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The problem of exact evaluation of the mean service cycle time in tandem systems of single-server queues with both infinite and finite buffers is considered. It is assumed that the interarrival and service times of customers form sequences…

Optimization and Control · Mathematics 2012-12-24 N. K. Krivulin , V. B. Nevzorov

We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…

Probability · Mathematics 2015-12-01 Gianmarco Bet , Remco van der Hofstad , Johan S. H. van Leeuwaarden

We analyze the latency or sojourn time L(m,n) for the last customer in a batch of n customers to exit from the m-th queue in a tandem of m queues in the setting where the queues are in equilibrium before the batch of customers arrives at…

Probability · Mathematics 2014-04-21 Jinho Baik , Raj Rao Nadakuditi

We consider an $M/M/1$ queueing system with impatient customers with multiple and single vacations. It is assumed that customers are impatient whenever the state of the server. We derive the probability generating functions of the number of…

Probability · Mathematics 2016-04-12 Assia Boumahdaf

This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded $G/Ph/n+GI$ queues, where the…

Probability · Mathematics 2010-11-10 J. G. Dai , Shuangchi He , Tolga Tezcan

This paper studies the diffusion limit for a network of infinite-server queues operating under Markov modulation (meaning that the system's parameters depend on an autonomously evolving background process). In previous papers on (primarily…

Probability · Mathematics 2017-12-13 H. M. Jansen , M. Mandjes , K. De Turck , S. Wittevrongel

Freshness of status update packets is essential for enabling services where a destination needs the most recent measurements of various sensors. In this paper, we study the information freshness of single-server multi-source queueing models…

Information Theory · Computer Science 2020-04-02 Mohammad Moltafet , Markus Leinonen , Marian Codreanu

This paper proposes a stochastic framework to evaluate the performance of public transit systems under short random service suspensions. We aim to derive closed-form formulations of the mean and variance of the queue length and waiting…

Probability · Mathematics 2023-01-04 Baichuan Mo , Li Jin , Haris N. Koutsopoulos , Zuo-Jun Max Shen , Jinhua Zhao

This self-contained discussion relates the long-run average holding cost per unit time to the long-run average response time per customer in a $G/G/1$ queue with no assumption made on the order of service. The only restriction established…

Performance · Computer Science 2021-08-18 Dylan Solms

We study multiclass many-server queues for which the arrival, service and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the "averaged" Halfin-Whitt regime, which means…

Probability · Mathematics 2019-07-15 Ari Arapostathis , Anirban Das , Guodong Pang , Yi Zheng

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

The $M/GI/m/n$ queueing system with $m$ homogeneous servers and the finite number $n$ of waiting spaces is studied. Let $\lambda$ be the customers arrival rate, and let $\mu$ be the reciprocal of the expected service time of a customer.…

Probability · Mathematics 2010-03-25 Vyacheslav M. Abramov

The problems arising when the moments of service time distributions, for which the MGinf queue system busy period and busy cycle become very easy to study, are presented and it is shown how to overcome them. The busy cycle renewal function…

Probability · Mathematics 2021-10-08 Manuel Alberto M. Ferreira

Burke's theorem can be seen as a fixed-point result for an exponential single-server queue; when the arrival process is Poisson, the departure process has the same distribution as the arrival process. We consider extensions of this result…

Probability · Mathematics 2010-03-17 James B. Martin , Balaji Prabhakar

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

This paper considers the queueing performance of a system that transmits coded data over a time-varying erasure channel. In our model, the queue length and channel state together form a Markov chain that depends on the system parameters.…

Information Theory · Computer Science 2021-03-26 Parimal Parag , Jean-Francois Chamberland , Henry D. Pfister , Krishna R. Narayanan

This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a…

Optimization and Control · Mathematics 2023-07-31 K. Jeganathan , T. Harikrishnan , K. Prasanna Lakshmi , D. Nagarajan

We are interested in a large queue in a $GI/G/k$ queue with heterogeneous servers. For this, we consider tail asymptotics and weak limit approximations for the stationary distribution of its queue length process in continuous time under a…

Probability · Mathematics 2017-03-10 Masakiyo Miyazawa

In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the…

Networking and Internet Architecture · Computer Science 2020-12-22 Antzela Kosta , Nikolaos Pappas , Anthony Ephremides , Vangelis Angelakis

In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…

Probability · Mathematics 2020-06-02 Ioannis Dimitriou