DSpace Collection:
http://hdl.handle.net/2117/3645
Fri, 01 Aug 2014 06:13:12 GMT2014-08-01T06:13:12Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoRegenerative randomization: theory and application examples
http://hdl.handle.net/2117/23553
Title: Regenerative randomization: theory and application examples
Authors: Carrasco, Juan A.; Calderón Alvarez, Angel
Abstract: Randomization is a popular method for the transient solution of continuous-time Markov models. Its primary advantages over other methods (i.e., ODE solvers) are robustness and ease of implementation. It is however well-known that the performance of the method deteriorates with theFri, 18 Jul 2014 09:02:02 GMThttp://hdl.handle.net/2117/235532014-07-18T09:02:02ZCarrasco, Juan A.; Calderón Alvarez, AngelnoRandomization is a popular method for the transient solution of continuous-time Markov models. Its primary advantages over other methods (i.e., ODE solvers) are robustness and ease of implementation. It is however well-known that the performance of the method deteriorates with theEvaluation of safety-oriented two-version architectures
http://hdl.handle.net/2117/23547
Title: Evaluation of safety-oriented two-version architectures
Authors: Carrasco, Juan A.; Figueras Pàmies, Joan; Kuntzman, A
Abstract: A Markov model taking into account physical and design faults for a two-version architecture oriented to safety-related applications is developed. Only a probabilistic knowledge of the initial state of the versions in relation to the presence of design faults is assumed. The model can be split into two submodels accounting separately for physical and design faults, and a closed form expression for the unsafety of the system is obtained. The parameter estimation problem is discussed and a method to predict the probability distribution of the number of related design faults at the beginning of the operational life of the system is proposed. The method uses a pool model to process fault-occurrence data collected during a “face-to-face” debugging of the two versions. It has by nature a limited capability for proving version diversity, but it is shown that the limit is of the order of the diversity reported by recent experiments on real software. Finally, the impact of version correction during operation is shown to be negligible for critical applications.Fri, 18 Jul 2014 07:48:02 GMThttp://hdl.handle.net/2117/235472014-07-18T07:48:02ZCarrasco, Juan A.; Figueras Pàmies, Joan; Kuntzman, AnoA Markov model taking into account physical and design faults for a two-version architecture oriented to safety-related applications is developed. Only a probabilistic knowledge of the initial state of the versions in relation to the presence of design faults is assumed. The model can be split into two submodels accounting separately for physical and design faults, and a closed form expression for the unsafety of the system is obtained. The parameter estimation problem is discussed and a method to predict the probability distribution of the number of related design faults at the beginning of the operational life of the system is proposed. The method uses a pool model to process fault-occurrence data collected during a “face-to-face” debugging of the two versions. It has by nature a limited capability for proving version diversity, but it is shown that the limit is of the order of the diversity reported by recent experiments on real software. Finally, the impact of version correction during operation is shown to be negligible for critical applications.Corrigendum: "Transient Analysis of Rewarded Continuous Time Markov Models by Regenerative Randomization with Laplace Transform Inversion"
http://hdl.handle.net/2117/23426
Title: Corrigendum: "Transient Analysis of Rewarded Continuous Time Markov Models by Regenerative Randomization with Laplace Transform Inversion"
Authors: Carrasco, Juan A.
Abstract: Clarifications regarding paper with same title and authors published in the same journal.Tue, 08 Jul 2014 10:05:11 GMThttp://hdl.handle.net/2117/234262014-07-08T10:05:11ZCarrasco, Juan A.noClarifications regarding paper with same title and authors published in the same journal.Corrections on “Failure Transition Distance-Based Importance Sampling Schemes for the Simulation of Repairable Fault-Tolerant Computer Systems"
http://hdl.handle.net/2117/23425
Title: Corrections on “Failure Transition Distance-Based Importance Sampling Schemes for the Simulation of Repairable Fault-Tolerant Computer Systems"
Authors: Carrasco, Juan A.
Abstract: Various corrections to the above titled paper (ibid., vol. 55, no. 2, pp. 207-236) are presented. The corrections do not propagate to any other part of the paper and do not affect the correctness of the experimental results reported in the paper.Tue, 08 Jul 2014 10:01:13 GMThttp://hdl.handle.net/2117/234252014-07-08T10:01:13ZCarrasco, Juan A.noVarious corrections to the above titled paper (ibid., vol. 55, no. 2, pp. 207-236) are presented. The corrections do not propagate to any other part of the paper and do not affect the correctness of the experimental results reported in the paper.Transient analysis of Markov models of fault-tolerant systems with deferred repair using split regenerative randomization
http://hdl.handle.net/2117/23392
Title: Transient analysis of Markov models of fault-tolerant systems with deferred repair using split regenerative randomization
Authors: Carrasco, Juan A.; Temsamani, Jamal
Abstract: The (standard) randomization method is an attractive alternative for the transient analysis of continuous time Markov models. The main advantages of the method are numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, the fact that the method can be computationally very expensive limits its applicability. In this paper, we develop a new method called split regenerative randomization, which, having the same good properties as standard randomization, can be significantly more efficient. The method covers reliability-like models with a particular but quite general structure and requires the selection of a subset of states and a regenerative state satisfying some conditions. For a class of continuous time Markov models, model class C_2, including typical failure/repair reliability-like models with exponential failure and repair time distributions and deferred repair, natural selections are available for both the subset of states and the regenerative state and,
for those natural selections, theoretical results are available assessing the efficiency of the method in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive. We illustrate the application of the method using a large class C_2 model and show that for models in that class the method can indeed be significantly more efficient than previously available randomization-based methodsThu, 03 Jul 2014 06:38:15 GMThttp://hdl.handle.net/2117/233922014-07-03T06:38:15ZCarrasco, Juan A.; Temsamani, JamalnoThe (standard) randomization method is an attractive alternative for the transient analysis of continuous time Markov models. The main advantages of the method are numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, the fact that the method can be computationally very expensive limits its applicability. In this paper, we develop a new method called split regenerative randomization, which, having the same good properties as standard randomization, can be significantly more efficient. The method covers reliability-like models with a particular but quite general structure and requires the selection of a subset of states and a regenerative state satisfying some conditions. For a class of continuous time Markov models, model class C_2, including typical failure/repair reliability-like models with exponential failure and repair time distributions and deferred repair, natural selections are available for both the subset of states and the regenerative state and,
for those natural selections, theoretical results are available assessing the efficiency of the method in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive. We illustrate the application of the method using a large class C_2 model and show that for models in that class the method can indeed be significantly more efficient than previously available randomization-based methodsA Numerical method for the evaluation of the distribution of cumulative reward till exit of a Subset of transient states of a Markov reward model
http://hdl.handle.net/2117/23376
Title: A Numerical method for the evaluation of the distribution of cumulative reward till exit of a Subset of transient states of a Markov reward model
Authors: Carrasco, Juan A.; Suñé, Víctor
Abstract: Markov reward models have interesting modeling applications, particularly those addressing fault-tolerant hardware/software systems. In this paper, we consider a Markov reward model with a reward structure including only reward rates associated with states, in which both positive and negative reward rates are present and null reward rates are allowed, and develop a numerical method to compute the distribution function of the cumulative reward till exit of a subset
of transient states of the model. The method combines a model transformation step with the solution of the transformed model using a randomization construction with two randomization rates. The method introduces a truncation error, but that error is strictly bounded from above by a user-specified error control parameter. Further, the method is numerically stable and takes advantage of the sparsity of the infinitesimal generator of the transformed model. Using a Markov
reward model of a fault-tolerant hardware/software system, we illustrate the application of the method and analyze its computational cost. Also, we compare the computational cost of the method with that of the (only) previously available method for the problem. Our numerical experiments seem to indicate that the new method can be efficient and that for medium-size and large models can be substantially faster than the previously available method.Wed, 02 Jul 2014 08:08:06 GMThttp://hdl.handle.net/2117/233762014-07-02T08:08:06ZCarrasco, Juan A.; Suñé, VíctornoFault tolerance, Markov reward models, modeling techniques, numerical algorithmsMarkov reward models have interesting modeling applications, particularly those addressing fault-tolerant hardware/software systems. In this paper, we consider a Markov reward model with a reward structure including only reward rates associated with states, in which both positive and negative reward rates are present and null reward rates are allowed, and develop a numerical method to compute the distribution function of the cumulative reward till exit of a subset
of transient states of the model. The method combines a model transformation step with the solution of the transformed model using a randomization construction with two randomization rates. The method introduces a truncation error, but that error is strictly bounded from above by a user-specified error control parameter. Further, the method is numerically stable and takes advantage of the sparsity of the infinitesimal generator of the transformed model. Using a Markov
reward model of a fault-tolerant hardware/software system, we illustrate the application of the method and analyze its computational cost. Also, we compare the computational cost of the method with that of the (only) previously available method for the problem. Our numerical experiments seem to indicate that the new method can be efficient and that for medium-size and large models can be substantially faster than the previously available method.FPGA implementation of a PWM for a three-phase DC-AC multilevel active-clamped converter
http://hdl.handle.net/2117/23223
Title: FPGA implementation of a PWM for a three-phase DC-AC multilevel active-clamped converter
Authors: Lupón Roses, Emilio; Busquets Monge, Sergio; Nicolás Apruzzese, Joan
Abstract: With the aim to implement a suitable controller for a three-phase dc-ac multilevel active-clamped converter to enable its use in practice, and as a first step toward a full closed-loop converter control implementation into a single field-programmable gate array (FPGA) device, this paper presents the structure and features of an FPGA implementation of an appropriate pulsewidth modulation (PWM) strategy. The selected PWM strategy guarantees dc-link capacitor voltage balance in every switching cycle, and covers both the undermodulation and overmodulation regions. A flexible implementation is conceived, allowing the variation of important operating parameters, such as the modulation index and switching frequency, through a simple user interface. The key aspects to achieve an efficient and robust FPGA implementation are discussed. Experimental results in a four-level converter prototype controlled with an Altera Cyclone III device under different operating conditions match fairly well with the expected results obtained through simulation, thus verifying the accurate performance of the FPGA-based modulatorSat, 14 Jun 2014 14:54:29 GMThttp://hdl.handle.net/2117/232232014-06-14T14:54:29ZLupón Roses, Emilio; Busquets Monge, Sergio; Nicolás Apruzzese, JoannoField-programmable gate array (FPGA), multilevel active-clamped (MAC) converter, pulsewidth modulation (PWM)With the aim to implement a suitable controller for a three-phase dc-ac multilevel active-clamped converter to enable its use in practice, and as a first step toward a full closed-loop converter control implementation into a single field-programmable gate array (FPGA) device, this paper presents the structure and features of an FPGA implementation of an appropriate pulsewidth modulation (PWM) strategy. The selected PWM strategy guarantees dc-link capacitor voltage balance in every switching cycle, and covers both the undermodulation and overmodulation regions. A flexible implementation is conceived, allowing the variation of important operating parameters, such as the modulation index and switching frequency, through a simple user interface. The key aspects to achieve an efficient and robust FPGA implementation are discussed. Experimental results in a four-level converter prototype controlled with an Altera Cyclone III device under different operating conditions match fairly well with the expected results obtained through simulation, thus verifying the accurate performance of the FPGA-based modulatorA generalized method for the transient analysis of Markov models of fault-tolerant systems with deferred repair
http://hdl.handle.net/2117/21537
Title: A generalized method for the transient analysis of Markov models of fault-tolerant systems with deferred repair
Authors: Temsamani, J; Carrasco, Juan A.
Abstract: Randomization is an attractive alternative for the transient analysis of continuous
time Markov models. The main advantages of the method are numerical stability,
well-controlled computation error, and ability to specify the computation error
in advance. However, the fact that the method can be computationally expensive
limits its applicability. Recently, a variant of the (standard) randomization method, called split regenerative randomization has been proposed for the efficient analysis of reliability-like models of fault-tolerant systems with deferred repair. In this article, we generalize that method so that it covers more general reward measures: the expected transient reward rate and the expected averaged reward rate. The generalized method has the same good properties as the standard randomization method and, for large models and large values of the time t at which the
measure has to be computed, can be significantly less expensive. The method
requires the selection of a subset of states and a regenerative state satisfying some
conditions. For a class of continuous time Markov models, class C'_2, including
typical failure/repair reliability models with exponential failure and repair time
distributions and deferred repair, natural selections for the subset of states and
the regenerative state exist and results are available assessing approximately the
computational cost of the method in terms of “visible” model characteristics. Using
a large model class C'_2 example, we illustrate the performance of the method and show that it can be significantly faster than previously proposed randomizationbased methods.Wed, 12 Feb 2014 09:02:55 GMThttp://hdl.handle.net/2117/215372014-02-12T09:02:55ZTemsamani, J; Carrasco, Juan A.noRandomization is an attractive alternative for the transient analysis of continuous
time Markov models. The main advantages of the method are numerical stability,
well-controlled computation error, and ability to specify the computation error
in advance. However, the fact that the method can be computationally expensive
limits its applicability. Recently, a variant of the (standard) randomization method, called split regenerative randomization has been proposed for the efficient analysis of reliability-like models of fault-tolerant systems with deferred repair. In this article, we generalize that method so that it covers more general reward measures: the expected transient reward rate and the expected averaged reward rate. The generalized method has the same good properties as the standard randomization method and, for large models and large values of the time t at which the
measure has to be computed, can be significantly less expensive. The method
requires the selection of a subset of states and a regenerative state satisfying some
conditions. For a class of continuous time Markov models, class C'_2, including
typical failure/repair reliability models with exponential failure and repair time
distributions and deferred repair, natural selections for the subset of states and
the regenerative state exist and results are available assessing approximately the
computational cost of the method in terms of “visible” model characteristics. Using
a large model class C'_2 example, we illustrate the performance of the method and show that it can be significantly faster than previously proposed randomizationbased methods.Reliability bounds for fault-tolerant systems with deferred repair using bounding split regenerative randomization
http://hdl.handle.net/2117/21510
Title: Reliability bounds for fault-tolerant systems with deferred repair using bounding split regenerative randomization
Authors: Temsamani, Jamal; Carrasco, Juan A.
Abstract: A numerically stable method is developed which computes seemingly tight bounds at
a small computational cost relative to the model size, when that model size is large,
for the unreliability and bounds for the unreliability using, respectively, exact and
bounding failure/repair continuous-time Markov chain models of fault-tolerant systems
with exponential failure and repair time distributions, in which repair is deferred until
some condition on the collection of failed components is satisfied, and, then, proceeds
until reaching the state without failed components, with failure rates much smaller than repair rates and not too different output rates from states with deferred repair.Tue, 11 Feb 2014 12:30:01 GMThttp://hdl.handle.net/2117/215102014-02-11T12:30:01ZTemsamani, Jamal; Carrasco, Juan A.noBounds, Continuous-time Markov chains, Deferred repair, Fault-tolerant systems, RandomizationA numerically stable method is developed which computes seemingly tight bounds at
a small computational cost relative to the model size, when that model size is large,
for the unreliability and bounds for the unreliability using, respectively, exact and
bounding failure/repair continuous-time Markov chain models of fault-tolerant systems
with exponential failure and repair time distributions, in which repair is deferred until
some condition on the collection of failed components is satisfied, and, then, proceeds
until reaching the state without failed components, with failure rates much smaller than repair rates and not too different output rates from states with deferred repair.Transient analysis of large Markov models with absorbing states using regenerative randomization
http://hdl.handle.net/2117/21508
Title: Transient analysis of large Markov models with absorbing states using regenerative randomization
Authors: Carrasco, Juan A.
Abstract: In this article, we develop a new method, called regenerative randomization, for
the transient analysis of continuous time Markov models with absorbing states.
The method has the same good properties as standard randomization: numerical
stability, well-controlled computation error, and ability to specify the computation
error in advance. The method has a benign behavior for large t and is significantly
less costly than standard randomization for large enough models and large enough t.
For a class of models, class C, including typical failure/repair reliability models
with exponential failure and repair time distributions and repair in every state with
failed components, stronger theoretical results are available assessing the efficiency
of the method in terms of “visible” model characteristics. A large example belonging
to that class is used to illustrate the performance of the method and to show that it
can indeed be much faster than standard randomization.Tue, 11 Feb 2014 11:59:26 GMThttp://hdl.handle.net/2117/215082014-02-11T11:59:26ZCarrasco, Juan A.noIn this article, we develop a new method, called regenerative randomization, for
the transient analysis of continuous time Markov models with absorbing states.
The method has the same good properties as standard randomization: numerical
stability, well-controlled computation error, and ability to specify the computation
error in advance. The method has a benign behavior for large t and is significantly
less costly than standard randomization for large enough models and large enough t.
For a class of models, class C, including typical failure/repair reliability models
with exponential failure and repair time distributions and repair in every state with
failed components, stronger theoretical results are available assessing the efficiency
of the method in terms of “visible” model characteristics. A large example belonging
to that class is used to illustrate the performance of the method and to show that it
can indeed be much faster than standard randomization.Una propuesta de evaluación de competencias genéricas en grados de Ingeniería
http://hdl.handle.net/2117/21264
Title: Una propuesta de evaluación de competencias genéricas en grados de Ingeniería
Authors: Martínez Martínez, María del Rosario; Amante García, Beatriz; Cadenato Matia, Ana María; Rodríguez Montañés, Rosa
Abstract: In genetic association studies, tests for Hardy-Weinberg proportions are often employed as a quality control checking procedure. Missing genotypes are typically discarded prior to testing. In this paper we show that inference for Hardy-Weinberg proportions can be biased when missing values are discarded. We propose to use multiple imputation of missing values in order to improve inference for Hardy-Weinberg proportions. For imputation we employ a multinomial logit model that uses information from allele intensities and/or neighbouring markers. Analysis of an empirical data set of single nucleotide polymorphisms possibly related to colon cancer reveals that missing genotypes are not missing completely at random. Deviation from Hardy-Weinberg proportions is mostly due to a lack of heterozygotes. Inbreeding coefficients estimated by multiple imputation of the missings are typically lowered with respect to inbreeding coefficients estimated by discarding the missings. Accounting for missings by multiple imputation qualitatively changed the results of 10 to 17% of the statistical tests performed. Estimates of inbreeding coefficients obtained by multiple imputation showed high correlation with estimates obtained by single imputation using an external reference panel. Our conclusion is that imputation of missing data leads to improved statistical inference for Hardy-Weinberg proportions.Fri, 17 Jan 2014 12:23:16 GMThttp://hdl.handle.net/2117/212642014-01-17T12:23:16ZMartínez Martínez, María del Rosario; Amante García, Beatriz; Cadenato Matia, Ana María; Rodríguez Montañés, RosanoInstrumentos de evaluación, rúbricas, Proyectos de Ingeniería Química, Evaluación
continua, EvalCOMIX, competencias genéricasIn genetic association studies, tests for Hardy-Weinberg proportions are often employed as a quality control checking procedure. Missing genotypes are typically discarded prior to testing. In this paper we show that inference for Hardy-Weinberg proportions can be biased when missing values are discarded. We propose to use multiple imputation of missing values in order to improve inference for Hardy-Weinberg proportions. For imputation we employ a multinomial logit model that uses information from allele intensities and/or neighbouring markers. Analysis of an empirical data set of single nucleotide polymorphisms possibly related to colon cancer reveals that missing genotypes are not missing completely at random. Deviation from Hardy-Weinberg proportions is mostly due to a lack of heterozygotes. Inbreeding coefficients estimated by multiple imputation of the missings are typically lowered with respect to inbreeding coefficients estimated by discarding the missings. Accounting for missings by multiple imputation qualitatively changed the results of 10 to 17% of the statistical tests performed. Estimates of inbreeding coefficients obtained by multiple imputation showed high correlation with estimates obtained by single imputation using an external reference panel. Our conclusion is that imputation of missing data leads to improved statistical inference for Hardy-Weinberg proportions.Tight upper bounds for the expected loss of lexicographic heuristics in binary multiattribute choice
http://hdl.handle.net/2117/21073
Title: Tight upper bounds for the expected loss of lexicographic heuristics in binary multiattribute choice
Authors: Carrasco, Juan A.; Baucells, M
Abstract: Tight upper bounds for the expected loss of the DEBA (Deterministic-Elimination-By-Aspects) lexicographic selection heuristic are obtained for the case of an additive separable utility function
with unknown non-negative, non-increasing attribute weights for numbers of alternatives
and attributes as large as 10 under two probabilistic models: one in which attributes are assumed to be independent Bernouilli random variables and another one with positive inter-attribute correlation.
The upper bounds improve substantially previous bounds and extend significantly the
cases in which a good performance of DEBA can be guaranteed under the assumed cognitive
limitations.Fri, 20 Dec 2013 09:19:48 GMThttp://hdl.handle.net/2117/210732013-12-20T09:19:48ZCarrasco, Juan A.; Baucells, MnoTight upper bounds for the expected loss of the DEBA (Deterministic-Elimination-By-Aspects) lexicographic selection heuristic are obtained for the case of an additive separable utility function
with unknown non-negative, non-increasing attribute weights for numbers of alternatives
and attributes as large as 10 under two probabilistic models: one in which attributes are assumed to be independent Bernouilli random variables and another one with positive inter-attribute correlation.
The upper bounds improve substantially previous bounds and extend significantly the
cases in which a good performance of DEBA can be guaranteed under the assumed cognitive
limitations.Combinatorial methods for the evaluation of yield and operational reliability of fault-tolerant systems-on-chip
http://hdl.handle.net/2117/21071
Title: Combinatorial methods for the evaluation of yield and operational reliability of fault-tolerant systems-on-chip
Authors: Carrasco, Juan A.; Suñé, Víctor
Abstract: In this paper we develop combinatorial methods for the evaluation of yield and operational reliability of fault-tolerant systems-on-chip. The method for yield computation assumes that defects are produced according to a model in which defects are lethal and affect given components of the system following a distribution common to all defects; the method for the computation of operational reliability also assumes that the fault-tree function of the system is increasing.
The distribution of the number of defects is arbitrary. The methods are based on the formulation of, respectively, the yield and the operational reliability as the probability that a given boolean function with multiple-valued variables has value 1. That probability is computed by analyzing
a ROMDD (reduced ordered multiple-value decision diagram) representation of the function.
For efficiency reasons, a coded ROBDD (reduced ordered binary decision diagram) representation of the function is built first and, then, that coded ROBDD is transformed into the ROMDD required by the methods. We present numerical experiments showing that the methods are able to cope with quite large systems in moderate CPU times.Fri, 20 Dec 2013 09:03:38 GMThttp://hdl.handle.net/2117/210712013-12-20T09:03:38ZCarrasco, Juan A.; Suñé, VíctornoIn this paper we develop combinatorial methods for the evaluation of yield and operational reliability of fault-tolerant systems-on-chip. The method for yield computation assumes that defects are produced according to a model in which defects are lethal and affect given components of the system following a distribution common to all defects; the method for the computation of operational reliability also assumes that the fault-tree function of the system is increasing.
The distribution of the number of defects is arbitrary. The methods are based on the formulation of, respectively, the yield and the operational reliability as the probability that a given boolean function with multiple-valued variables has value 1. That probability is computed by analyzing
a ROMDD (reduced ordered multiple-value decision diagram) representation of the function.
For efficiency reasons, a coded ROBDD (reduced ordered binary decision diagram) representation of the function is built first and, then, that coded ROBDD is transformed into the ROMDD required by the methods. We present numerical experiments showing that the methods are able to cope with quite large systems in moderate CPU times.Two methods for computing bounds for the distribution of cumulative reward for large Markov models
http://hdl.handle.net/2117/21070
Title: Two methods for computing bounds for the distribution of cumulative reward for large Markov models
Authors: Carrasco, Juan A.
Abstract: Degradable fault-tolerant systems can be evaluated using rewarded continuous-time Markov chain (CTMC) models. In that context, a useful measure to consider is the distribution of the cumulative reward over a time interval [0, t]. All currently available numerical methods for computing that measure tend to be very expensive when the product of the maximum output rate of the CTMC model and t is large and, in that case, their application is limited to CTMC
models of moderate size. In this paper, we develop two methods to compute bounds for the cumulative reward distribution of CTMC models with reward rates associated with states: BT/RT (Bounding Transformation/Regenerative Transformation) and BT/BRT (Bounding Transformation/
Bounding Regenerative Transformation). The methods require the selection of a regenerative state, are numerically stable and compute the bounds with well-controlled error. For a class of rewarded CTMC models, class C′′′_1 , and a particular, natural selection for the regenerative state the BT/BRT method allows to trade off bounds tightness with computational cost and
will provide bounds at a moderate computational cost in many cases of interest. For a class of models, class C′′_1, slightly wider than class C′′′_1 , and a particular, natural selection for the regenerative state, the BT/RT method will yield tighter bounds at a higher computational cost. Under additional conditions, the bounds obtained by the less expensive version of BT/BRT and BT/RT
seem to be tight for any value of t or not small values of t, depending on the initial probability distribution of the model. Class C′′_1 and class C′′′_1 models with those additional conditions include both exact and bounding typical failure/repair performability models of fault-tolerant
systems with exponential failure and repair time distributions and repair in every state with failed components and a reward rate structure which is a non-increasing function of the collection of failed components. We illustrate both the applicability and the performance of the methods using a large CTMC performability example of a fault-tolerant multiprocessor system.Fri, 20 Dec 2013 08:52:22 GMThttp://hdl.handle.net/2117/210702013-12-20T08:52:22ZCarrasco, Juan A.noDegradable fault-tolerant systems can be evaluated using rewarded continuous-time Markov chain (CTMC) models. In that context, a useful measure to consider is the distribution of the cumulative reward over a time interval [0, t]. All currently available numerical methods for computing that measure tend to be very expensive when the product of the maximum output rate of the CTMC model and t is large and, in that case, their application is limited to CTMC
models of moderate size. In this paper, we develop two methods to compute bounds for the cumulative reward distribution of CTMC models with reward rates associated with states: BT/RT (Bounding Transformation/Regenerative Transformation) and BT/BRT (Bounding Transformation/
Bounding Regenerative Transformation). The methods require the selection of a regenerative state, are numerically stable and compute the bounds with well-controlled error. For a class of rewarded CTMC models, class C′′′_1 , and a particular, natural selection for the regenerative state the BT/BRT method allows to trade off bounds tightness with computational cost and
will provide bounds at a moderate computational cost in many cases of interest. For a class of models, class C′′_1, slightly wider than class C′′′_1 , and a particular, natural selection for the regenerative state, the BT/RT method will yield tighter bounds at a higher computational cost. Under additional conditions, the bounds obtained by the less expensive version of BT/BRT and BT/RT
seem to be tight for any value of t or not small values of t, depending on the initial probability distribution of the model. Class C′′_1 and class C′′′_1 models with those additional conditions include both exact and bounding typical failure/repair performability models of fault-tolerant
systems with exponential failure and repair time distributions and repair in every state with failed components and a reward rate structure which is a non-increasing function of the collection of failed components. We illustrate both the applicability and the performance of the methods using a large CTMC performability example of a fault-tolerant multiprocessor system.Numerical iterative methods for Markovian dependability and performability models: new results and a comparison
http://hdl.handle.net/2117/21068
Title: Numerical iterative methods for Markovian dependability and performability models: new results and a comparison
Authors: Suñé, Víctor; Domingo Fuster, José Luis; Carrasco, Juan A.
Abstract: In this paper we deal with iterative numerical methods to solve linear systems arising in continuous-time Markov chain (CTMC) models. We develop an algorithm to dynamically tune the relaxation parameter of the successive over-relaxation method. We give a sufficient condition for the Gauss-Seidel method to converge when computing the steady-state probability vector of a finite irreducible CTMC, an a suffient condition for the Generalized Minimal Residual
projection method not to converge to the trivial solution 0 when computing that vector. Finally, we compare several splitting-based iterative methods an a variant of the Generalized Minimal Residual projection method.Fri, 20 Dec 2013 08:33:50 GMThttp://hdl.handle.net/2117/210682013-12-20T08:33:50ZSuñé, Víctor; Domingo Fuster, José Luis; Carrasco, Juan A.noIn this paper we deal with iterative numerical methods to solve linear systems arising in continuous-time Markov chain (CTMC) models. We develop an algorithm to dynamically tune the relaxation parameter of the successive over-relaxation method. We give a sufficient condition for the Gauss-Seidel method to converge when computing the steady-state probability vector of a finite irreducible CTMC, an a suffient condition for the Generalized Minimal Residual
projection method not to converge to the trivial solution 0 when computing that vector. Finally, we compare several splitting-based iterative methods an a variant of the Generalized Minimal Residual projection method.