Related papers: Fluid limits of many-server queues with reneging
The large-time behavior of a nonlinearly coupled pair of measure-valued transport equations with discontinuous boundary conditions, parameterized by a positive real-valued parameter $\lambda$, is considered. These equations describe 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…
We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers…
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 consider a heterogeneous queueing system consisting of one large pool of $O(r)$ identical servers, where $r\to\infty$ is the scaling parameter. The arriving customers belong to one of several classes which determines the service times in…
The synchronization process inherent to the Bitcoin network gives rise to an infinite-server model with the unusual feature that customers interact. Among the closed-form characteristics that we derive for this model is the busy period…
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…
A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…
A queueing model has $J\ge2$ heterogeneous service stations, each consisting of many independent servers with identical capabilities. Customers of $I\ge2$ classes can be served at these stations at different rates, that depend on both the…
The interest to retrial queueing systems is due to their application to telephone systems. The paper studies multiserver retrial queueing systems with $n$ servers. Arrival process is a quite general point process. An arriving customer…
In this paper, we consider modeling time-dependent multi-server queues that include abandonments and retrials. For the performance analysis of those, fluid and diffusion models called "strong approximations" have been widely used in the…
A many-server queue operating under the earliest deadline first discipline, where the distributions of service time and deadline are generic, is studied at the law of large numbers scale. Fluid model equations, formulated in terms of the…
In this paper we present the fluid limit of an heavily loaded Earliest Deadline First queue with impatient customers, represented by a measure-valued process keeping track of residual time-credits of lost and waiting customers. This fluid…
We study the information-theoretic limit of reliable information processing by a server with queue-length dependent quality of service. We define the capacity for such a system as the number of bits reliably processed per unit time, and…
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…
Motivated by applications such as urban traffic control and make-to-order systems, we study a fluid model of a single-server, on-off system that can accommodate multiple queues. The server visits each queue in order: when a queue is served,…
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 focus of this paper is on the asymptotics of large-time numbers of customers in time-periodic Markovian many-server queues with customer abandonment in heavy traffic. Limit theorems are obtained for the periodic number-of-customers…
We investigate a processor sharing queue with renewal arrivals and generally distributed service times. Impatient jobs may abandon the queue, or renege, before completing service. The corresponding stochastic processes are represented by…
Fluid models have become an important tool for the study of many-server queues with general service and patience time distributions. The equilibrium state of a fluid model has been revealed by Whitt (2006) and shown to yield reasonable…