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Related papers: Non-Stationary Queues with Batch Arrivals

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We investigate, under general stationary ergodic assumptions, the stability of systems of $S$ parallel queues in which any incoming customer joins the queue of the server having the $p+1$-th shortest workload ($p < S$), or a free server if…

Probability · Mathematics 2015-12-16 Pascal Moyal

Consider a system of $N$ parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate $\lambda(N)$. When a task arrives, the dispatcher assigns it to…

Probability · Mathematics 2019-01-25 Sayan Banerjee , Debankur Mukherjee

Network capacity region of multi-queue multi-server queueing system with random ON-OFF connectivities and stationary arrival processes is derived in this paper. Specifically, the necessary and sufficient conditions for the stability of the…

Information Theory · Computer Science 2010-01-14 Hassan Halabian , Ioannis Lambadaris , Chung-Horng Lung

In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\equiv\{X(t):t\in\mathbb R\}$ with stationary increments and variance…

Probability · Mathematics 2012-06-07 Krzysztof Debicki , Kamil Marcin Kosinski , Michel Mandjes

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

We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…

Probability · Mathematics 2018-09-17 Maria Clara Fittipaldi , Matthieu Jonckheere , Sergio I. Lopez

Traffic to any server is rarely constant over time. In addition, the workload brought by each service request is typically unknown in advance, and each request may bring a different workload to the server. Cha and Lee (2011) proposed a…

Probability · Mathematics 2015-11-16 Rachel Traylor

We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding…

Probability · Mathematics 2009-12-10 Rishi Talreja , Ward Whitt

This contribution investigates asymptotic properties of transient queue length process $$ Q(t)=\max\left(x+X(t)-ct, \sup_{0\leq s\leq t}\left(X(t)-X(s)-c(t-s)\right)\right),\ \ \ t\geq 0 $$ in Gaussian fluid queueing model, where input…

Probability · Mathematics 2018-06-18 Krzysztof Debicki , Peng Liu

We consider queueing systems with n parallel queues under a Join the Shortest Queue (JSQ) policy in the Halfin-Whitt heavy traffic regime. We use the martingale method to prove that a scaled process counting the number of idle servers and…

Probability · Mathematics 2015-09-22 Patrick Eschenfeldt , David Gamarnik

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 work considers a many-server queueing system in which impatient customers with i.i.d., generally distributed service times and i.i.d., generally distributed patience times enter service in the order of arrival and abandon the queue if…

Probability · Mathematics 2010-11-15 Weining Kang , Kavita Ramanan

We provide power series approximations for a structured batch arrival single server retrial system with two infinite capacity weighted fair orbit queues, i.e., the re-transmission rate of an orbit depends on the state of the other orbit…

Probability · Mathematics 2018-07-02 Ioannis Dimitriou

This paper considers a particular renewal-reward process with multivariate discounted rewards (inputs) where the arrival epochs are adjusted by adding some random delays. Then this accumulated reward can be regarded as multivariate…

Probability · Mathematics 2018-03-05 Landy Rabehasaina , Jae-Kyung Woo

We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…

Data Structures and Algorithms · Computer Science 2025-12-09 Jacob Bergquist , Adam N. Elmachtoub

Queueing systems with batch Markovian arrival process (BMAP) have paramount applications in the domain of wireless communication. The BMAP has been used to model the superposition of video sources and to approximate the super-position of…

Probability · Mathematics 2020-01-13 S. Pradhan , U. C. Gupta

We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…

Probability · Mathematics 2017-11-28 Lam M. Nguyen , Alexander Stolyar

A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the…

Probability · Mathematics 2011-08-05 Samantha Molinaro , Myron Hlynka , Shan Xu

In this paper, we present a condition to obtain instability for a class of queueing networks where the arrival rates in each server are constant and the departure rate in each server is a decreasing function of the queue lengths of other…

Probability · Mathematics 2023-08-01 Pierre Popineau , Seva Shneer

We introduce a novel single-server queue with general retrial times and event-dependent arrivals. This is a versatile model for the study of service systems, in which the server needs a non-negligible time to retrieve waiting customers upon…

Probability · Mathematics 2022-03-08 Ioannis Dimitriou