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The model is formulated as a multivariate stochastic process with certain semi-Markov structure. The exponentiality assumption prevalent in the literature is totally eliminated. ... A numerical example is given, demonstrating speed, accuracy and stability of these procedures. Ergodic theorems Pettis Mean Convergence of Martingales and Amarts ... Transient Analysis of a Semi-Markov Availability/Reliability Model: Numerical Exploration via the Matrix Laguerre Transform Ushio Sumita* and Yasushi Masuda, University of Rochester, New York, USA We consider ...doi:10.1016/0304-4149(85)90363-1 fatcat:j6hy7qi2yjadpnm6qhci6rvc6e
We also show that the distribution of time to deadlock can be computed by conducting a transient analysis of the Markov chain model. ... In this paper, we show that Markov chains with absorbing states provide a natural model of manufacturing systems with deadlocks. ... If we are interested in the distributions of the time to deadlock, then we need to conduct a transient analysis of the Markov chain model. ...doi:10.1007/bf02811330 fatcat:dnhvcp6lhzhqtcwaue77hb6564
Lecture Notes in Computer Science
This paper describes a set of analysis components that open the way to perform performance and dependability analysis with the Cadp toolbox, originally designed for verifying the functional correctness ... Three new tools (named Bcg Steady, Bcg Transient and Determinator) have been added to the toolbox. ... The tools Bcg Transient and Bcg Steady are based on code provided by Vassilis Mertsiotakis (Lucent Technologies) as part of the TIPPtool, which was developed at the University of Erlangen-Nürnberg. ...doi:10.1007/3-540-36577-x_30 fatcat:psz3672jqjfzvns52sihddnyq4
The unique feature of DSPNexpress constitute numerical solvers for transient and steady-state analysis of generalized-semi Markov processes with exponential and deterministic events, which may be concurrently ... The computational effort required by DSPNexpress for transient and steady-state analysis is plotted for varying model size. Furthermore, a performance curve for a measure of interest is presented. ... Numerical computation of kernel elements of the GSSMC relies also on transient analysis of subordinated Markov chains and subsequent summation of appropriately selected transient probabilities  . ...doi:10.1145/350391.350396 dblp:conf/wosp/LindemannTKLW00 fatcat:jxvya73nbner7ic7trfolfu36q
REFERENCE  Carrasco, J.A. (2003) Transient analysis of rewarded continuous time Markov models by regenerative randomization with Laplace transform inversion, Comput. ... The Laplace transform inversion algorithm used in the numerical method described in the paper  differs essentially from the one implemented in the DLAINV FORTRAN subroutine described in  only in ... REFERENCE [ 1 ] 1 Carrasco, J.A. (2003) Transient analysis of rewarded continuous time Markov models by regenerative randomization with Laplace transform inversion, Comput. J., 46, 84 -99; doi: 10. ...doi:10.1093/comjnl/bxn033 fatcat:326yjxy3cbfttcmm7xewdexp3m
Automation and Remote Control
Trivedi, “Numerical transient analysis of Markov models," Computers and Op. Res. , 15, No. 1, 19-36 (1988). A. L. Reibman and K. S. ... Trivedi, "Transient analysis of cumulative measures of Markov model behavior," Commun. Stat. — Stochastic Models, 5, No. 4, 683-710 (1989). ...
Lecture Notes in Computer Science
The tool offers both model specification and quantitative model analysis in a compositional fashion, wrapped in a userfriendly graphical front-end. ... analysis of the underlying Markov chain, -Functions for the calculation of performance and dependability measures, -Support of experiment series, -Output of numerical results using the tool pxgraph, - ... For a particular Markov chain, a system of ordinary differential equations needs to be solved in order to obtain the state probabilities at a particular time instant t (transient analysis). ...doi:10.1007/3-540-48683-6_42 fatcat:rmc24nctvfdppf6qpkhbv5ddoi
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 ... For stiff models, computation of Poisson probabilities using traditional methods runs into underflow problems. ... V, Ramesh for many useful suggestions and insights into the numerical methods. The help of Dr. Christoph Lindemann is gratefully acknowledged. ...doi:10.1016/0026-2714(94)90137-6 fatcat:g6nfzjjoqzczhdsqzftgaykxhe
modelling and analysis. ... Modelling techniques are a fundamental prerequisite for actually doing performability analysis. ... However, even when computer support is available for the numerical analysis there are a number of problems that hinder the use of the state-of-the-art Markov reward model evaluation techniques: (1) system ...doi:10.1016/0166-5316(94)00038-7 fatcat:z3en5yre2rczpg6hyh6du7sn2u
Journal of the Society of Materials Science Japan
Numerical calculations are carried out, assuming that the random initial temperature of the FGM plates is a white noise disturbance or a homogeneous Markov random field. ... The associated transient thermal stress is obtained by using the closed-form solution derived by one of the authors for a nonhomogeneous plate with arbitrary variations in mechanical properties. ... Relationship between the gradual changes in the material composition and the mean square value of transient thermal stress in FGM plates having the initial temperature that is modeled as Markov random ...doi:10.2472/jsms.51.653 fatcat:hmdif2dsrrecra64ffmf3zbh2m
); Trivedi, Kishor (1-DUKE-C) Transient analysis of cumulative measures of Markov model behavior. ... In this paper, we consider the transient analysis of ‘cumula- Software 90m:68018 tive’ or ‘integral’ measures of Markov and Markov reward model behavior. ...
The comparisons of results of transient analysis for Markovian and phase-type controlled arrival rate systems are also done. ... Performance evaluation based on transient analysis has significant importance to those systems which never reached at equilibrium. ... STRUCTURED MARKOV CHAIN WITH HYPEREXPONENTIAL DISTRIBUTION FIG. 4 . 4 TRANSIENT ANALYSIS: MEAN NUMBER IN THE SYSTEM: COMPARISON OF TRANSIENT ANALYSIS WITH MARKOVIAN, HYPO AND HYPEREXPONENTIAL DISTRIBUTION ...doaj:791a44582d5a4cbc86559a931c9442b1 fatcat:taocj5jmzzfvhe3kbrdfda5av4
.” 2002m:60185 60K25 Sen, Kanwar (6-DELHI-S; Delhi) Lattice path approach to transient analysis of M/G/1/N non- Markovian queues using Cox distributions. ... In addition, we use a Brownian-motion model to approximate the identity. This produces an approximation of the expected transient delay. ...
This paper presents an iterative technique for transient and passage time analysis of large structurally unrestricted semi-Markov processes. ... Semi-Markov processes (SMPs) are expressive tools for modelling parallel and distributed systems; they are a generalisation of Markov processes that allow for arbitrarily distributed sojourn times. ... Distributed System Modelling Introduction We demonstrate the SMP analysis techniques of the previous sections with a semi-Markov model of a distributed voting system. ...doi:10.1016/j.future.2006.02.011 fatcat:va4b6mr3ybdjlffvqycs7vact4
In this paper, we focus on transient analysis of Markovian models of manufacturing systems. ... The first problem is concerned with the computation of distribution of time to absorption in Markov models of manufacturing systems with deadlocks or failures, and the second problem shows the relevance ... ACKNOWLEDGMENT The first author gratefully acknowledges the excellent academic and computing facilities at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, where ...doi:10.1109/70.282547 fatcat:th7zpz7g6featdempta5pq6nnq
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