Related papers: A restless time-fractional multiclass queue
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…
Due to the widespread applicability of discrete-time queues in wireless networks or telecommunication systems, this paper analyzes an infinite-buffer batch-service queue with single and multiple vacation where customers/messages arrive…
We study the optimal sequencing of a batch of tasks on a machine subject to random disruptions driven by a non-homogeneous Poisson process (NHPP), such that every disruption requires the interrupted task to be re-processed from scratch, and…
A "scheduled" arrival process is one in which the n th arrival is scheduled for time n, but instead occurs at a different time. The difference between the scheduled time and the arrival time is called the perturbation. The sequence of…
A Large Deviation Principle (LDP) is established for the stationary distribution of the number of customers in a many--server queue in heavy traffic for a moderate deviation scaling akin to the Halfin--Whitt regime. The interarrival and…
A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials,…
We consider an infinite-server queue into which customers arrive according to a Cox process and have independent service times with a general distribution. We prove a functional large deviations principle for the equilibrium queue length…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…
We consider many-server queueing systems with heterogeneous exponential servers and renewal arrivals. The service rate of each server is a random variable drawn from a given distribution. We develop a framework for analyzing the heavy…
We consider a class of multi-agent distributed synchronization systems, which are modeled as $n$ particles moving on the real line. This class generalizes the model of a multi-server queueing system, considered in [15], employing so-called…
We consider a service system with an infinite number of exponential servers sharing a finite service capacity. The servers are ordered according to their speed, and arriving customers join the fastest idle server. A capacity allocation is…
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 fractional counting process with jumps of amplitude $1,2,\ldots,k$, with $k\in \mathbb{N}$, whose probabilities satisfy a suitable system of fractional difference-differential equations. We obtain the moment generating…
In multitasking operating systems, requests for free memory are traditionally modeled as a stochastic counting process with independent, exponentially-distributed interarrival times because of the analytic simplicity such Poisson models…
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…
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the…
In this article, we study the classical shortest queue problem under the influence of malicious attacks, which is relevant to a variety of engineering system including transportation, manufacturing, and communications. We consider a…
We consider a two-node tandem queueing network in which the upstream queue is GI/GI/1 and each job reuses its upstream service requirement when moving to the downstream queue. Both servers employ the first-in-first-out policy. To…
In the supermarket model there are n queues, each with a unit rate server. Customers arrive in a Poisson process at rate \lambda n, where 0<\lambda <1. Each customer chooses d > 2 queues uniformly at random, and joins a shortest one. It is…
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…