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Academic literature on the topic 'Markovian Arrival Process'

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Published: 4 June 2021
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Journal articles on the topic "Markovian Arrival Process"

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HUNTER, JEFFREY J. "MARKOVIAN QUEUES WITH CORRELATED ARRIVAL PROCESSES." Asia-Pacific Journal of Operational Research 24, no. 04 (August 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 usual M/M/1 model. The aim of the paper is to compare conditions for stability and explore the queueing behavior of the different models.
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Cao, Jianyu, and Weixin Xie. "Joint arrival process of multiple independent batch Markovian arrival processes." Statistics & Probability Letters 133 (February 2018): 42–49. http://dx.doi.org/10.1016/j.spl.2017.09.012.

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Pérez-Ocón, Rafael, and Maria del Carmen Segovia. "Shock models under a Markovian arrival process." Mathematical and Computer Modelling 50, no. 5-6 (September 2009): 879–84. http://dx.doi.org/10.1016/j.mcm.2008.12.020.

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Neuts, Marcel F., LIU Dan, and NARAYANA Surya. "Local poissonification of the markovian arrival process." Communications in Statistics. Stochastic Models 8, no. 1 (January 1992): 87–129. http://dx.doi.org/10.1080/15326349208807216.

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Asmussen, Søren, and Ger Koole. "Marked point processes as limits of Markovian arrival streams." Journal of Applied Probability 30, no. 2 (June 1993): 365–72. http://dx.doi.org/10.2307/3214845.

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A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.
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Asmussen, Søren, and Ger Koole. "Marked point processes as limits of Markovian arrival streams." Journal of Applied Probability 30, no. 02 (June 1993): 365–72. http://dx.doi.org/10.1017/s0021900200117371.

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A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.
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Johnson, Mary A., and Surya Narayana. "Descriptors of arrival-process burstiness with application to the discrete Markovian arrival process." Queueing Systems 23, no. 1-4 (March 1996): 107–30. http://dx.doi.org/10.1007/bf01206553.

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Jin, Fang, Chengxun Wu, and Hui Ou. "Compound Binomial Model with Batch Markovian Arrival Process." Mathematical Problems in Engineering 2020 (November 28, 2020): 1–10. http://dx.doi.org/10.1155/2020/1932704.

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A compound binomial model with batch Markovian arrival process was studied, and the specific definitions are introduced. We discussed the problem of ruin probabilities. Specially, the recursion formulas of the conditional finite-time ruin probability are obtained and the numerical algorithm of the conditional finite-time nonruin probability is proposed. We also discuss research on the compound binomial model with batch Markovian arrival process and threshold dividend. Recursion formulas of the Gerber–Shiu function and the first discounted dividend value are provided, and the expressions of the total discounted dividend value are obtained and proved. At the last part, some numerical illustrations were presented.
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Ramírez-Cobo, Pepa, Rosa E. Lillo, and Michael P. Wiper. "Nonidentifiability of the Two-State Markovian Arrival Process." Journal of Applied Probability 47, no. 03 (September 2010): 630–49. http://dx.doi.org/10.1017/s0021900200006975.

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In this paper we consider the problem of identifiability for the two-state Markovian arrival process (MAP2). In particular, we show that the MAP2 is not identifiable, providing the conditions under which two different sets of parameters induce identical stationary laws for the observable process.
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Ramírez-Cobo, Pepa, Rosa E. Lillo, and Michael P. Wiper. "Nonidentifiability of the Two-State Markovian Arrival Process." Journal of Applied Probability 47, no. 3 (September 2010): 630–49. http://dx.doi.org/10.1239/jap/1285335400.

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In this paper we consider the problem of identifiability for the two-state Markovian arrival process (MAP2). In particular, we show that the MAP2 is not identifiable, providing the conditions under which two different sets of parameters induce identical stationary laws for the observable process.
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Dissertations / Theses on the topic "Markovian Arrival Process"

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Narayana, Surya 1962. "Some descriptors of the Markovian arrival process." Thesis, The University of Arizona, 1991. http://hdl.handle.net/10150/291729.

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The Markovian Arrival Process (MAP) is a tractable, versatile class of Markov renewal processes which has been extensively used to model arrival (or service) processes in queues. This thesis mainly deals with the first two moment matrices of the counts for the MAP. We derive asymptotic expansions for these two moment matrices and also derive efficient and stable algorithms to compute these matrices numerically. Simpler expressions for some of the classical mathematical descriptors of the superposition of independent MAPs also are derived.
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Frigui, Imed. "Analysis of a time-limited polling system with Markovian arrival process and phase type service." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq23604.pdf.

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Eum, Suyong, and suyong@ist osaka-u. ac jp. "Traffic Matrix Estimation in IP Networks." RMIT University. Electrical and Computer Engineering, 2007. http://adt.lib.rmit.edu.au/adt/public/adt-VIT20080215.155526.

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An Origin-Destination (OD) traffic matrix provides a major input to the design, planning and management of a telecommunications network. Since the Internet is being proposed as the principal delivery mechanism for telecommunications traffic at the present time, and this network is not owned or managed by a single entity, there are significant challenges for network planners and managers needing to determine equipment and topology configurations for the various sections of the Internet that are currently the responsibility of ISPs and traditional telcos. Planning of these sub-networks typically requires a traffic matrix of demands that is then used to infer the flows on the administrator's network. Unfortunately, computation of the traffic matrix from measurements of individual flows is extremely difficult due to the fact that the problem formulation generally leads to the need to solve an under-determined system of equations. Thus, there has been a major effort f rom among researchers to obtain the traffic matrix using various inference techniques. The major contribution of this thesis is the development of inference techniques for traffic matrix estimation problem according to three different approaches, viz: (1) deterministic, (2) statistical, and (3) dynamic approaches. Firstly, for the deterministic approach, the traffic matrix estimation problem is formulated as a nonlinear optimization problem based on the generalized Kruithof approach which uses the Kullback distance to measure the probabilistic distance between two traffic matrices. In addition, an algorithm using the Affine scaling method is developed to solve the constrained optimization problem. Secondly, for the statistical approach, a series of traffic matrices are obtained by applying a standard deterministic approach. The components of these matrices represent estimates of the volumes of flows being exchanged between all pairs of nodes at the respective measurement points and they form a stochastic counting process. Then, a Markovian Arrival Process of order two (MAP-2) is applied to model the counting processes formed from this series of estimated traffic matrices. Thirdly, for the dynamic approach, the dual problem of the multi-commodity flow problem is formulated to obtain a set of link weights. The new weight set enables flows to be rerouted along new paths, which create new constraints to overcome the under-determined nature of traffic matrix estimation. Since a weight change disturbs a network, the impact of weight changes on the network is investigated by using simulation based on the well-known ns2 simulator package. Finally, we introduce two network applications that make use of the deterministic and the statistical approaches to obtain a traffic matrix respectively and also describe a scenario for the use of the dynamic approach.
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Baey, Sébastien. "Contribution à la qualité de service d'une pile radio flexible pour la transmission de données multimédia en mode paquet sur interface radio UMTS WCDMA." Paris 11, 2004. http://www.theses.fr/2004PA112111.

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Cette thèse traite de l'intégration du trafic multimédia sur la voie montante de l'interface radio de l'UMTS. Le problème est abordé dans sa globalité, considérant à la fois les possibilités de partage de la ressource, une bonne caractérisation du trafic à transmettre et les possibilités ouvertes dans la norme UMTS. L'attention est plus particulièrement portée sur la vidéo MPEG4 et les données de type Internet. La première partie de la thèse dégage une approche du partage de ressource radio en mode WCDMA. Les performances du mécanisme de multiplexage de niveau couche physique avec qualité de transmission différenciée et l'impact du mécanisme d'adaptation de débit sont évalués. Cette analyse débouche sur la construction d'une fonction de coût pour l'estimation de la capacité cellulaire multiservice et la proposition d'une méthode d'équilibrage adaptatif de la qualité de transmission. La seconde partie de la thèse présente un nouveau modèle statistique pour le trafic vidéo MPEG4. Ce modèle consiste en une particularisation du processus DBMAP et permet d'évaluer analytiquement les performances de transmission à la traversée d'un système à file d'attente. La dernière partie de la thèse intègre l'ensemble de ces travaux pour aboutir à une stratégie d'ordonnancement coopérative multiplexant efficacement les paquets issus d'applications multimédia temps réel et non temps réel, dans le respect des contraintes d'intégrité et de retard. Une méthode analytique faisant appel à la théorie des files d'attente de type M/G/1 est fournie pour le calcul des retards subis par les paquets vidéo MPEG4 et les données lorsque cette stratégie est mise en œuvre au sein d'un réseau UMTS
This thesis deals with the integration of multimedia traffic on the uplink of the UMTS radio interface. The problem is tackled in its globality, considering jointly the resource sharing possibilities, a good characterization of the traffic to transmit and the possibilities opened in the UMTS standard. The attention is more particularly focused on MPEG4 video and data of the Internet type. The first part of the thesis provides an approach of radio resource sharing in WCDMA mode. The performances of the physical layer multiplexing mechanism with quality of transmission differentiation and the impact of the rate matching mechanism are evaluated. This analysis serves as a basis for the construction of a cost function for estimating the multiservice cellular capacity and the proposition of a quality of transmission adaptive balancing method. The second part of the thesis presents a new statistical model for MPEG4 video traffic. This model consists in a customization of the DBMAP process and allows evaluating the queueing performances analytically. The last part of the thesis integrates this set of works yielding a cooperative scheduling strategy that efficiently multiplexes the packets generated by real time and non real time multimedia applications while respecting the integrity and delay constraints. An analytical method based on M/G/1 type queueing systems theory is given for computing the delays incurred by MPEG4 video and data packets when this strategy is implemented in a UMTS network
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Klemm, Alexander, Christoph Lindemann, and Marco Lohmann. "Modeling IP traffic using the batch Markovian arrival process." 2003. https://ul.qucosa.de/id/qucosa%3A32407.

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In this paper, we show how to utilize the expectation-maximization (EM) algorithm for efficient and numerical stable parameter estimation of the batch Markovian arrival process (BMAP). In fact, effective computational formulas for the E-step of the EM algorithm are presented, which utilize the well-known randomization technique and a stable calculation of Poisson jump probabilities. Moreover, we identify the BMAP as an analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the BMAP such that different lengths of IP packets are represented by rewards of the BMAP. Using measured traffic data, a comparative study with the MMPP and the Poisson process illustrates the effectiveness of the customized BMAP for IP traffic modeling by visual inspection of sample paths over several time scales, by presenting important statistical properties as well as by investigations of queuing behavior.
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Frigui, Imed. "Analysis of a tim -limited polling system with Markovian arrival process and phase type service." 1997. http://hdl.handle.net/1993/787.

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Polling systems have been the subject of many studies and are of interest in the analysis of communication systems, operating systems scheduler, traffic intersections, and manufacturing systems. For communication and operating systems, the time-limited service discipline is very important since it allows one to limit the time the server is away from a particular queue. Nevertheless, it has received little attention, whereas, the exhaustive and gated service discipline have been studied extensively. In addition, most of the available results ignore correlation between arrivals. In this thesis, we have modeled the Fair Share Scheduler as a discrete time polling system. In this polling system, each queue is visited according to the exhaustive time-limited service discipline, customers arrive according to the Markovian arrival process and their service time has a phase type distribution. Both cyclic and table polling are considered. In addition, we consider, separately, the case when all the queues have infinite buffer capacity and when all the queues have finite buffer capacity. Our solution is based on the decomposition approach. Thus, for the infinite buffer capacity case, each queue in the polling system is treated as a MAP/PH/1 with vacation periods and is analyzed using the matrix-analytic approach. On the other hand, for the finite buffer capacity case, each queue is considered as a MAP/PH/1/K with vacation periods, for which the queue length distribution is obtained using the block Gauss-Seidel iterative procedure. The results of the MAP/PH/1 or the MAP/PH/1/K are then incorporated nto an iterative procedure to obtain the mean waiting time for each queue in a polling system. Because of the time-limited service discipline, the vacation and visit period distributions are represented by discrete-time phase distribution in the case of cyclic polling. However, for table polling, since the type of vacation the server takes depends on its position in the polling table, the vacation period looks like the convolution of discrete phase distributions and is represented by a MAP. In order to incorporate the correlation between the vacation and visit period distributions, the vacation period is obtained as the sum of an independent and a dependent part. The independent part is the convolution of the visit period of the queues visited while the server is on vacation. The dependent part is computed using an approach similar to that of Lee and Sengupta. The convergence of the iterative procedure is proved for the cyclic polling case using stochastic dominance. We have also proved that if we start with a stable system, then the iterative procedure is stable (for cyclic polling). Comparison between the iterative results and the simulation results shows that the iterative procedure provides reasonable results over a wide range of input parameters. However, the computational time increases as the dimension of the vacation period becomes large. In our case, the dimension of the vacation period distribution depends on (1) the number of queues in the polling system, (2) the time threshold for the queues visited while the server is on vacation, and (3) the number of visits in the case of table polling. In order to reduce the computational time, the dimension of each phase type vacation period distribution is reduced using the moments matching approach. Comparison between the original and reduced MAP shows that the error in the probability mass function and the coefficient of correlation is very small.
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Li, W., Demetres D. Kouvatsos, and Rod J. Fretwell. "On the Analytic Assessment of the Impact of Traffic Correlation on Queues in Continuous Time Domain." 2016. http://hdl.handle.net/10454/11031.

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Given only the traffic correlations of counts and intervals, a Batch Renewal Arrival Process (BRAP) is completely determined, as the least biased choice and thus, it provides the analytic means to construct suitable traffic models for the study of queueing systems independently of any other traffic characteristics. In this context, the BRAP and the Batch Markovian Arrival Process (BMAP) are employed in the continuous time domain towards the analysis of the stable BRAP/GE/1 and BMAP/GE/1 queues with infinite capacity, single servers and generalized exponential (GE) service times. Novel closed form expressions for the steady state probabilities of these queues are obtained, based on the embedded Markov chains (EMCs) technique and the matrix-geometric (M-G) method, respectively. Moreover, the stable GEsGGeo/GE/1 queue with GE-type service times and a GEsGGeo BRAP consisting of bursty GE-type batch interarrival times and a shifted generalized geometric (sGGeo) batch size distribution is adopted to assess analytically the combined adverse effects of varying degrees of correlation of intervals between individual arrivals and the burstiness of service times upon the typical quality of service (QoS) measure of the mean queue length (MQL). Moreover, a comprehensive experimental study is carried out to investigate numerically the relative impact of count and interval traffic correlations as well as other traffic characteristics upon the performance of stable BRAP/GE/1 and BMAP/GE/1 queues. It is suggested via a conjecture that the BRAP/GE/1 queue is likely to yield pessimistic performance metrics in comparison to those of the stable BMAP/GE/1 queues under the worst case scenario (i.e., a worst case scenario) of the same positive count and interval traffic correlations arising from long sojourn in each phase.
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Book chapters on the topic "Markovian Arrival Process"

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Gass, Saul I., and Carl M. Harris. "Markovian arrival process (Map)." In Encyclopedia of Operations Research and Management Science, 486. New York, NY: Springer US, 2001. http://dx.doi.org/10.1007/1-4020-0611-x_581.

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He, Qi-Ming. "From the Poisson Process to Markovian Arrival Processes." In Fundamentals of Matrix-Analytic Methods, 85–154. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7330-5_2.

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Moiseev, Alexander, and Anatoly Nazarov. "Tandem of Infinite-Server Queues with Markovian Arrival Process." In Communications in Computer and Information Science, 323–33. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30843-2_34.

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Klemm, Alexander, Christoph Lindemann, and Marco Lohmann. "Traffic Modeling of IP Networks Using the Batch Markovian Arrival Process." In Computer Performance Evaluation: Modelling Techniques and Tools, 92–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-46029-2_6.

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Klimenok, Valentina. "Two-Server Queueing System with Unreliable Servers and Markovian Arrival Process." In Information Technologies and Mathematical Modelling. Queueing Theory and Applications, 42–55. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68069-9_4.

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Mei, Liu, and Alexander Dudin. "Analysis of Retrial Queue with Heterogeneous Servers and Markovian Arrival Process." In Infosys Science Foundation Series, 29–49. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-5951-8_3.

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Claeys, Dieter, Joris Walraevens, Koenraad Laevens, Bart Steyaert, and Herwig Bruneel. "A Batch-Service Queueing Model with a Discrete Batch Markovian Arrival Process." In Analytical and Stochastic Modeling Techniques and Applications, 1–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13568-2_1.

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Klimenok, Valentina, and Alexander Dudin. "Algorithmic Analysis of Dual Tandem Queue with Batch Markovian Arrival Process and Repeated Attempts at the First Station." In Communications in Computer and Information Science, 190–203. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-14228-9_17.

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Breuer, Lothar. "Spatial Markovian Arrival Processes." In From Markov Jump Processes to Spatial Queues, 91–105. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0239-4_7.

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Breuer, Lothar. "Examples of Markovian Arrival Processes." In From Markov Jump Processes to Spatial Queues, 43–51. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0239-4_3.

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Conference papers on the topic "Markovian Arrival Process"

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Fang, Jin, and Mo Xiaoyun. "Dynamic Multi-Mode Portfolio Optimization Strategy for Markovian Arrival Process." In 2017 International Conference on Robots & Intelligent System (ICRIS). IEEE, 2017. http://dx.doi.org/10.1109/icris.2017.42.

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Grigoreva, Elena, Maximilian Laurer, Mikhail Vilgelm, Thomas Gehrsitz, and Wolfgang Kellerer. "Coupled Markovian Arrival Process for Automotive Machine Type Communication traffic modeling." In ICC 2017 - 2017 IEEE International Conference on Communications. IEEE, 2017. http://dx.doi.org/10.1109/icc.2017.7996498.

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Okamura, Hiroyuki, Junjun Zheng, and Tadashi Dohi. "Formulation of Opportunity-Based Age Replacement Models with Markovian Arrival Process." In 2020 Asia-Pacific International Symposium on Advanced Reliability and Maintenance Modeling (APARM). IEEE, 2020. http://dx.doi.org/10.1109/aparm49247.2020.9209344.

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Arivudainambi, D., and P. Godhandaraman. "Analysis of a single server batch Markovian arrival process with feedback." In 2011 3rd International Conference on Electronics Computer Technology (ICECT). IEEE, 2011. http://dx.doi.org/10.1109/icectech.2011.5942072.

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Okamura, Hiroyuki, Hidenari Kishikawa, and Tadashi Dohi. "Application of Deterministic Annealing EM Algorithm to Markovian Arrival Process Parameter Estimation." In Trusted Computing (UIC/ATC). IEEE, 2010. http://dx.doi.org/10.1109/uic-atc.2010.61.

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Bouchti, Abdelali El, and Abdelkrim Haqiq. "Quality of Service analysis of control access scheme of multimedia traffic in HSDPA channel using Markovian Arrival Process and stochastic reward Nets." In 2012 Second International Conference on Innovative Computing Technology (INTECH). IEEE, 2012. http://dx.doi.org/10.1109/intech.2012.6457819.

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Chydzinski, Andrzej. "Packet Loss Process in a Queue with Markovian Arrivals." In 2008 Seventh International Conference on Networking ICN. IEEE, 2008. http://dx.doi.org/10.1109/icn.2008.104.

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