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Journal articles on the topic 'Nearly completely decomposable (NCD)'

Author: Grafiati

Published: 5 June 2025

Last updated: 16 July 2025

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1

Kontovasilis, Kimon P., and Nikolas M. Mitrou. "Markov-modulated traffic with nearly complete decomposability characteristics and associated fluid queueing models." Advances in Applied Probability 27, no. 4 (1995): 1144–85. http://dx.doi.org/10.2307/1427937.

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This paper considers fluid queuing models of Markov-modulated traffic that, due to large differences in the time-scales of events, possess structural characteristics that yield a nearly completely decomposable (NCD) state-space. Extension of domain decomposition and aggregation techniques that apply to approximating the eigensystem of Markov chains permits the approximate subdivision of the full system to a number of small, independent subsystems (decomposition phase), plus an ‘aggregative' system featuring a state-space that distinguishes only one index per subsystem (aggregation phase). Perturbation analysis reveals that the error incurred by the approximation is of an order of magnitude equal to the weak coupling of the NCD Markov chain.The study in this paper is then extended to the structure of NCD fluid models describing source superposition (multiplexing). It is shown that efficient spectral factorization techniques that arise from the Kronecker sum form of the global matrices can be applied through and combined with the decomposition and aggregation procedures. All structural characteristics and system parameters are expressible in terms of the individual sources multiplexed together, rendering the construction of the global system unnecessary.Finally, besides providing efficient computational algorithms, the work in this paper can be recast as a conceptual framework for the better understanding of queueing systems under the presence of events happening in widely differing time-scales.

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2

Kontovasilis, Kimon P., and Nikolas M. Mitrou. "Markov-modulated traffic with nearly complete decomposability characteristics and associated fluid queueing models." Advances in Applied Probability 27, no. 04 (1995): 1144–85. http://dx.doi.org/10.1017/s0001867800047820.

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This paper considers fluid queuing models of Markov-modulated traffic that, due to large differences in the time-scales of events, possess structural characteristics that yield a nearly completely decomposable (NCD) state-space. Extension of domain decomposition and aggregation techniques that apply to approximating the eigensystem of Markov chains permits the approximate subdivision of the full system to a number of small, independent subsystems (decomposition phase), plus an ‘aggregative' system featuring a state-space that distinguishes only one index per subsystem (aggregation phase). Perturbation analysis reveals that the error incurred by the approximation is of an order of magnitude equal to the weak coupling of the NCD Markov chain. The study in this paper is then extended to the structure of NCD fluid models describing source superposition (multiplexing). It is shown that efficient spectral factorization techniques that arise from the Kronecker sum form of the global matrices can be applied through and combined with the decomposition and aggregation procedures. All structural characteristics and system parameters are expressible in terms of the individual sources multiplexed together, rendering the construction of the global system unnecessary. Finally, besides providing efficient computational algorithms, the work in this paper can be recast as a conceptual framework for the better understanding of queueing systems under the presence of events happening in widely differing time-scales.

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3

Agboola, Sunday Olanrewaju. "The Decomposition and Aggregation Algorithmic Numerical Iterative Solution Methods for the Stationary Distribution of Markov Chain." Journal of Scientific and Engineering Research 9, no. 1 (2022): 116–23. https://doi.org/10.5281/zenodo.10498342.

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<strong>Abstract</strong> The evolution of a system is represented by transitions from one state to the next, and the system's physical or mathematical behavior can also be depicted by defining all of the numerous states it can be in and demonstrating how it moves between them. In this study, the iterative solution methods for the stationary distribution of Markov chains which start with an initial estimate of the solution vector and then alter it in such a way that it gets closer and closer to the genuine solution with each step or iteration., and also involved the matrices operation such as multiplication with one or more vectors,  which leaves the transition matrices unchanged and saves time has been investigated, in order to provide some insight into the solutions of stationary distribution of Markov chain. Our quest is to compute the solutions using decomposition and aggregation algorithmic numerical iterative methods by considering the following three steps: the left-hand eigenvector <em> </em>of length  corresponding to the eigenvalue closest to 1,  , in each block <em> </em>is computed; the weights <em>,</em> an approximate solution to the stationary probability vector  is estimated and the global solution  is computed. Concept of eigen values and vectors, Matrix operations such as Lower, upper and diagonal matrices and normalization principle are used with the help of some existing laws, theorems and formulas of Markov chain. The global solution are obtained for the illustrative examples in each block  

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4

Louchard, Guy, and Guy Latouche. "Geometric bounds on iterative approximations for nearly completely decomposable Markov chains." Journal of Applied Probability 27, no. 3 (1990): 521–29. http://dx.doi.org/10.2307/3214538.

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We consider a finite Markov chain with nearly-completely decomposable stochastic matrix. We determine bounds for the error, when the stationary probability vector is approximated via a perturbation analysis.

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5

Louchard, Guy, and Guy Latouche. "Geometric bounds on iterative approximations for nearly completely decomposable Markov chains." Journal of Applied Probability 27, no. 03 (1990): 521–29. http://dx.doi.org/10.1017/s0021900200039085.

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We consider a finite Markov chain with nearly-completely decomposable stochastic matrix. We determine bounds for the error, when the stationary probability vector is approximated via a perturbation analysis.

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6

Dey, S. "Reduced-complexity filtering for partially observed nearly completely decomposable Markov chains." IEEE Transactions on Signal Processing 48, no. 12 (2000): 3334–44. http://dx.doi.org/10.1109/78.886997.

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7

Mattingly, R. Bruce. "A Revised Stochastic Complementation Algorithm for Nearly Completely Decomposable Markov Chains." ORSA Journal on Computing 7, no. 2 (1995): 117–24. http://dx.doi.org/10.1287/ijoc.7.2.117.

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8

Lu, Yingdong, Mark S. Squillante, and Chai Wah Wu. "Nearly Completely Decomposable Epidemic-Like Stochastic Processes with Time-Varying Behavior." ACM SIGMETRICS Performance Evaluation Review 45, no. 2 (2017): 48–50. http://dx.doi.org/10.1145/3152042.3152059.

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9

Bhuvaneshwari G, Selvarani R, Suriyamathi B, Allwyn Moses M, and Kalichwaran S. "A study to evaluate the magnitude of understanding on harm’s way associated with heart disease among clients attending NCD clinic at nemam PHC." International Journal of Research in Pharmaceutical Sciences 10, no. 4 (2019): 2983–87. http://dx.doi.org/10.26452/ijrps.v10i4.1583.

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Non-communicable Disease (NCD), almost completely heart diseases, malignancy, diabetes and chronic obstructive pulmonary diseases are the main source of demise worldwide killing additional human beings further wise entire further sources merge. In 2008 nearly two-thirds of the demises were due to NCD, a 36 million out of 57. Out of this almost completely 80% of demise happens in little and medium earnings nation with over 50% of them happening amid human beings completely amount 70 years old and 29% under 60 years of age. At current heart diseases (CVD) are the numeral single sources of demise worldwide with little and medium earning nations existence pretentious uneven. So the current research is ready to evaluate the magnitude of understanding on harm’s way associated with heart disease among clients attending NCD clinic at nemam PHC. A descriptive research design was chosen to evaluate the magnitude of understanding on harm’s way associated with heart disease among clients attending NCD clinic at nemam PHC 100 samples are included within our study. Prospective sampling techniques method was utilized in selecting the samples. A self-arranged questionnaire was utilized to gather statistics. The evaluate the magnitude of understanding on harm’s way associated with heart disease among clients attending NCD clinic at nemam PHC are Inadequate knowledge: 23%Moderate knowledge: 56% Adequate knowledge: 21%. The study concludes that there is moderation risk factors associated with heart disease among clients attending NCD clinic at Nemam PHC.

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10

Aldhaheri, R. W., and H. K. Khalil. "Aggregation of the policy iteration method for nearly completely decomposable Markov chains." IEEE Transactions on Automatic Control 36, no. 2 (1991): 178–87. http://dx.doi.org/10.1109/9.67293.

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11

Dayar, Tugrul, and William J. Stewart. "Quasi Lumpability, Lower-Bounding Coupling Matrices, and Nearly Completely Decomposable Markov Chains." SIAM Journal on Matrix Analysis and Applications 18, no. 2 (1997): 482–98. http://dx.doi.org/10.1137/s0895479895294277.

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12

Yin, G., and S. Dey. "Weak Convergence of Hybrid Filtering Problems Involving Nearly Completely Decomposable Hidden Markov Chains." SIAM Journal on Control and Optimization 41, no. 6 (2003): 1820–42. http://dx.doi.org/10.1137/s0363012901388464.

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13

Pekergin, Nihal, Tuğrul Dayar, and Denizhan N. Alparslan. "Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering." European Journal of Operational Research 165, no. 3 (2005): 810–25. http://dx.doi.org/10.1016/j.ejor.2001.09.001.

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14

Krishnamurthy, Vikram. "Adaptive estimation of hidden nearly completely decomposable Markov chains with applications in blind equalization." International Journal of Adaptive Control and Signal Processing 8, no. 3 (1994): 237–60. http://dx.doi.org/10.1002/acs.4480080303.

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15

Borges, Carlos F., and Craig S. Peters. "Computing approximate stationary distributions for discrete Markov processes with banded infinitesimal generators." Journal of Applied Probability 36, no. 4 (1999): 1086–100. http://dx.doi.org/10.1239/jap/1032374757.

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We develop an algorithm for computing approximations to the stationary distribution of a discrete birth-and-death process, provided that the infinitesimal generator is a banded matrix. We begin by computing stationary distributions for processes whose infinitesimal generators are Hessenberg. Our derivation in this special case is different from the classical case but it leads to the same result. We then show how to extend these ideas to processes where the infinitesimal generator is banded (or half-banded) and to quasi-birth–death processes. Finally, we give an example of the application of this method to a nearly completely decomposable Markov chain to demonstrate the general applicability of the technique.

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16

Borges, Carlos F., and Craig S. Peters. "Computing approximate stationary distributions for discrete Markov processes with banded infinitesimal generators." Journal of Applied Probability 36, no. 04 (1999): 1086–100. http://dx.doi.org/10.1017/s0021900200017885.

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We develop an algorithm for computing approximations to the stationary distribution of a discrete birth-and-death process, provided that the infinitesimal generator is a banded matrix. We begin by computing stationary distributions for processes whose infinitesimal generators are Hessenberg. Our derivation in this special case is different from the classical case but it leads to the same result. We then show how to extend these ideas to processes where the infinitesimal generator is banded (or half-banded) and to quasi-birth–death processes. Finally, we give an example of the application of this method to a nearly completely decomposable Markov chain to demonstrate the general applicability of the technique.

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17

Haviv, Moshe, and Y. Ritov. "An Approximation to the Stationary Distribution of a Nearly Completely Decomposable Markov Chain and Its Error Bound." SIAM Journal on Algebraic Discrete Methods 7, no. 4 (1986): 583–88. http://dx.doi.org/10.1137/0607064.

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18

Haviv, Moshe. "An Approximation to the Stationary Distribution of a Nearly Completely Decomposable Markov Chain and Its Error Analysis." SIAM Journal on Algebraic Discrete Methods 7, no. 4 (1986): 589–93. http://dx.doi.org/10.1137/0607065.

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19

Jelenković, Predrag R., Ana Radovanović, and Mark S. Squillante. "Critical sizing of LRU caches with dependent requests." Journal of Applied Probability 43, no. 4 (2006): 1013–27. http://dx.doi.org/10.1239/jap/1165505204.

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It was recently proved by Jelenković and Radovanović (2004) that the least-recently-used (LRU) caching policy, in the presence of semi-Markov-modulated requests that have a generalized Zipf's law popularity distribution, is asymptotically insensitive to the correlation in the request process. However, since the previous result is asymptotic, it remains unclear how small the cache size can become while still retaining the preceding insensitivity property. In this paper, assuming that requests are generated by a nearly completely decomposable Markov-modulated process, we characterize the critical cache size below which the dependency of requests dominates the cache performance. This critical cache size is small relative to the dynamics of the modulating process, and in fact is sublinear with respect to the sojourn times of the modulated chain that determines the dependence structure.

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20

Jelenković, Predrag R., Ana Radovanović, and Mark S. Squillante. "Critical sizing of LRU caches with dependent requests." Journal of Applied Probability 43, no. 04 (2006): 1013–27. http://dx.doi.org/10.1017/s0021900200002394.

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It was recently proved by Jelenković and Radovanović (2004) that the least-recently-used (LRU) caching policy, in the presence of semi-Markov-modulated requests that have a generalized Zipf's law popularity distribution, is asymptotically insensitive to the correlation in the request process. However, since the previous result is asymptotic, it remains unclear how small the cache size can become while still retaining the preceding insensitivity property. In this paper, assuming that requests are generated by a nearly completely decomposable Markov-modulated process, we characterize the critical cache size below which the dependency of requests dominates the cache performance. This critical cache size is small relative to the dynamics of the modulating process, and in fact is sublinear with respect to the sojourn times of the modulated chain that determines the dependence structure.

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