Related papers: Exact tail asymptotics for a discrete-time preempt…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this…
By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.
We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends…
We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\rho$ which is the ratio of mean service and mean…
In this paper, we analyze a discrete-time queue that is motivated from studying hospital inpatient flow management, where the customer count process captures the midnight inpatient census. The stationary distribution of the customer count…
A single server retrial queueing system with two-classes of orbiting customers, and general class dependent service times is considered. If an arriving customer finds the server unavailable, it enters a virtual queue, called the orbit,…
In this paper, we consider the number of both arrivals and departures seen by a tagged customer while in service in a classical $M/M/1$ processor sharing queue. By exploiting the underlying orthogonal structure of this queuing system…
The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…
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,…
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…
We study a single-server priority queue with a finite number of classes, in which the arrivals follow a fractional Poisson process of index $\alpha \in (0,1]$ and the service completions are triggered by an independent fractional Poisson…
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…
The main contribution of this paper is to present a new sufficient condition for the subexponential asymptotics of the stationary distribution of a GI/GI/1-type Markov chain without jumps from level "infinity" to level zero. For simplicity,…
We consider the asymptotic distribution of a cell in a 2 x ... x 2 contingency table as the fixed marginal totals tend to infinity. The asymptotic order of the cell variance is derived and a useful diagnostic is given for determining…
The busy period for a queue is cast as the area swept under the random walk until it first returns to zero, $B$. Encompassing non-i.i.d. increments, the large-deviations asymptotics of $B$ is addressed, under the assumption that the…
This paper addresses heavy-tailed large deviation estimates for the distribution tail of functionals of a class of spectrally one-sided L\'evy process. Our contribution is to show that these estimates remain valid in a near-critical regime.…
In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a…
We consider a queueing system with $n$ parallel queues operating according to the so-called "supermarket model" in which arriving customers join the shortest of $d$ randomly selected queues. Assuming rate $n\lambda_{n}$ Poisson arrivals and…
In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and…