Related papers: Analyzing homogenous and heterogeneous multi-serve…
The paper is based on Noar's model of charged queues. We extend this model into multi-server systems with information about length and service rate disclosed for all the customers, and the customers can choose the optimal options. We…
Applications of stochastic models often involve the evaluation of steady-state performance, which requires solving a set of balance equations. In most cases of interest, the number of equations is infinite or even uncountable. As a result,…
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…
This work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if…
We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer's sojourn time in two regimes: the customer…
This paper considers the stationary distribution of the age of information (AoI) in information update systems. We first derive a general formula for the stationary distribution of the AoI, which holds for a wide class of information update…
We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…
We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…
This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. For such systems, referred to as real-time queueing systems,…
In this paper we solve a particular stochastic recursion in the stationary ergodic framework, and propose some applications of this result to the study of regenerativity (that is, finiteness of busy cycles) and stationarity of some queueing…
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…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
Queue networks describe complex stochastic systems of both theoretical and practical interest. They provide the means to assess alterations, diagnose poor performance and evaluate robustness across sets of interconnected resources. In the…
We provide the first algorithm that under minimal assumptions allows to simulate the stationary waiting-time sequence of a single-server queue backwards in time, jointly with the input processes of the queue (inter-arrival and service…
Modern Internet services, such as those at Google, Yahoo!, and Amazon, handle billions of requests per day on clusters of thousands of computers. Because these services operate under strict performance requirements, a statistical…
We consider a distributed cloud service deployed at a set of distinct server pools. Arriving jobs are classified into heterogeneous types, in accordance with their setup times which are differentiated at each of the pools. A dispatcher for…
Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where…
We consider a stochastic bipartite matching model consisting of multi-class customers and multi-class servers. Compatibility constraints between the customer and server classes are described by a bipartite graph. Each time slot, exactly one…
We study the accumulation of resources within a target due to the interplay between continual delivery, driven by 1D stochastic search processes, and sequential consumption. The assumption of sequential consumption is key because it changes…
We consider a GI/H/n queueing system. In this system, there are multiple servers in the queue. The inter-arrival time is general and independent, and the service time follows hyper-exponential distribution. Instead of stochastic…