Related papers: Finite-pool queues with heavy-tailed services
We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service…
In this paper we revisit the results of Loynes (1962) on stability of queues for ergodic arrivals and services, and show examples when the arrivals are bounded and ergodic, the service rate is constant, and under stability the limit…
We consider a discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process for short) $\{(\boldsymbol{X}_n,J_n)\}$ on $\mathbb{Z}_+^2\times S_0$, where $\boldsymbol{X}_n=(X_{1,n},X_{2,n})$ is the level state, $J_n$ the phase…
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…
In this paper, we study the tail behavior of $\max_{i\leq N}\sup_{s>0}\left(W_i(s)+W_A(s)-\beta s\right)$ as $N\to\infty$, with $(W_i,i\leq N)$ i.i.d. Brownian motions and $W_A$ an independent Brownian motion. This random variable can be…
We study the tail asymptotic of the stationary joint queue length distribution for a generalized Jackson network (GJN for short), assuming its stability. For the two station case, this problem has been recently solved in the logarithmic…
For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of…
We investigate the relaxation of long-tailed distributions under stochastic dynamics that do not support such tails. Linear relaxation is found to be a borderline case in which long tails are exponentially suppressed in time but not…
We study a many-server queueing model with server vacations, where the population size dynamics of servers and customers are coupled: a server may leave for vacation only when no customers await, and the capacity available to customers is…
We consider a broad class of queueing models with random state-dependent vacation periods, which arise in the analysis of queue-based back-off algorithms in wireless random-access networks. In contrast to conventional models, the vacation…
We study the problem of scheduling jobs in a queueing system, specifically an M/G/1 with light-tailed job sizes, to asymptotically optimize the response time tail. This means scheduling to make $\mathbf{P}[T > t]$, the chance a job's…
In this paper, we study the stability of queues with impatient customers. Under general stationary ergodic assumptions, we first provide some conditions for such a queue to be regenerative (i.e. to empty a.s. an infinite number of times).…
A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…
We investigate the asymptotic behavior as time goes to infinity of Hawkes processes whose regression kernel has $L^1$ norm close to one and power law tail of the form $x^{-(1+\alpha)}$, with $\alpha\in(0,1)$. We in particular prove that…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
The asymptotic decay rate of the sojourn time of a customer in the stationary M/G/1 queue under the Foreground Background (FB) service discipline is studied. The FB discipline gives service to those customers that have received the least…
In this article, a new mathematical model of human population growth as an autonomous non-Markov queuing system with an unlimited number of servers and two types of applications is proposed. The research of this system was carried out a…
In this work, we study the stationary distribution of the scaled queue length vector process in multiclass queueing networks operating under static buffer priority service policies. We establish that when subjected to a multi-scale heavy…
We consider the following distributed service model: jobs with unit mean, exponentially distributed, and independent processing times arrive as a Poisson process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched by a…
Imagine, you enter a grocery store to buy food. How many peopledo you overlap with in this store? How much time do you overlap witheach person in the store? In this paper, we answer these questions bystudying the overlap times between…