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In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic…

Probability · Mathematics 2010-07-13 Guodong Pang , Ward Whitt

In this paper, we consider a $G_t/G_t/\infty$ infinite server queueing model in a random environment. More specifically, the arrival rate in our server is modeled as a highly fluctuating stochastic process, which arguably takes into account…

Probability · Mathematics 2020-04-13 Harsha Honnappa , Yiran Liu , Samy Tindel , Aaron Yip

This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements and the server work rate are modulated by a general c\`{a}dl\`{a}g stochastic background process. To prove a large…

Probability · Mathematics 2015-02-04 H. M. Jansen , M. R. H. Mandjes , K. De Turck , S. Wittevrongel

This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the…

Probability · Mathematics 2025-06-10 Hritika Gupta , Michel Mandjes , Liron Ravner , Jiesen Wang

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

We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…

Probability · Mathematics 2025-11-03 Chang Feng , John J. Hasenbein , Guodong Pang

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 the infinite server queue model in semi-Markov random environment with k Markov arrival streams, random resources of customers, and catastrophes is considered. After catastrophes occur, all customers in the model are flashed…

Performance · Computer Science 2018-05-25 Khanik Kerobyan , Ruben Kerobyan , Koffi Enakoutsa

In this paper, we equip the conventional discrete-time queueing network with a Markovian input process, that, in addition to the usual short-term stochastics, governs the mid- to long-term behavior of the links between the network nodes.…

Systems and Control · Electrical Eng. & Systems 2020-04-07 Richard Schoeffauer , Gerhard Wunder

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 study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…

Probability · Mathematics 2017-01-02 Carlo Lancia , Gianluca Guadagni , Sokol Ndreca , Benedetto Scoppola

We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…

Networking and Internet Architecture · Computer Science 2019-07-26 Iqra Altaf Gillani , Amitabha Bagchi , Pooja Vyavahare

This paper introduces and analyzes the notion of throughput suboptimality for many-server queueing systems in heavy traffic. The queueing model under consideration has multiple customer classes, indexed by a finite set $\mathcal{I}$, and…

Probability · Mathematics 2009-06-15 Rami Atar , Gennady Shaikhet

We consider a finite population processor-sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing…

Probability · Mathematics 2013-09-12 Qiang Zhen , Johan S. H. van Leeuwaarden , Charles Knessl

We consider exponential single server queues with state-dependent arrival and service rates which evolve under influences of external environments. The transitions of the queues are influenced by the environment's state and the movements of…

Probability · Mathematics 2023-07-19 Sonja Otten , Ruslan Krenzler , Hans Daduna , Karsten Kruse

We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…

Probability · Mathematics 2013-10-17 Salvatore Federico , Peter Tankov

We consider the so-called GI/GI/N queue, in which a stream of jobs with independent and identically distributed service times arrive as a renewal process to a common queue that is served by $N$ identical parallel servers in a…

Probability · Mathematics 2017-12-06 Reza Aghajani , Kavita Ramanan

We study growing open Jackson networks where each station is a single-server queue that follows the first-come first-served discipline with Poisson arrivals and exponentially distributed service times, characterized by node-specific rates.…

Probability · Mathematics 2026-05-19 Louis T. Clarke , Guodong Pang , Ruoyu Wu

We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…

Applications · Statistics 2020-08-05 Michael Lin , Nuno C. Martins , Richard J. La

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