Related papers: Fluid Limits for Shortest Job First with Aging
Load balancing algorithms play a vital role in enhancing performance in data centers and cloud networks. Due to the massive size of these systems, scalability challenges, and especially the communication overhead associated with load…
We study a simple rate control scheme for a multiclass queuing network for which customers are partitioned into distinct flows that are queued separately at each station. The control scheme discards customers that arrive to the network…
We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…
We consider a sequence of single-server queueing models operating under a service policy that incorporates batches into processor sharing: arriving jobs build up behind a gate while waiting to begin service, while jobs in front of the gate…
In this paper, we present a functional fluid limit theorem and a functional central limit theorem for a queue with an infinity of servers M/GI/$\infty$. The system is represented by a point-measure valued process keeping track of the…
We study in this paper a variation of the acclaimed CSMA random access protocol. We will focus on the case where back-off rates at each node is polynomial in the size of the queue. Under a condition relating the exponent in the polynomial…
Fork-Join (FJ) queueing models capture the dynamics of system parallelization under synchronization constraints, for example, for applications such as MapReduce, multipath transmission and RAID systems. Arriving jobs are first split into…
In this paper, we study an age of information minimization problem in continuous-time and discrete-time status updating systems that involve multiple packet flows, multiple servers, and transmission errors. Four scheduling policies are…
In this paper, we study an $N$ server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as $N\to\infty$. This fluid limit depends on the initial number…
We study the problem of preemptively scheduling jobs online over time on a single machine to minimize the total flow time. In the traditional clairvoyant scheduling model, the scheduler learns about the processing time of a job at its…
We consider an overloaded multiclass nonidling first-in-first-out single-server queue with abandonment. The interarrival times, service times, and deadline times are sequences of independent and identically, but generally distributed random…
The PS-model treated in this paper is motivated by freelance job websites where multiple freelancers compete for a single job. In the context of such websites, multistage service of a job means collection of applications from multiple…
We analyze the so-called Shortest Queue First (SQF) queueing discipline whereby a unique server addresses queues in parallel by serving at any time that queue with the smallest workload. Considering a stationary system composed of two…
We consider an information update system consisting of $N$ sources sending status packets at random instances according to a Poisson process to a remote monitor through a single server. We assume a heteregeneous server with exponentially…
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…
In this paper, we study an age of information minimization problem, where multiple flows of update packets are sent over multiple servers to their destinations. Two online scheduling policies are proposed. When the packet generation and…
We consider the problem of scheduling non preemptively a set of jobs on parallel identical machines with prior setup operations on a single shared server, where the objective is to minimise the makespan. We develop an arc-flow formulation…
We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies…
We study deterministic fluid approximations of parallel service systems operating under first come first served policy (FCFS). The condition for complete resource pooling is identified in terms of the system structure and the customer…
The Skorokhod map on the half-line has proved to be a useful tool for studying processes with non-negativity constraints. In this work we introduce a measure-valued analog of this map that transforms each element $\zeta$ of a certain class…