large scale systems consisting of multiple dispatchers and FCFS servers. In the absence of any information on job sizes, dispatchers typically use queue length information reported by the servers…
We study the Multiserver-Job Queuing Model (MJQM) with general independent arrivals and service times under FCFS scheduling, using stochastic recurrence equations (SREs) and ergodic theory. We prove the monotonicity and separability…
We characterize heavy-traffic process and steady-state limits for systems staffed according to the square-root safety rule, when the service requirements of the customers are perfectly correlated with their individual patience for waiting…
We consider the $N$-model queueing system with a waiting time dependent threshold on the diagonal: the service discipline is First--Come--First--Served, but type-1 jobs can only be served by server 2 if their waiting time exceeds a…
The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of $N$ single-server queues. We discuss recent advances on scalable load balancing schemes which provide favorable…
A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a…
Consider a system with $K$ parallel queues in which the server for each queue processes jobs at rate $n$ and the total arrival rate to the system is $nK-\upsilon \sqrt{n}$ where $\upsilon \in (0, \infty)$ and $n$ is large. We study…
We consider a system of $N$ parallel single-server queues with unit exponential service rates and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to a server…
We consider the FCFS $GI/GI/n$ queue, and prove the first simple and explicit bounds that scale as $\frac{1}{1-\rho}$ under only the assumption that inter-arrival times have finite second moment, and service times have finite $2+\epsilon$…
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…
We consider the fundamental problem of managing a bounded size queue buffer where traffic consists of packets of varying size, where each packet requires several rounds of processing before it can be transmitted from the queue buffer. The…
We study a two-type server queueing system where flexible Type-I servers, upon their initial interaction with jobs, decide in real time whether to process them independently or in collaboration with dedicated Type-II servers. Independent…
We are given a set of jobs, each one specified by its release date, its deadline and its processing volume (work), and a single (or a set of) speed-scalable processor(s). We adopt the standard model in speed-scaling in which if a processor…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
A queue is required when a service provider is not able to handle jobs arriving over the time. In a highly flexible and dynamic environment, some jobs might demand for faster execution at run-time especially when the resources are limited…
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…
We analyze randomized dynamic load balancing schemes for multi-server processor sharing systems when the number of servers in the system is large and the servers have heterogeneous service rates. In particular, we focus on the classical…