English
Related papers

Related papers: Explicit Results for the Distributions of Queue Le…

200 papers

We study three non-equivalent queueing models in continuous time that each generalise the classical M/M/1 queue in a different way. Inter-event times in all models are Mittag-Leffler distributed, which is a heavy tail distribution with no…

Probability · Mathematics 2022-11-24 Jacob Butt , Nicos Georgiou , Enrico Scalas

In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and…

Probability · Mathematics 2014-08-04 Marko Boon , Ivo Adan , Onno Boxma

In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…

Probability · Mathematics 2018-12-07 Abhishek , Rudesindo Núñez Queija , Marko Boon

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…

Probability · Mathematics 2010-03-17 James B. Martin , Balaji Prabhakar

Consider an M/M/$s$ queue with the additional feature that the arrival rate is a random variable of which only the mean, variance, and range are known. Using semi-infinite linear programming and duality theory for moment problems, we…

In this paper continuity theorems are established for the number of losses during a busy period of the $M/M/1/n$ queue. We consider an $M/GI/1/n$ queueing system where the service time probability distribution, slightly different in a…

Probability · Mathematics 2008-08-01 Vyacheslav M. Abramov

For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…

Probability · Mathematics 2025-12-09 Predrag Jelenkovic , Petar Momcilovic

Utilizing customers' service-time information, we study an easy-to-implement scheduling policy with two priority classes. By carefully designing the classes, the two-class priority rule achieves near-optimal performance. In particular, for…

Optimization and Control · Mathematics 2021-05-24 Yan Chen , Jing Dong

This report considers a fairly general model of constrained queuing networks that allows us to represent both MMBP (Markov Modulated Bernoulli Processes) arrivals and time-varying service constraints. We derive a set of sufficient…

Performance · Computer Science 2014-03-18 Emilio Leonardi

In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other…

Statistics Theory · Mathematics 2017-03-22 Cornelia Wichelhaus , Moritz von Rohrscheidt

It is interesting and challenging to study double-ended queues with First-Come-First-Match discipline under customers' impatient behavior and non-Poisson inputs. The system stability can be guaranteed by the customers' impatient behavior,…

Probability · Mathematics 2022-04-29 Heng-Li Liu , Quan-Lin Li , Yan-Xia Chang , Chi Zhang

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…

Probability · Mathematics 2024-11-06 J. G. Dai , Dongyan Huo

In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system consisting of three M/M/1 queues with threshold policy. It turns out that the scaled queue-length of the…

Probability · Mathematics 2014-08-20 Zaiming Liu , Yuqing Chu , Jinbiao Wu

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: the distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a…

Probability · Mathematics 2017-05-02 Marko Boon , Onno Boxma , Offer Kella , Masakiyo Miyazawa

Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…

Probability · Mathematics 2025-04-25 Bernardo D'Auria , Ivo J. B. F. Adan , René Bekker , Vidyadhar Kulkarni

Approximations for the mean performance indices for the M/G/c queue rely on the approximate computation of the probability that an arriving request has to wait for service and of the minimum of residual service times if all servers are…

Networking and Internet Architecture · Computer Science 2008-03-14 Thomas Begin , Alexandre Brandwajn

This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffic intensities and overflow levels. In particular, we provide…

Probability · Mathematics 2011-03-22 Mariana Olvera-Cravioto , Peter W. Glynn

In this paper we consider a single-server cyclic polling system. Between visits to successive queues, the server is delayed by a random switch-over time. The order in which customers are served in each queue is determined by a priority…

Probability · Mathematics 2014-08-05 Marko Boon , Ivo Adan , Onno Boxma

Priority queues with parallel access are an attractive data structure for applications like prioritized online scheduling, discrete event simulation, or greedy algorithms. However, a classical priority queue constitutes a severe bottleneck…

Data Structures and Algorithms · Computer Science 2021-07-23 Marvin Williams , Peter Sanders , Roman Dementiev

We consider a Markovian single server queue in which customers are preemptively scheduled by exogenously assigned priority levels. The novelty in our model is that the priority levels are randomly assigned from a continuous probability…

Probability · Mathematics 2017-01-09 Neal Master , Zhengyuan Zhou , Nicholas Bambos