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On the time-dependent behavior of preemptive single-server queueing systems with Poisson arrivals Queueing Syst. (IF 1.2) Pub Date : 2024-03-14 Brian Fralix
We present a detailed study of the time-dependent behavior of both the queue-length process and the workload process of various types of preemptive Last-Come-First-Served queueing systems, such as the preemptive repeat different and preemptive repeat identical models recently studied in Asmussen and Glynn (Queue Syst 87:1–22, 2017) and Bergquist and Sigman (Stoch Models 38:515–544, 2022). Our main
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Heavy traffic analysis of multi-class bipartite queueing systems under FCFS Queueing Syst. (IF 1.2) Pub Date : 2024-03-02
Abstract This paper examines the performance of multi-class, multi-server bipartite queueing systems, where each arriving customer is compatible with only a subset of servers. We focus on the system’s performance under a first-come, first-served-assign longest idle server service discipline. In this discipline, an idle server is matched with the compatible customer who has been waiting the longest
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Whittle index approach to multiserver scheduling with impatient customers and DHR service times Queueing Syst. (IF 1.2) Pub Date : 2024-02-19 Samuli Aalto
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A queueing model of dynamic pricing and dispatch control for ride-hailing systems incorporating travel times Queueing Syst. (IF 1.2) Pub Date : 2024-02-04
Abstract A system manager makes dynamic pricing and dispatch control decisions in a queueing network model motivated by ride hailing applications. A novel feature of the model is that it incorporates travel times. Unfortunately, this renders the exact analysis of the problem intractable. Therefore, we study this problem in the heavy traffic regime. Under the assumptions of complete resource pooling
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Adaptive service rate control of an M/M/1 queue with server breakdowns Queueing Syst. (IF 1.2) Pub Date : 2024-01-05 Yi Zheng, Juxihong Julaiti, Guodong Pang
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Exact and asymptotic analysis of infinite server batch service queues with random batch sizes Queueing Syst. (IF 1.2) Pub Date : 2023-12-16 Ayane Nakamura, Tuan Phung-Duc
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Some reflected autoregressive processes with dependencies Queueing Syst. (IF 1.2) Pub Date : 2023-12-14 Ioannis Dimitriou, Dieter Fiems
Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Among others, we study cases where the interarrival and service times are proportionally dependent on additive and/or subtracting delay, as well as cases where interarrival times depend on whether the service duration of the previous arrival exceeds or not a random threshold. Moreover, we study
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Data flow dissemination in a network Queueing Syst. (IF 1.2) Pub Date : 2023-11-21 Aditya Gopalan, Alexander L. Stolyar
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Join-Up-To(m): improved hyperscalable load balancing Queueing Syst. (IF 1.2) Pub Date : 2023-11-15 Grzegorz Kielanski, Tim Hellemans, Benny Van Houdt
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Reflected Brownian motion with drift in a wedge Queueing Syst. (IF 1.2) Pub Date : 2023-10-24 Peter Lakner, Ziran Liu, Josh Reed
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Asymptotic behavior of a system of two coupled queues when the content of one queue is very high Queueing Syst. (IF 1.2) Pub Date : 2023-10-17 Herwig Bruneel, Arnaud Devos
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Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals Queueing Syst. (IF 1.2) Pub Date : 2023-10-07 Somya Mehra, Peter G. Taylor
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A fluid approximation for a matching model with general reneging distributions Queueing Syst. (IF 1.2) Pub Date : 2023-09-26 Angelos Aveklouris, Amber L. Puha, Amy R. Ward
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Sojourns of fractional Brownian motion queues: transient asymptotics Queueing Syst. (IF 1.2) Pub Date : 2023-09-10 Krzysztof Dȩbicki, Enkelejd Hashorva, Peng Liu
We study the asymptotics of sojourn time of the stationary queueing process \(Q(t),t\ge 0\) fed by a fractional Brownian motion with Hurst parameter \(H\in (0,1)\) above a high threshold u. For the Brownian motion case \(H=1/2\), we derive the exact asymptotics of $$\begin{aligned} {\mathbb {P}} \left\{ \int _{T_1}^{T_2}{\mathbb {I}}(Q(t)>u+h(u))d t>x \Big |Q(0) >u \right\} \end{aligned}$$ as \(u\rightarrow
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Large deviations and long-time behavior of stochastic fluid queues with generalized fractional Brownian motion input Queueing Syst. (IF 1.2) Pub Date : 2023-09-13 Sumith Reddy Anugu, Guodong Pang
We study the large deviation behaviors of a stochastic fluid queue with an input being a generalized Riemann–Liouville (R–L) fractional Brownian motion (FBM), referred to as GFBM. The GFBM is a continuous mean-zero Gaussian process with non-stationary increments, extending the standard FBM with stationary increments. We first derive the large deviation principle for the GFBM by using the weak convergence
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Proofs of conjectures on the competition between observable and unobservable servers Queueing Syst. (IF 1.2) Pub Date : 2023-09-01 Bara Kim, Jeongsim Kim, Yan Su, Chia-Li Wang
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Minimizing the mean slowdown in the M/G/1 queue Queueing Syst. (IF 1.2) Pub Date : 2023-09-04 Samuli Aalto, Ziv Scully
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Gaussian limits for scheduled traffic with super-heavy tailed perturbations Queueing Syst. (IF 1.2) Pub Date : 2023-08-16 Victor F. Araman, Peter W. Glynn
A scheduled arrival model is one in which the jth customer is scheduled to arrive at time jh but the customer actually arrives at time \(jh + \xi _j\), where the \(\xi _j\)’s are independent and identically distributed. It has previously been shown that the arrival counting process for scheduled traffic obeys a functional central limit theorem (FCLT) with fractional Brownian motion (fBM) with Hurst
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On a modified version of the Lindley recursion Queueing Syst. (IF 1.2) Pub Date : 2023-08-17 Dongzhou Huang
This paper concerns a modified version of the Lindley recursion, where the recursion equation is given by \(W_{i+1} = [V_{i} W_{i} + Y_{i}]^{+}\), with \(\{V_i\}_{i=0}^{\infty }\) and \(\{Y_i\}_{i=0}^{\infty }\) being two independent sequences of i.i.d. random variables. Additionally, we assume that the \(V_i\) take values in \((-\infty , 1]\) and the \(Y_i\) have a rational Laplace–Stieltjes transform
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Queueing networks with path-dependent arrival processes Queueing Syst. (IF 1.2) Pub Date : 2023-08-02 Kerry Fendick, Ward Whitt
This paper develops a Gaussian model for an open network of queues having a path-dependent net-input process, whose evolution depends on its early history, and satisfies a non-ergodic law of large numbers. We show that the Gaussian model arises as the heavy-traffic limit for a sequence of open queueing networks, each with a multivariate generalization of a Polya arrival process. We show that the net-input
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Stability of a cascade system with two stations and its extension for multiple stations Queueing Syst. (IF 1.2) Pub Date : 2023-07-26 Masakiyo Miyazawa, Evsey Morozov
We consider a two-station cascade system in which waiting or externally arriving customers at station 1 move to the station 2 if the queue size of station 1 including an arriving customer itself and a customer being served is greater than a given threshold level \(c_{1} \ge 1\) and if station 2 is empty. Assuming that external arrivals are subject to independent renewal processes satisfying certain
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On the speed of convergence of Piterbarg constants Queueing Syst. (IF 1.2) Pub Date : 2023-07-04 Krzysztof Bisewski, Grigori Jasnovidov
In this paper, we derive an upper bound for the difference between the continuous and discrete Piterbarg constants. Our result allows us to approximate the classical Piterbarg constants by their discrete counterparts using Monte Carlo simulations with an explicit error rate.
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Proof of the conjecture on the stability of a multi-class retrial queue with constant retrial rates Queueing Syst. (IF 1.2) Pub Date : 2023-06-22 Bara Kim, Jeongsim Kim
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On the maxima of suprema of dependent Gaussian models Queueing Syst. (IF 1.2) Pub Date : 2023-06-19 Lanpeng Ji, Xiaofan Peng
In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima. The obtained results not only have potential applications in estimating the delay of certain Gaussian fork-join queueing systems but also provide interesting insights
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Externalities in the M/G/1 queue: LCFS-PR versus FCFS Queueing Syst. (IF 1.2) Pub Date : 2023-06-08 Royi Jacobovic, Nikki Levering, Onno Boxma
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Thirty-six years of contributions to queueing systems: a content analysis, topic modeling, and graph-based exploration of research published in the QUESTA journal Queueing Syst. (IF 1.2) Pub Date : 2023-06-02 Aminath Shausan, Aapeli Vuorinen
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Exponential asymptotic optimality of Whittle index policy Queueing Syst. (IF 1.2) Pub Date : 2023-05-21 Nicolas Gast, Bruno Gaujal, Chen Yan
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Refined tail asymptotic properties for the $$M^X/G/1$$ retrial queue Queueing Syst. (IF 1.2) Pub Date : 2023-03-28 Bin Liu, Jie Min, Yiqiang Q. Zhao
In the literature, retrial queues with batch arrivals and heavy-tailed service times have been studied and the so-called equivalence theorem has been established under the condition that the service time is heavier than the batch size. The equivalence theorem provides the distribution (or tail) equivalence between the total number of customers in the system for the retrial queue and the total number
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Comparison of stability regions for a line distribution network with stochastic load demands Queueing Syst. (IF 1.2) Pub Date : 2023-03-15 M. H. M. Christianen, J. Cruise, A. J. E. M. Janssen, S. Shneer, M. Vlasiou, B. Zwart
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Stability regions of systems with compatibilities and ubiquitous measures on graphs Queueing Syst. (IF 1.2) Pub Date : 2023-02-22 Jocelyn Begeot, Irène Marcovici, Pascal Moyal
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Stability of a cascade system with multiple stations Queueing Syst. (IF 1.2) Pub Date : 2023-02-22 Bara Kim, Jeongsim Kim
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Further results of Markovian bulk-arrival and bulk-service queues with general-state-dependent control Queueing Syst. (IF 1.2) Pub Date : 2023-01-05 Xiaohan Wu, Anyue Chen
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Diffusion parameters of flows in stable multi-class queueing networks Queueing Syst. (IF 1.2) Pub Date : 2022-11-24 Sarat Babu Moka, Yoni Nazarathy, Werner Scheinhardt
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Estimating customer delay and tardiness sensitivity from periodic queue length observations Queueing Syst. (IF 1.2) Pub Date : 2022-11-10 Liron Ravner, Jiesen Wang
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Applications of fluid models in service operations management Queueing Syst. (IF 1.2) Pub Date : 2022-11-05 Noa Zychlinski
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Retrial queues with constant retrial times Queueing Syst. (IF 1.2) Pub Date : 2022-10-29 Dieter Fiems
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Large deviations for stochastic fluid networks with Weibullian tails Queueing Syst. (IF 1.2) Pub Date : 2022-09-27 Mihail Bazhba, Chang-Han Rhee, Bert Zwart
We consider a stochastic fluid network where the external input processes are compound Poisson with heavy-tailed Weibullian jumps. Our results comprise of large deviations estimates for the buffer content process in the vector-valued Skorokhod space which is endowed with the product \(J_1\) topology. To illustrate our framework, we provide explicit results for a tandem queue. At the heart of our proof
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State space collapse for multi-class queueing networks under SBP service policies Queueing Syst. (IF 1.2) Pub Date : 2022-09-13 Chang Cao, J. G. Dai, Xiangyu Zhang
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Functional equations with multiple recursive terms Queueing Syst. (IF 1.2) Pub Date : 2022-09-04 Ivo Adan, Onno Boxma, Jacques Resing
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Fork–join and redundancy systems with heavy-tailed job sizes Queueing Syst. (IF 1.2) Pub Date : 2022-09-01 Youri Raaijmakers, Sem Borst, Onno Boxma
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Subexponential asymptotics of asymptotically block-Toeplitz and upper block-Hessenberg Markov chains Queueing Syst. (IF 1.2) Pub Date : 2022-08-30 Hiroyuki Masuyama
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Queueing and risk models with dependencies Queueing Syst. (IF 1.2) Pub Date : 2022-08-29 O. J. Boxma, M. R. H. Mandjes
This paper analyzes various stochastic recursions that arise in queueing and insurance risk models with a ‘semi-linear’ dependence structure. For example, an interarrival time depends on the workload, or the capital, immediately after the previous arrival; or the service time of a customer depends on her waiting time. In each case, we derive and solve a fixed-point equation for the Laplace–Stieltjes
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Derivative of the expected supremum of fractional Brownian motion at $$H=1$$ H = 1 Queueing Syst. (IF 1.2) Pub Date : 2022-08-30 Krzysztof Bisewski, Krzysztof Dȩbicki, Tomasz Rolski
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Tail asymptotics in any direction of the stationary distribution in a two-dimensional discrete-time QBD process Queueing Syst. (IF 1.2) Pub Date : 2022-08-30 Toshihisa Ozawa
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Optimal staffing for ticket queues Queueing Syst. (IF 1.2) Pub Date : 2022-08-26 Li Xiao, Susan H. Xu, David D. Yao, Hanqin Zhang
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On busy periods of the critical GI/G/1 queue and BRAVO Queueing Syst. (IF 1.2) Pub Date : 2022-08-22 Yoni Nazarathy, Zbigniew Palmowski
We study critical GI/G/1 queues under finite second-moment assumptions. We show that the busy-period distribution is regularly varying with index half. We also review previously known M/G/1/ and M/M/1 derivations, yielding exact asymptotics as well as a similar derivation for GI/M/1. The busy-period asymptotics determine the growth rate of moments of the renewal process counting busy cycles. We further
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Age of information using Markov-renewal methods Queueing Syst. (IF 1.2) Pub Date : 2022-08-17 George Kesidis, Takis Konstantopoulos, Michael A. Zazanis
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A dual skew symmetry for transient reflected Brownian motion in an orthant Queueing Syst. (IF 1.2) Pub Date : 2022-08-13 Sandro Franceschi, Kilian Raschel
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Birth and death processes in interactive random environments Queueing Syst. (IF 1.2) Pub Date : 2022-08-12 Guodong Pang, Andrey Sarantsev, Yuri Suhov
This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered: a continuous-time Markov chain (finite or countably infinite) and a reflected (jump) diffusion process. The background is determined by a joint Markov process carrying
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The periodic steady-state solution for queues with Erlang arrivals and service and time-varying periodic transition rates Queueing Syst. (IF 1.2) Pub Date : 2022-08-10 B. H. Margolius
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A transient symmetry analysis for the M/M/1/k queue Queueing Syst. (IF 1.2) Pub Date : 2022-08-07 William A. Massey, Emmanuel Ekwedike, Robert C. Hampshire, Jamol J. Pender
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WCFS: a new framework for analyzing multiserver systems Queueing Syst. (IF 1.2) Pub Date : 2022-07-28 Isaac Grosof, Mor Harchol-Balter, Alan Scheller-Wolf
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Uniform stability of some large-scale parallel server networks Queueing Syst. (IF 1.2) Pub Date : 2022-07-23 Hassan Hmedi, Ari Arapostathis, Guodong Pang
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On the Whittle index of Markov modulated restless bandits Queueing Syst. (IF 1.2) Pub Date : 2022-06-27 S. Duran, U. Ayesta, I. M. Verloop
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A load balancing system in the many-server heavy-traffic asymptotics Queueing Syst. (IF 1.2) Pub Date : 2022-06-21 Daniela Hurtado-Lange, Siva Theja Maguluri
We study a load balancing system in the many-server heavy-traffic regime. We consider a system with N servers, where jobs arrive to the system according to a Poisson process and have an exponentially distributed size with mean 1. We parametrize the arrival rate so that the arrival rate per server is \(1-N^{-\alpha }\), where \(\alpha >0\) is a parameter that represents how fast the load grows with
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Asymptotics of waiting time distributions in the accumulating priority queue Queueing Syst. (IF 1.2) Pub Date : 2022-05-10 Joris Walraevens, Thomas Van Giel, Stijn De Vuyst, Sabine Wittevrongel
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Validating state-dependent queues in health care. Queueing Syst. (IF 1.2) Pub Date : 2022-05-11 René Bekker
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Perishable inventories and queues with impatience Queueing Syst. (IF 1.2) Pub Date : 2022-05-07 D. Perry, W. Stadje
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New frontiers for stochastic matching Queueing Syst. (IF 1.2) Pub Date : 2022-05-05 Jean Mairesse, Pascal Moyal