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Related papers: Heavy Traffic Limit for a Tandem Queue with Identi…

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We study a single server FIFO queue that offers general service. Each of n customers enter the queue at random time epochs that are inde- pendent and identically distributed. We call this the random scattering traffic model, and the…

Probability · Mathematics 2017-08-21 Peter W. Glynn , Harsha Honnappa

The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…

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

We consider a horizontal traffic queue (HTQ) on a periodic road segment, where vehicles arrive according to a spatio-temporal Poisson process, and depart after traveling a distance that is sampled independently and identically from a…

Dynamical Systems · Mathematics 2016-05-25 Mohammad Motie , Ketan Savla

The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the…

Probability · Mathematics 2015-02-13 Rahul Singh , Alexander Stolyar

We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…

Probability · Mathematics 2015-12-01 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

We consider a regulated multi-class instantaneous matching system with reneging, in which each event requires $K \geq 2$ distinct impatient agents who wait in their respective queues. Each agent class is subject to a buffer capacity,…

Probability · Mathematics 2025-07-15 Bowen Xie

Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume…

Probability · Mathematics 2024-11-13 Eliran Sherzer

This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…

Probability · Mathematics 2009-09-29 H. Christian Gromoll , Łukasz Kruk

We study a general $k$ dimensional infinite server queues process with Markov switching, Poisson arrivals and where the service times are fat tailed with index $\alpha\in (0,1)$. When the arrival rate is sped up by a factor $n^\gamma$, the…

Probability · Mathematics 2021-06-21 Landy Rabehasaina

We consider a two-queue polling model with switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$) in each queue. The major benefit of the $k$-limited service discipline is that it -…

Probability · Mathematics 2016-03-07 Marko Boon , Erik Winands

This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves…

Probability · Mathematics 2016-11-09 Marko Boon , Rob van der Mei , Erik Winands

This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (two-node) tandem queue, fed by a large number of Gaussian…

Probability · Mathematics 2007-05-23 Michel Mandjes , Miranda van Uitert

This is an expository review paper illustrating the ``martingale method'' for proving many-server heavy-traffic stochastic-process limits for queueing models, supporting diffusion-process approximations. Careful treatment is given to an…

Probability · Mathematics 2007-12-28 Guodong Pang , Rishi Talreja , Ward Whitt

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

In this paper, we investigate overlap times in a two-dimensional infinite server tandem queue. Specifically, we analyze the amount of time that a pair of customers spend overlapping in any station of the two dimensional tandem network. We…

Probability · Mathematics 2024-03-13 Ruici Gao , Jamol Pender

This paper focuses on an infinite-server queue modulated by an independently evolving finite-state Markovian background process, with transition rate matrix $Q\equiv(q_{ij})_{i,j=1}^d$. Both arrival rates and service rates are depending on…

Probability · Mathematics 2015-06-17 Joke Blom , Koen De Turck , Michel Mandjes

In this paper, we study a controllable tandem queueing system consisting of two nodes and a controller, in which customers arrive according to a Poisson process and must receive service at both nodes before leaving the system. A decision…

Probability · Mathematics 2015-04-07 Liu Zaiming , Chen Gang , Wu Jinbiao

Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length distribution, which is not addressed in [1]. In this paper,…

Probability · Mathematics 2026-04-13 Masahiro Kobayashi , Masakiyo Miyazawa , Yutaka Sakuma

In this paper, we analyze a two-queue random time-limited Markov modulated polling model. In the first part of the paper, we investigate the fluid version: Fluid arrives at the two queues as two independent flows with deterministic rate.…

Probability · Mathematics 2021-12-10 Stella Kapodistria , Mayank Saxena , Onno Boxma , Offer Kella

We consider a tandem queue with coupled processors, which is subject to global breakdowns. When the network is in the operating mode and both queues are non empty, the total service capacity is shared among the stations according to fixed…

Probability · Mathematics 2019-03-08 Ioannis Dimitriou