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This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate $\Lambda$ from a given distribution every $\Delta$…

Probability · Mathematics 2016-02-02 Mariska Heemskerk , Johan van Leeuwaarden , Michel Mandjes

We consider a single-server GI/GI/1 queueing system with feedback. We assume the service times distribution to be (intermediate) regularly varying. We find the tail asymptotics for a customer's sojourn time in two regimes: the customer…

Probability · Mathematics 2018-08-01 Sergey Foss , Masakiyo Miyazawa

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

Consider the batch-arrival $GI^X/M/c/N$ model with $c$ servers, general inter-arrival batch times, finite buffer, and exponential service times. Inter-arrival batch times, batch sizes, and service times are $i.i.d.$ and independent of each…

Probability · Mathematics 2022-12-20 Muhammad El-Taha , Thomas Michaud

We study ergodic properties of Markovian multiclass many-server queues which are uniform over scheduling policies, as well as the size n of the system. The system is heavily loaded in the Halfin-Whitt regime, and the scheduling policies are…

Optimization and Control · Mathematics 2019-11-25 Ari Arapostathis , Hassan Hmedi , Guodong Pang

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 work, we consider a computational model of a distributed system formed by a set of servers in which jobs, that are continuously arriving, have to be executed. Every job is formed by a set of dependent tasks (i.~e., each task may…

Networking and Internet Architecture · Computer Science 2019-10-07 Vicent Cholvi , Juan Echagüe , Antonio Fernández Anta , Christopher Thraves Caro

Single-server queues with customer abandonment arise in call centers and many service systems, but steady-state performance measures remain analytically intractable beyond Markovian assumptions. This paper develops Robust Queueing (RQ)…

Probability · Mathematics 2026-03-03 Wei You

AM/M/N+Mqueueingnetworkisconsideredwithdindependentcustomerclasses and d server pools in Halfin-Whitt regime. Class i customers has priority for service in pool i for i = 1, . . . , d, and may access some other pool if the pool has an idle…

Probability · Mathematics 2017-07-18 Anup Biswas

We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…

Probability · Mathematics 2013-04-09 Anup Biswas

This paper examines a continuous-time routing system with general interarrival and service time distributions, operating under the join-the-shortest-queue and power-of-two-choices policies. Under a weaker set of assumptions than those…

Probability · Mathematics 2025-03-28 Jin Guang , Yaosheng Xu , J. G. Dai

In this work, nonparametric statistical inference is provided for the continuous-time M/G/1 queueing model from a Bayesian point of view. The inference is based on observations of the inter-arrival and service times. Beside other…

Statistics Theory · Mathematics 2017-03-22 Cornelia Wichelhaus , Moritz von Rohrscheidt

In this paper, we prove a characterization theorem on the number of losses during a busy period in $GI^X/GI^Y/1/n$ queueing systems, in which interarrival time distribution belongs to the class NWUE.

Probability · Mathematics 2013-01-16 Vyacheslav M. Abramov

Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to the current queue length. For this model, they proved that…

Probability · Mathematics 2026-01-07 Masahiro Kobayashi , Masakiyo Miyazawa , Yutaka Sakuma

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 work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the…

Probability · Mathematics 2007-08-08 Haya Kaspi , Kavita Ramanan

Motivated by call center practice, we propose a tractable model for $\mbox{GI}/\mbox{GI}/n+\mbox{GI}$ queues in the efficiency-driven (ED) regime. We use a one-dimensional diffusion process to approximate the virtual waiting time process…

Probability · Mathematics 2015-09-17 Shuangchi He

A many-server heavy-traffic FCLT is proved for the $G_t/M/s_t+\mathit {GI}$ queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment…

Probability · Mathematics 2014-01-17 Yunan Liu , Ward Whitt

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

The paper studies a closed queueing network containing two types of node. The first type (server station) is an infinite server queueing system, and the second type (client station) is a single server queueing system with autonomous…

Probability · Mathematics 2021-07-01 Vyacheslav M. Abramov