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Recurrence and ergodic properties are established for a single--server queueing system with variable intensities of arrivals and service. Convergence to stationarity is also interpreted in terms of reliability theory.

Probability · Mathematics 2016-11-01 Alexander Veretennikov

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

We study an admissions control problem, where a queue with service rate $1-p$ receives incoming jobs at rate $\lambda\in(1-p,1)$, and the decision maker is allowed to redirect away jobs up to a rate of $p$, with the objective of minimizing…

Probability · Mathematics 2014-07-03 Joel Spencer , Madhu Sudan , Kuang Xu

We consider a model inspired by compatibility constraints that arise between tasks and servers in data centers, cloud computing systems and content delivery networks. The constraints are represented by a bipartite graph or network that…

Probability · Mathematics 2024-04-10 Diego Goldsztajn , Sem C. Borst , Johan S. H. van Leeuwaarden

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…

Probability · Mathematics 2020-01-01 Michel Mandjes , Nicos Starreveld , René Bekker

We consider a Markovian single server queue with impatient customers. There is a customer abandonment cost and a holding cost for customers in the system. We consider two versions of the problem. In the first version, customers pay a reward…

Optimization and Control · Mathematics 2025-11-12 Runhua Wu , Hayriye Ayhan

We consider a queue to which only a finite pool of $n$ customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement $S$ arrives to the queue after an exponentially distributed time…

Probability · Mathematics 2017-04-12 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

We present the explicit construction of a stable queue with several servers and impatient customers, under stationary ergodic assumptions. Using a stochastic comparison of the (multivariate) workload sequence with two monotonic stochastic…

Probability · Mathematics 2017-11-20 Pascal Moyal

In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction $p$ of an available resource is deployed in a centralized manner…

Distributed, Parallel, and Cluster Computing · Computer Science 2012-03-23 Kuang Xu

Motivated by timeouts in Internet services, we consider networks of infinite server queues in which routing decisions are based on deadlines. Specifically, at each node in the network, the total service time equals the minimum of several…

Performance · Computer Science 2016-09-20 Neal Master , Nicholas Bambos

This paper considers a network of infinite-server queues with the special feature that, triggered by specific events, the network population vector may undergo a linear transformation (a `multiplicative transition'). For this model we…

Probability · Mathematics 2017-11-15 Dieter Fiems , Michel Mandjes , Brendan Patch

We consider a queue with renewal arrivals and n exponential servers in the Halfin-Whitt heavy traffic regime, where n and the arrival rate increase without bound, so that a critical loading condition holds. Server k serves at rate $\mu_k $,…

Probability · Mathematics 2007-11-15 Rami Atar , Adam Shwartz

We consider an $M/G/\infty$ queue with infinite expected service time. We then provide the transience/recurrence classification of the states (the system is said to be at state $n$ if there are $n$ customers being served), observing also…

Probability · Mathematics 2024-07-12 Serguei Popov

We prove that the scaled maximum steady-state waiting time and the scaled maximum steady-state queue length among $N$ $GI/GI/1$-queues in the $N$-server fork-join queue, converge to a normally distributed random variable as $N\to\infty$.…

Probability · Mathematics 2023-09-18 Dennis Schol , Maria Vlasiou , Bert Zwart

We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit…

Probability · Mathematics 2010-01-14 Anatolii A. Puhalskii , Josh E. Reed

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…

Probability · Mathematics 2013-12-03 Ruslan Krenzler , Hans Daduna

We consider the following distributed service model: jobs with unit mean, general distribution, and independent processing times arrive as a renewal process of rate $\lambda n$, with $0<\lambda<1$, and are immediately dispatched to one of…

Probability · Mathematics 2018-07-10 David Gamarnik , John N. Tsitsiklis , Martin Zubeldia

We consider a critically-loaded multiclass queueing control problem with model uncertainty. The model consists of $I$ types of customers and a single server. At any time instant, a decision-maker (DM) allocates the server's effort to the…

Probability · Mathematics 2021-03-31 Asaf Cohen , Subhamay Saha

We introduce the mobile server problem, inspired by current trends to move computational tasks from cloud structures to multiple devices close to the end user. An example for this are embedded systems in autonomous cars that communicate in…

Data Structures and Algorithms · Computer Science 2019-04-11 Björn Feldkord , Friedhelm Meyer auf der Heide

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