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Adaptive Relaxation for the Steady-State Analysis of Markov Chains [chapter]

Graham Horton
1995 Computations with Markov Chains  
We consider a variant of the well-known Gauss-Seidel method for the solution of Markov chains in steady state.  ...  We consider the adaptive approach both as a solver in its own right and as a relaxation method within the multi-level algorithm.  ...  Acknowledgements The Markov chains were generated using the SPNP software package of G. Ciardo [I], who also supplied the GSPN models for the second and third test problems.  ... 
doi:10.1007/978-1-4615-2241-6_32 fatcat:3einap7npndcnluaardjhtulky

A multi-level solution algorithm for steady-state Markov chains

Graham Horton, Scott T. Leutenegger
1994 Proceedings of the 1994 ACM SIGMETRICS conference on Measurement and modeling of computer systems - SIGMETRICS '94  
aI A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented.  ...  The paper also contrasts and compares the multi-level method with the iterative aggregation-disaggregation algorithm of Takahashi.  ...  Ciardo for permission to use the SPNP tool.  ... 
doi:10.1145/183018.183040 dblp:conf/sigmetrics/HortonL94 fatcat:vgsd7ql6kjgnjpn6lhwqn74tbe

A multi-level solution algorithm for steady-state Markov chains

Graham Horton, Scott T. Leutenegger
1994 Performance Evaluation Review  
aI A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented.  ...  The paper also contrasts and compares the multi-level method with the iterative aggregation-disaggregation algorithm of Takahashi.  ...  Ciardo for permission to use the SPNP tool.  ... 
doi:10.1145/183019.183040 fatcat:5aaeya74e5bnti7thkuwdm7ow4

On the Utility of the Multi-Level Algorithm for the Solution of Nearly Completely Decomposable Markov Chains [chapter]

Scott T. Leutenegger, Graham Horton
1995 Computations with Markov Chains  
Recently the Multi-Level algorithm was introduced as a general purpose solver for the solution of steady state Markov c hains.  ...  In this paper we consider the performance of the Multi-Level algorithm for solving Nearly Completely Decomposable (NCD) Markov c hains, for which special-purpose iterative aggregation/disaggregation algorithms  ...  The KMS algorithm is an attractive algorithm since it easily parallelizes and allows the ecient solution of problems that are larger than memory when the chain is NCD.  ... 
doi:10.1007/978-1-4615-2241-6_24 fatcat:b24fx5dqcrf7zelywciqvljrnq

Transition Analysis Using Markov Chains In Denim Manufacturing

S. Sathyapriya, S. Sweka, S. Vishalakshi
2019 International Journal of Scientific Research in Science and Technology  
Markov chains plays a very important role in determining transition probabilities in the products, retention probabilities in dyeing, optimum acid level in washing denim.  ...  This paper particularly explores the use of markov chains in the denim manufacturing.  ...  METHODS AND MATERIAL ALGORITHM IN MARKOV CHAINS METHOD 1 PROCEDURE FOR DETERMINING TRASITION PROBABILITY STEP 1 -Multi -Period transition probabilities One of the purposes of Markov chain is  ... 
doi:10.32628/ijsrst196437 fatcat:6esa6zloejf5fldtcldjo5dsxa

An inventory model with returns and lateral transshipments

W-K Ching, W-O Yuen, A W Loh
2003 Journal of the Operational Research Society  
We order the states of the Markov chain according to the inventory levels in ascending order and get the following Markov chain.  ...  We give the generator matrix for the model and a closed-form solution for the system steady-state probability distribution is also derived.  ... 
doi:10.1057/palgrave.jors.2601521 fatcat:6lya5ivumnahhkp4gyzynkvxeu

marmoteCore

Alain Jean-Marie
2017 Proceedings of the 11th EAI International Conference on Performance Evaluation Methodologies and Tools - VALUETOOLS 2017  
We present the marmoteCore software project, an open environment for modeling with Markov chains.  ...  This platform aims at providing the general scientific user with tools for creating Markov models and accessing the many solution algorithms available for their analysis.  ...  This is the case for the computation of (approximate) steady-state distributions for Markov chains, the basic problem of the field.  ... 
doi:10.1145/3150928.3150960 dblp:conf/valuetools/Jean-Marie17 fatcat:7zdoxuwovzau5lnuyjh32hragm

A Markov model for multi-criteria multi-person decision making

Rene Chelvier, Kristina Dammasch, Graham Horton, Stefan-Werner Knoll, Claudia Krull, Benjamin Rauch-Gebbensleben
2008 2008 International Conference on Innovations in Information Technology  
The algorithm is based on a Markov chain model which is derived from pairwise comparisons of ideas. The steady-state solution of this Markov chain yields a ranking vector for the alternatives.  ...  This paper describes a new algorithm for the evaluation of alternatives by a group of decision makers according to multiple criteria.  ...  This results in a discrete-time Markov chain, whose steady-state solution vector represents a ranking of the alternatives.  ... 
doi:10.1109/innovations.2008.4781672 fatcat:l72bmtoewrcbrn5cehnexkbrwa

Analysis of Cross-Layer Interaction in Multirate 802.11 WLANs

Jaehyuk Choi, Kihong Park, Chong-kwon Kim
2009 IEEE Transactions on Mobile Computing  
We advance station-centric Markov chain models of ARF, ARF-DCF with and without RTS/CTS, and TCP over DCF that may be viewed as multi-protocol extensions of Bianchi's IEEE 802.11 model.  ...  Our results complement empirical and simulation-based findings, demonstrating the versatility and efficacy of station-centric Markov chain analysis for capturing cross-layer WLAN dynamics.  ...  Steady-state Solution of ARF Markov Chain Although different in structure from Bianchi's DCF chain [5] , the ARF Markov chain possesses regularities that admit to a closed-form solution for Π i as a function  ... 
doi:10.1109/tmc.2008.166 fatcat:5bndvudbibfs7prlx2g27gvjim

Cross-Layer Analysis of Rate Adaptation, DCF and TCP in Multi-Rate WLANs

J. Choi, K. Park, C.-k. Kim
2007 IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications  
Our results complement empirical and simulation-based findings, demonstrating the versatility and efficacy of station-centric Markov chain analysis for capturing cross-layer WLAN dynamics.  ...  In this paper, we present station-centric Markov chain models of WLAN cross-layer performance aimed at capturing complex interactions between ARF, DCF, and TCP.  ...  The authors would like to thank Sunwoong Choi of Samsung Electronics for his valuable discussion. This research was supported, in part, by NSF grant ANI-0082861, and a BK-21 grant.  ... 
doi:10.1109/infcom.2007.127 dblp:conf/infocom/ChoiPK07 fatcat:4okczuno6jgohn5ahq6vjry63y

Stiffness-tolerant methods for transient analysis of stiff Markov chains

Manish Malhotra, Jogesh K. Muppala, Kishor S. Trivedi
1994 Microelectronics and reliability  
Steady-state detection in Jensen's method results in large savings of computation time for Markov chains when mission time extends beyond the steady-state point.  ...  Three methods for numerical transient analysis of Markov chains, the modified Jensen's method (Jensen's method with steady-state detection of the underlying DTMC and computation of Poisson probabilities  ...  The authors would also like to thank Dr. Ricardo Pantazis and Dr. A. V, Ramesh for many useful suggestions and insights into the numerical methods. The help of Dr.  ... 
doi:10.1016/0026-2714(94)90137-6 fatcat:g6nfzjjoqzczhdsqzftgaykxhe

Bounding of performance measures for a threshold-based queueing system with hysteresis

Leana Golubchik, John C. S. Lui
1997 Performance Evaluation Review  
In this paper, we consider a K-server threshold-based queueing system with hysteresis in which the number of servers, employed for servicing customers, is governed by a forward threshold vector F= (Fl,  ...  Acknowledgement: The authors are grateful to the anonymous referees for their helpful and insightful comments. Leana Golubchik's research was supported in part by the NSF CAREER grant CCR-96-25013.  ...  Lui's research was supported in part by the RGC and CUHK Direct Grant.  ... 
doi:10.1145/258623.258684 fatcat:rqbl5oghsjh4bgsosmgxi2huvm

Bounding of performance measures for a threshold-based queueing system with hysteresis

Leana Golubchik, John C. S. Lui
1997 Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems - SIGMETRICS '97  
In this paper, we consider a K-server threshold-based queueing system with hysteresis in which the number of servers, employed for servicing customers, is governed by a forward threshold vector F= (Fl,  ...  Acknowledgement: The authors are grateful to the anonymous referees for their helpful and insightful comments. Leana Golubchik's research was supported in part by the NSF CAREER grant CCR-96-25013.  ...  Lui's research was supported in part by the RGC and CUHK Direct Grant.  ... 
doi:10.1145/258612.258684 dblp:conf/sigmetrics/GolubchikL97 fatcat:zhxacynarfhpnpruvjbihfbexm

Reviving the Two-state Markov Chain Approach (Technical Report) [article]

Andrzej Mizera, Jun Pang, Qixia Yuan
2016 arXiv   pre-print
Second, we conduct an extensive experimental comparison of the two-state Markov chain approach and another approach based on the Skart method and we show that statistically the two-state Markov chain has  ...  In fact, statistical methods for steady-state approximation are the only viable means when dealing with large networks.  ...  Experiments presented in this paper were carried out using the HPC facilities of the University of Luxembourg [31] (http://hpc.uni.lu).  ... 
arXiv:1501.01779v4 fatcat:bbgpulpwbbh6fb7lvgoexwgxoy

Multi-echelon inventory production system solution

Toshio Odanaka, Keiichi Yamaguchi, Tadayuki Masui
1994 Computers & industrial engineering  
The steady state probability distribution and the operating characteristics are obtained explicitly. The required algorithm is designed and it is executed using MATLAB.  ...  The optimization criterion is to minimize the total cost rate incurred at all the location subject to the performance level constrains.  ...  can be written as Steady state analysis: The structure of the infinitesimal matrix R reveals that the state space E of the Markov process Algorithm The algorithm to compute the long run expected  ... 
doi:10.1016/0360-8352(94)90270-4 fatcat:hicesvihdfefpgia2zd4t7xf2u
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