Related papers: Fluid Models of Many-server Queues with Abandonmen…
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…
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 develops fluid limits for nonstationary many-server loss systems with general service-time distributions. For the zero-buffer $M_t/G/n/n$ queuing model, we prove a functional strong law of large numbers for the fraction of busy…
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…
We propose a unified approach to establishing diffusion approximations for queues with impatient customers within a general framework of scaling customer patience time. The approach consists of two steps. The first step is to show that the…
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 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 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…
We consider a service system where agents (or, servers) are invited on-demand. Customers arrive as a Poisson process and join a customer queue. Customer service times are i.i.d. exponential. Agents' behavior is random in two respects.…
We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding…
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…
Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they…
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…
We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…
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…
This paper studies a diffusion model that arises as the limit of a queueing system scheduling problem in the asymptotic heavy traffic regime of Halfin and Whitt. The queueing system consists of several customer classes and many servers…
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…
The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence…
A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…
In this thesis, we study the queueing systems with heterogeneous servers and service rate uncertainty under the Halfin-Whitt heavy traffic regime. First, we analyse many server queues with abandonments when service rates are i.i.d. random…