English
Related papers

Related papers: Perturbation analysis of an M/M/1 queue in a diffu…

200 papers

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,…

Probability · Mathematics 2018-02-22 Ioannis Dimitriou

Perturbations around autonomous one-dimensional single-species reaction-diffusion systems are investigated. It is shown that the parameter space corresponding to the autonomous systems is divided into two parts: In one part, the system is…

Statistical Mechanics · Physics 2007-05-23 Mohammad Khorrami , Amir Aghamohammadi

The interest to retrial queueing systems is due to their application to telephone systems. The paper studies multiserver retrial queueing systems with $n$ servers. Arrival process is a quite general point process. An arriving customer…

Probability · Mathematics 2021-06-30 Vyacheslav M. Abramov

We consider transmission of packets over queue-length sensitive unreliable links, where packets are randomly corrupted through a noisy channel whose transition probabilities are modulated by the queue-length. The goal is to characterize the…

Information Theory · Computer Science 2020-09-01 Daewon Seo , Avhishek Chatterjee , Lav R. Varshney

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

We develop a robust queueing network analyzer algorithm to approximate the steady-state performance of a single-class open queueing network of single-server queues with Markovian routing. The algorithm allows non-renewal external arrival…

Probability · Mathematics 2020-03-26 Ward Whitt , Wei You

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

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

In many systems, servers do not turn on instantly; instead, a setup time must pass before a server can begin work. These "setup times" can wreak havoc on a system's queueing; this is especially true in modern systems, where servers are…

Performance · Computer Science 2025-12-19 Jalani Williams , Weina Wang , Mor Harchol-Balter

We investigate the steady-state diffusion-approximation error for continuous-time queueing systems with generally distributed primitives. Across four canonical systems -- the $G/G/1$ and $G/M/\infty$ queues, the join-the-shortest-queue…

Probability · Mathematics 2025-09-03 Anton Braverman , Ziv Scully

In this paper one presents method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically one considers inhomogeneous $M/M/S$ queueing system with…

We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer…

Probability · Mathematics 2007-05-23 Ger Koole , Misja Nuyens , Rhonda Righter

We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit…

Probability · Mathematics 2014-04-23 Maria Vlasiou , Bert Zwart

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

It is a very hard task to compute an exact solution for the differential equations, with differences, system that allows the determination of the M|M|m|m system transient probabilities. The respective complexity grows with m. The…

Probability · Mathematics 2023-12-08 Manuel Alberto M. Ferreira

A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the model is shown to be governed by a…

Optimization and Control · Mathematics 2014-07-03 Rami Atar , Anup Biswas

We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. We study the probability density function (PDF) $P(t_{\rm m}|T)$ of the time $t_{\rm m}$ at which $x(\tau)$ reaches its global maximum. By using a path…

Statistical Mechanics · Physics 2021-10-15 Francesco Mori , Satya N. Majumdar , Gregory Schehr

We develop a heavy traffic diffusion limit theorem under nonstandard spatial scaling for the queue length process in a single server queue employing shortest remaining processing time (SRPT). For processing time distributions with unbounded…

Probability · Mathematics 2015-10-29 Amber L. Puha

In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…

Statistics Theory · Mathematics 2020-05-25 Holger Dette , Florian Heinrichs

We present an example of a single-server polling system with two queues and an adaptive service policy where the stability region depends on the expected values of all the primitives and also on a certain exponential moment of the…

Probability · Mathematics 2014-10-09 Natalia Chernova , Sergey Foss , Bara Kim