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Journal articles on the topic 'Markovian queueing models'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

García-Sanz, M. D., F. R. Fernández, M. G. Fiestras-Janeiro, I. García-Jurado, and J. Puerto. "Cooperation in Markovian queueing models." European Journal of Operational Research 188, no. 2 (2008): 485–95. http://dx.doi.org/10.1016/j.ejor.2007.04.053.

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2

Patrick Wang, P. "Markovian queueing models with periodic-review." Computers & Operations Research 23, no. 8 (1996): 741–54. http://dx.doi.org/10.1016/0305-0548(96)82076-4.

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3

Sen, Kanwar, and J. L. Jain. "Combinatorial approach to Markovian queueing models." Journal of Statistical Planning and Inference 34, no. 2 (1993): 269–79. http://dx.doi.org/10.1016/0378-3758(93)90011-t.

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4

HUNTER, JEFFREY J. "MARKOVIAN QUEUES WITH CORRELATED ARRIVAL PROCESSES." Asia-Pacific Journal of Operational Research 24, no. 04 (2007): 593–611. http://dx.doi.org/10.1142/s021759590700136x.

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In an attempt to examine the effect of dependencies in the arrival process on the steady state queue length process in single server queueing models with exponential service time distribution, four different models for the arrival process, each with marginally distributed exponential inter-arrivals to the queueing system, are considered. Two of these models are based upon the upper and lower bounding joint distribution functions given by the Fréchet bounds for bivariate distributions with specified marginals, the third is based on Downton's bivariate exponential distribution and fourthly the u

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5

Gwiżdż, Piotr. "Applications of Stochastic Semigroups to Queueing Models." Annales Mathematicae Silesianae 33, no. 1 (2019): 121–42. http://dx.doi.org/10.2478/amsil-2018-0007.

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AbstractNon-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.

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6

ERRAMILLI, ASHOK, WALTER WILLINGER, and PARAG PRUTHI. "FRACTAL TRAFFIC FLOWS IN HIGH-SPEED COMMUNICATIONS NETWORKS." Fractals 02, no. 03 (1994): 409–12. http://dx.doi.org/10.1142/s0218348x94000545.

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Traditional queueing models for traffic flows in communications networks are based on Markovian assumptions. However, recent studies within Bellcore of large sets of real-time network traffic measurements have revealed that traffic in computer and emerging high-speed networks has features that are more accurately and more efficiently described in terms of fractal models, rather than traditional Markovian models. This paper briefly reviews these measurement studies, and motivates the application of fractals to describe and analyze traffic flows in modern communications networks.

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7

Domański, Adam, Joanna Domańska, Katarzyna Filus, Jakub Szyguła, and Tadeusz Czachórski. "Self-Similar Markovian Sources." Applied Sciences 10, no. 11 (2020): 3727. http://dx.doi.org/10.3390/app10113727.

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Markov queueing models are a powerful tool to evaluate the performance of computer networks and have been used in telecommunication studies for over 100 years. To apply them to the evaluation of the modern Internet, we should not only adapt them to the contemporary network structures but also include a description of the complex stochastic patterns (self-similarity and long-range dependance) of transmitted flows. We examine the features of two Markov models of an almost self-similar process, keeping in mind the modeling of Internet traffic. We have found that the obtained results are comparabl

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8

Cruz, Frederico R. B., Márcio A. C. Almeida, Marcos F. S. V. D’Angelo, and Tom van Woensel. "Traffic Intensity Estimation in Finite Markovian Queueing Systems." Mathematical Problems in Engineering 2018 (June 26, 2018): 1–15. http://dx.doi.org/10.1155/2018/3018758.

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In many everyday situations in which a queue is formed, queueing models may play a key role. By using such models, which are idealizations of reality, accurate performance measures can be determined, such as traffic intensity (ρ), which is defined as the ratio between the arrival rate and the service rate. An intermediate step in the process includes the statistical estimation of the parameters of the proper model. In this study, we are interested in investigating the finite-sample behavior of some well-known methods for the estimation of ρ for single-server finite Markovian queues or, in Kend

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9

Ledoux, James, and Gerardo Rubino. "Simple formulae for counting processes in reliability models." Advances in Applied Probability 29, no. 04 (1997): 1018–38. http://dx.doi.org/10.1017/s000186780004800x.

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Dependability evaluation is a basic component in the assessment of the quality of repairable systems. We develop a model taking simultaneously into account the occurrence of failures and repairs, together with the observation of user-defined success events. The model is built from a Markovian description of the behavior of the system. We obtain the distribution function of the joint number of observed failures and of delivered services on a fixed mission period of the system. In particular, the marginal distribution of the number of failures can be directly related to the distribution of the M

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Ledoux, James, and Gerardo Rubino. "Simple formulae for counting processes in reliability models." Advances in Applied Probability 29, no. 4 (1997): 1018–38. http://dx.doi.org/10.2307/1427852.

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Dependability evaluation is a basic component in the assessment of the quality of repairable systems. We develop a model taking simultaneously into account the occurrence of failures and repairs, together with the observation of user-defined success events. The model is built from a Markovian description of the behavior of the system. We obtain the distribution function of the joint number of observed failures and of delivered services on a fixed mission period of the system. In particular, the marginal distribution of the number of failures can be directly related to the distribution of the M

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11

Asmussen, Søren. "The heavy traffic limit of a class of Markovian queueing models." Operations Research Letters 6, no. 6 (1987): 301–6. http://dx.doi.org/10.1016/0167-6377(87)90048-4.

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12

Kruk, Łukasz. "Stability of preemptive EDF queueing networks." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 73, no. 2 (2020): 105. http://dx.doi.org/10.17951/a.2019.73.2.105-134.

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We show stability of preemptive, strictly subcritical EDF networks with Markovian routing. To this end, we prove that the associated fluid limits satisfy the first-in-system, first-out (FISFO) fluid model equations and thus, by an extension of a result of Bramson (2001), the corresponding fluid models are stable. We also demonstrate that in a preemptive multiclass EDF network, after a time large enough to process all the initial customers to completion, the maximal number of partially served customers in the system over a finite time horizon converges to zero in \(L^1\) under fluid scaling.

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13

Abdelkader, Yousry H., and Maram Al-Wohaibi. "Computing the Performance Measures in Queueing Models via the Method of Order Statistics." Journal of Applied Mathematics 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/790253.

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This paper focuses on new measures of performance in single-server Markovian queueing system. These measures depend on the moments of order statistics. The expected value and the variance of the maximum (minimum) number of customers in the system as well as the expected value and the variance of the minimum (maximum) waiting time are presented. Application to an M/M/1 model is given to illustrate the idea and the applicability of the proposed measures.

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14

Masuyama, Hiroyuki. "TAIL ASYMPTOTICS FOR CUMULATIVE PROCESSES SAMPLED AT HEAVY-TAILED RANDOM TIMES WITH APPLICATIONS TO QUEUEING MODELS IN MARKOVIAN ENVIRONMENTS." Journal of the Operations Research Society of Japan 56, no. 4 (2013): 257–308. http://dx.doi.org/10.15807/jorsj.56.257.

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15

Dudin, Alexander N., and Shoichi Nishimura. "Optimal control for a BMAP/G/1 queue with two service modes." Mathematical Problems in Engineering 5, no. 3 (1999): 255–73. http://dx.doi.org/10.1155/s1024123x99001088.

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Queueing models with controllable service rate play an important role in telecommunication systems. This paper deals with a single-server model with a batch Markovian arrival process (BMAP) and two service modes, where switch-over times are involved when changing the service mode. The embedded stationary queue length distribution and the explicit dependence of operation criteria on switch-over levels and derived.

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16

Kryukova, Anastasia L. "On the rate of convergence for a class of Markovian queues with group services." Discrete and Continuous Models and Applied Computational Science 28, no. 3 (2020): 205–15. http://dx.doi.org/10.22363/2658-4670-2020-28-3-205-215.

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There are many queuing systems that accept single arrivals, accumulate them and service only as a group. Examples of such systems exist in various areas of human life, from traffic of transport to processing requests on a computer network. Therefore, our study is actual. In this paper some class of finite Markovian queueing models with single arrivals and group services are studied. We considered the forward Kolmogorov system for corresponding class of Markov chains. The method of obtaining bounds of convergence on the rate via the notion of the logarithmic norm of a linear operator function i

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17

Woudt, Edwin, Pieter-Tjerk de Boer, and Jan-Kees van Ommeren. "Improving Adaptive Importance Sampling Simulation of Markovian Queueing Models using Non-parametric Smoothing." SIMULATION 83, no. 12 (2007): 811–20. http://dx.doi.org/10.1177/0037549707087223.

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18

Vatamidou, E., I. J. B. F. Adan, M. Vlasiou, and B. Zwart. "Corrected Phase-Type Approximations of Heavy-Tailed Queueing Models in a Markovian Environment." Stochastic Models 30, no. 4 (2014): 598–638. http://dx.doi.org/10.1080/15326349.2014.956227.

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19

Onyuksel, I. H., and K. B. Irani. "Markovian queueing network models for performance analysis of a single-bus multiprocessor system." IEEE Transactions on Computers 39, no. 7 (1990): 975–80. http://dx.doi.org/10.1109/12.55702.

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20

Matendo, Sadrac K. "Some performance measures for vacation models with a batch Markovian arrival process." Journal of Applied Mathematics and Stochastic Analysis 7, no. 2 (1994): 111–24. http://dx.doi.org/10.1155/s1048953394000134.

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We consider a single server infinite capacity queueing system, where the arrival process is a batch Markovian arrival process (BMAP). Particular BMAPs are the batch Poisson arrival process, the Markovian arrival process (MAP), many batch arrival processes with correlated interarrival times and batch sizes, and superpositions of these processes. We note that the MAP includes phase-type (PH) renewal processes and non-renewal processes such as the Markov modulated Poisson process (MMPP).The server applies Kella's vacation scheme, i.e., a vacation policy where the decision of whether to take a new

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21

Zharkov, M. L., and M. M. Pavidis. "Simulation of railway marshalling yards using the methods of the queueing theory." Dependability 21, no. 3 (2021): 27–34. http://dx.doi.org/10.21683/1729-2646-2021-21-3-27-34.

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Aim. The paper primarily aims to simulate the operation of railway transportation systems using the queueing theory with the case study of marshalling yards. The goals also include the development of the methods and tools of mathematical simulation and queueing theory. Methods. One of the pressing matters of modern science is the development of methods of mathematical simulation of transportation systems for the purpose of analyzing the efficiency, stability and dependability of their operation while taking into account random factors. Research has shown that the use of the most mature class o

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22

Satin, Yacov, Alexander Zeifman, Alexander Sipin, Sherif I. Ammar, and Janos Sztrik. "On Probability Characteristics for a Class of Queueing Models with Impatient Customers." Mathematics 8, no. 4 (2020): 594. http://dx.doi.org/10.3390/math8040594.

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In this paper, a class of queueing models with impatient customers is considered. It deals with the probability characteristics of an individual customer in a non-stationary Markovian queue with impatient customers, the stationary analogue of which was studied previously as a successful approximation of a more general non-Markov model. A new mathematical model of the process is considered that describes the behavior of an individual requirement in the queue of requirements. This can be applied both in the stationary and non-stationary cases. Based on the proposed model, a methodology has been

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23

Aalto, Samuli. "Characterization of the Output Rate Process for a Markovian Storage Model." Journal of Applied Probability 35, no. 01 (1998): 184–99. http://dx.doi.org/10.1017/s0021900200014777.

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We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process

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24

Aalto, Samuli. "Characterization of the Output Rate Process for a Markovian Storage Model." Journal of Applied Probability 35, no. 1 (1998): 184–99. http://dx.doi.org/10.1239/jap/1032192561.

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We consider storage models where the input rate and the demand are modulated by a Markov jump process. One particular example from teletraffic theory is a fluid model of a multiplexer loaded by exponential on-off sources. Although the storage level process has been widely studied, little attention has been paid to the output rate process. We will show that, under certain assumptions, there exists another Markov jump process that modulates the output rate. The modulating process is explicitly constructed. It turns out to be a modification of a GI/G/1 queueing process

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25

Fralix, Brian. "A TIME-DEPENDENT STUDY OF THE KNOCKOUT QUEUE." Probability in the Engineering and Informational Sciences 27, no. 3 (2013): 309–17. http://dx.doi.org/10.1017/s0269964813000041.

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We examine the time-dependent behavior of a birth–death process, whose birth rates and death rates are decreasing and increasing, respectively, with respect to the current state. Such models can be used to describe Markovian queueing systems with exponential reneging, where potential arrivals balk with a certain probability that depends on the number of customers observed upon arrival. Our results are derived by interpreting the birth–death process as the queue-length process of what we refer to as the “knockout queue.”

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26

Zeifman, Alexander, Rostislav Razumchik, Yacov Satin, Ksenia Kiseleva, Anna Korotysheva, and Victor Korolev. "Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services." International Journal of Applied Mathematics and Computer Science 28, no. 1 (2018): 141–54. http://dx.doi.org/10.2478/amcs-2018-0011.

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AbstractIn this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of n

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27

Gupta, Umesh Chandra, Nitin Kumar, Sourav Pradhan, Farida Parvez Barbhuiya, and Mohan L. Chaudhry. "Complete analysis of a discrete-time batch service queue with batch-size-dependent service time under correlated arrival process: D-MAP/Gn(a,b)/1." RAIRO - Operations Research 55, no. 3 (2021): 1231–56. http://dx.doi.org/10.1051/ro/2021054.

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Discrete-time queueing models find a large number of applications as they are used in modeling queueing systems arising in digital platforms like telecommunication systems and computer networks. In this paper, we analyze an infinite-buffer queueing model with discrete Markovian arrival process. The units on arrival are served in batches by a single server according to the general bulk-service rule, and the service time follows general distribution with service rate depending on the size of the batch being served. We mathematically formulate the model using the supplementary variable technique

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28

De Haan, Roland, Ahmad Al Hanbali, Richard J. Boucherie, and Jan-Kees Van Ommeren. "Transient analysis for exponential time-limited polling models under the preemptive repeat random policy." Advances in Applied Probability 52, no. 1 (2020): 32–60. http://dx.doi.org/10.1017/apr.2019.51.

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AbstractPolling systems are queueing systems consisting of multiple queues served by a single server. In this paper we analyze two types of preemptive time-limited polling systems, the so-called pure and exhaustive time-limited disciplines. In particular, we derive a direct relation for the evolution of the joint queue length during the course of a server visit. The analysis of the pure time-limited discipline builds on and extends several known results for the transient analysis of an M/G/1 queue. For the analysis of the exhaustive discipline we derive several new results for the transient an

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29

Jagerman, David L., and Benjamin Melamed. "On Markovian traffic with applications to TES processes." Journal of Applied Mathematics and Stochastic Analysis 7, no. 3 (1994): 373–96. http://dx.doi.org/10.1155/s1048953394000316.

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Markov processes are an important ingredient in a variety of stochastic applications. Notable instances include queueing systems and traffic processes offered to them. This paper is concerned with Markovian traffic, i.e., traffic processes whose inter-arrival times (separating the time points of discrete arrivals) form a real-valued Markov chain. As such this paper aims to extend the classical results of renewal traffic, where interarrival times are assumed to be independent, identically distributed. Following traditional renewal theory, three functions are addressed: the probability of the nu

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30

Kim, Bara, and Khosrow Sohraby. "Tail behavior of the queue size and waiting time in a queue with discrete autoregressive arrivals." Advances in Applied Probability 38, no. 4 (2006): 1116–31. http://dx.doi.org/10.1017/s0001867800001476.

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Autoregressive arrival models are described by a few parameters and provide a simple means to obtain analytical models for matching the first- and second-order statistics of measured data. We consider a discrete-time queueing system where the service time of a customer occupies one slot and the arrival process is governed by a discrete autoregressive process of order 1 (a DAR(1) process) which is characterized by an arbitrary stationary batch size distribution and a correlation coefficient. The tail behaviors of the queue length and the waiting time distributions are examined. In particular, i

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31

Malyshev, V. A. "Networks and dynamical systems." Advances in Applied Probability 25, no. 01 (1993): 140–75. http://dx.doi.org/10.1017/s0001867800025210.

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A new approach to the problem of classification of (deflected) random walks inor Markovian models for queueing networks with identical customers is introduced. It is based on the analysis of the intrinsic dynamical system associated with the random walk. Earlier results for small dimensions are presented from this novel point of view. We give proofs of new results for higher dimensions related to the existence of a continuous invariant measure for the underlying dynamical system. Two constants are shown to be important: the free energyM&lt; 0 corresponds to ergodicity, the Lyapounov expone

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32

Malyshev, V. A. "Networks and dynamical systems." Advances in Applied Probability 25, no. 1 (1993): 140–75. http://dx.doi.org/10.2307/1427500.

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A new approach to the problem of classification of (deflected) random walks in or Markovian models for queueing networks with identical customers is introduced. It is based on the analysis of the intrinsic dynamical system associated with the random walk. Earlier results for small dimensions are presented from this novel point of view. We give proofs of new results for higher dimensions related to the existence of a continuous invariant measure for the underlying dynamical system. Two constants are shown to be important: the free energy M < 0 corresponds to ergodicity, the Lyapounov exponen

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33

Nair, Divya Velayudhan, Achyutha Krishnamoorthy, Agassi Melikov, and Sevinj Aliyeva. "MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback." Mathematics 9, no. 15 (2021): 1797. http://dx.doi.org/10.3390/math9151797.

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In this paper, we consider two single server queueing systems to which customers of two distinct priorities (P1 and P2) arrive according to a Marked Markovian arrival process (MMAP). They are served according to two distinct phase type distributions. The probability of a P1 customer to feedback is θ on completion of his service. The feedback (P1) customers, as well as P2 customers, join the low priority queue. Low priority (P2) customers are taken for service from the head of the line whenever the P1 queue is found to be empty at the service completion epoch. We assume a finite waiting space f

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34

Sama, Hanumantha Rao, Vasanta Kumar Vemuri, and Venkata Siva Nageswara Hari Prasad Boppana. "Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment." Ingénierie des systèmes d information 26, no. 4 (2021): 357–64. http://dx.doi.org/10.18280/isi.260403.

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The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estima

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35

Browne, Sid, and Karl Sigman. "Work-modulated queues with applications to storage processes." Journal of Applied Probability 29, no. 3 (1992): 699–712. http://dx.doi.org/10.2307/3214906.

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We study two FIFO single-server queueing models in which both the arrival and service processes are modulated by the amount of work in the system. In the first model, the nth customer's service time, Sn, depends upon their delay, Dn, in a general Markovian way and the arrival process is a non-stationary Poisson process (NSPP) modulated by work, that is, with an intensity that is a general deterministic function g of work in system V(t). Some examples are provided. In our second model, the arrivals once again form a work-modulated NSPP, but, each customer brings a job consisting of an amount of

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36

Browne, Sid, and Karl Sigman. "Work-modulated queues with applications to storage processes." Journal of Applied Probability 29, no. 03 (1992): 699–712. http://dx.doi.org/10.1017/s0021900200043515.

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We study two FIFO single-server queueing models in which both the arrival and service processes are modulated by the amount of work in the system. In the first model, the nth customer's service time, Sn , depends upon their delay, Dn , in a general Markovian way and the arrival process is a non-stationary Poisson process (NSPP) modulated by work, that is, with an intensity that is a general deterministic function g of work in system V(t). Some examples are provided. In our second model, the arrivals once again form a work-modulated NSPP, but, each customer brings a job consisting of an amount

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37

Chechelnitsky, O. A. "The properties of the queuing model with the parallel structure." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2020): 79–82. http://dx.doi.org/10.17721/1812-5409.2020/4.11.

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The present article is devoted to research the multi-channelk model with the parallel structure. It means that we consider the model which consists of two infinite-server queues. The service time in the each system has general function of distribution. In this case the stochastic dynamic of our model cannot be defined by Markov chain. As a result, analysis of such models is much more difficult than that of the corresponding Markovian queueing models. Besides we assume that customers arrive to our model according a bivariate Poisson input flow. This input process is characterized by the fact th

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38

Naumov, Valeriy, and Konstantin Samouylov. "PRODUCT-FORM MARKOVIAN QUEUEING SYSTEMS WITH MULTIPLE RESOURCES." Probability in the Engineering and Informational Sciences, June 14, 2019, 1–9. http://dx.doi.org/10.1017/s026996481900024x.

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In the paper, we study general Markovian models of loss systems with random resource requirements, in which customers at arrival occupy random quantities of various resources and release them at departure. Customers may request negative quantities of resources, but total amount of resources allocated to customers should be nonnegative and cannot exceed predefined maximum levels. Allocating a negative volume of a resource to a customer leads to a temporary increase in its volume in the system. We derive necessary and sufficient conditions for the product-form of the stationary probability distr

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39

Abbas, Mazlan, and Zainal Abidin Ahmad. "Matrix Analytic Methods For Evaluating Loss Performance In An ATM Networks." Jurnal Teknologi, May 15, 1992, 34–43. http://dx.doi.org/10.11113/jt.v20.1064.

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This paper will describe an analytical approach to the solutions of queueing models with finites capacity. The methods is chosen because its abilitiy to model exactly complex non-Markovian model which have correlated, non-renewal input process which is nearly impossible to get exact expressions by using classical methods of generating functions. We applied this methodology to compute the loss performance a of a queueing item specifically in the scenario of Asynchronous Transfer Mode (ATM) networks.

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40

Arapostathis, Ari, Hassan Hmedi, and Guodong Pang. "On Uniform Exponential Ergodicity of Markovian Multiclass Many-Server Queues in the Halfin–Whitt Regime." Mathematics of Operations Research, February 3, 2021. http://dx.doi.org/10.1287/moor.2020.1087.

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We study ergodic properties of Markovian multiclass many-server queues that are uniform over scheduling policies and the size of the system. The system is heavily loaded in the Halfin–Whitt regime, and the scheduling policies are work conserving and preemptive. We provide a unified approach via a Lyapunov function method that establishes Foster–Lyapunov equations for both the limiting diffusion and the prelimit diffusion-scaled queuing processes simultaneously. We first study the limiting controlled diffusion and show that if the spare capacity (safety staffing) parameter is positive, the diff

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