English
Related papers

Related papers: On the Distributions of Infinite Server Queues wit…

200 papers

Overlap times have been studied as a way of understanding the time of interaction between customers in a service facility. Most of the previous analysis relies on the single jump assumption for arrivals, which implies the queue increases by…

Probability · Mathematics 2023-02-16 Sergio D Palomo , Jamol Pender

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…

Probability · Mathematics 2017-01-19 Patrick Eschenfeldt , David Gamarnik

Proper management of resources whose arrival and consumption are subject to environmental randomness is an intrinsic process in both natural and artificial systems. This phenomenon can be modeled as a queuing process whose arrival…

Statistical Mechanics · Physics 2026-05-18 José Giral-Barajas , Paul C. Bressloff

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.…

Probability · Mathematics 2016-09-09 Lam Nguyen , Alexander Stolyar

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…

Probability · Mathematics 2021-02-16 V. F. Araman , H. Chen , P. W. Glynn , L. Xia

This paper considers the time evolution of a queue that is embedded in a Poisson point process of moving wireless interferers. The queue is driven by an external arrival process and is subject to a time-varying service process that is a…

Information Theory · Computer Science 2021-04-14 Nithin S. Ramesan , François Baccelli

We study a queueing system with Erlang arrivals with $k$ phases and Erlang service with $m$ phases. Transition rates among phases vary periodically with time. For these systems, we derive the asymptotic periodic distribution of the level…

Probability · Mathematics 2021-07-29 Barbara Margolius

A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers also can be of multiple types. Each customer has an independent exponentially…

Probability · Mathematics 2016-05-20 Alexander Stolyar

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…

Probability · Mathematics 2009-08-25 Christian H. Gromoll , Philippe Robert , Bert Zwart

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…

Probability · Mathematics 2007-05-23 Rami Atar

In this paper we models and studies a general vacation queueing model with impatient customers. We first propose a sufficient condition for the existence of the stationary workload process. We then give an integral equation for the…

Probability · Mathematics 2017-03-07 Assia Boumahdaf

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…

Probability · Mathematics 2025-02-21 Alexander Stolyar

We study the steady-state delay performance of load balancing in large-scale systems with heterogeneous servers in the heavy-traffic regimes. The system consists of $N$ servers, each with a local buffer of size $b-1$, serving jobs in the…

Probability · Mathematics 2026-02-27 Xin Liu , Lei Ying

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…

Probability · Mathematics 2018-08-23 Refael Hassin , Liron Ravner

The problem of exact evaluation of the mean service cycle time in tandem systems of single-server queues with both infinite and finite buffers is considered. It is assumed that the interarrival and service times of customers form sequences…

Optimization and Control · Mathematics 2012-12-24 N. K. Krivulin , V. B. Nevzorov

This paper considers a work-conserving FIFO single-server queue with multiple batch Markovian arrival streams governed by a continuous-time finite-state Markov chain. A particular feature of this queue is that service time distributions of…

Probability · Mathematics 2014-12-30 Hiroyuki Masuyama , Tetsuya Takine

A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…

Probability · Mathematics 2017-02-15 Sergey Foss , Alexander Stolyar

We consider a service system with two Poisson arrival queues. A server chooses which queue to serve at each moment. Once a queue is served, all the customers will be served within a fixed amount of time. This model is useful in studying…

Optimization and Control · Mathematics 2013-07-02 Yuhang Liu , Zizhuo Wang

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…

Probability · Mathematics 2015-10-06 Junfei Huang , Hanqin Zhang , Jiheng Zhang

The discrete time queueing system is highly applicable to modern telecommunication systems, where it provides adaptive packet handling, congestion controlled security/inspection, energy efficient operation, and supports bursty traffic…

Information Theory · Computer Science 2026-02-27 Ashish Verma , Sourav Pradhan