DSpace Community:
http://hdl.handle.net/2117/3644
Sat, 19 Apr 2014 12:00:25 GMT2014-04-19T12:00:25Zwebmaster.bupc@upc.eduUniversitat Politècnica de Catalunya. Servei de Biblioteques i DocumentaciónoA 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 López, Juan Antonio
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 López, Juan AntonionoRandomization 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 López, Juan Antonio
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 López, Juan AntonionoBounds, 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 López, Juan Antonio
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 López, Juan AntonionoIn 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.Differential scan-path: A novel solution for secure design-for-testability
http://hdl.handle.net/2117/21393
Title: Differential scan-path: A novel solution for secure design-for-testability
Authors: Manich Bou, Salvador; S. Wamser, Markus; M. Guillen, Oscar; Sigl, Georg
Abstract: In this paper, we present a new scan-path structure for improving the security of systems including scan paths, which normally introduce a security critical information leak channel into a design. Our structure, named differential scan path (DiSP), divides the internal state of the scan path in two sections. During the shift-out operation, only subtraction of the two sections is provided. Inferring the internal state from this subtraction requires much guesswork that increases exponen-tially with scan path length while the resulting fault coverage is only marginally altered. Subtraction does not preserve parity, thus avoiding attacks using parity information. The structure is simple, needs little area and does not require unlocking keys. Through implementing the DiSP in an elliptic curve crypto-graphic coprocessor, we demonstrate how easily it can be inte-grated into existing design tools. Simulations show that test effectiveness is preserved and that the internal state is effec-tively hidden.Wed, 29 Jan 2014 10:44:33 GMThttp://hdl.handle.net/2117/213932014-01-29T10:44:33ZManich Bou, Salvador; S. Wamser, Markus; M. Guillen, Oscar; Sigl, Georgnosecurity, testability, scan path, attack, BILBOIn this paper, we present a new scan-path structure for improving the security of systems including scan paths, which normally introduce a security critical information leak channel into a design. Our structure, named differential scan path (DiSP), divides the internal state of the scan path in two sections. During the shift-out operation, only subtraction of the two sections is provided. Inferring the internal state from this subtraction requires much guesswork that increases exponen-tially with scan path length while the resulting fault coverage is only marginally altered. Subtraction does not preserve parity, thus avoiding attacks using parity information. The structure is simple, needs little area and does not require unlocking keys. Through implementing the DiSP in an elliptic curve crypto-graphic coprocessor, we demonstrate how easily it can be inte-grated into existing design tools. Simulations show that test effectiveness is preserved and that the internal state is effec-tively hidden.Improving the security of scan path test using differential chains
http://hdl.handle.net/2117/21366
Title: Improving the security of scan path test using differential chains
Authors: Manich Bou, Salvador; Wamser, Markus S.; Sigl, Georg
Abstract: In this paper we present a new scan-path structure for improving the security of systems including a scan path, which normally introduces a security critical information channel into a design. The structure, named differential scan path
(DiSP), divides the internal state of the scan path into two sections.
During shift-out operation, only subtraction of the two sections is provided. The discovery of the internal state from this
subtraction requires guesswork that increases exponentially with scan path length. Subtraction does not preserve parity, a property sometimes used during attacks. Output subtraction cannot be reversed and hence it is not possible to restore the internal state of the chip from the output. The structure is simple, requires little area and no unlocking keys.Mon, 27 Jan 2014 10:53:51 GMThttp://hdl.handle.net/2117/213662014-01-27T10:53:51ZManich Bou, Salvador; Wamser, Markus S.; Sigl, Georgnosecurity, testability, scan path, attack, smartcard, bilboIn this paper we present a new scan-path structure for improving the security of systems including a scan path, which normally introduces a security critical information channel into a design. The structure, named differential scan path
(DiSP), divides the internal state of the scan path into two sections.
During shift-out operation, only subtraction of the two sections is provided. The discovery of the internal state from this
subtraction requires guesswork that increases exponentially with scan path length. Subtraction does not preserve parity, a property sometimes used during attacks. Output subtraction cannot be reversed and hence it is not possible to restore the internal state of the chip from the output. The structure is simple, requires little area and no unlocking keys.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.Information Leakage Reduction at the Scan-Path Output
http://hdl.handle.net/2117/21136
Title: Information Leakage Reduction at the Scan-Path Output
Authors: Manich Bou, Salvador; S. Wamser, Markus; Sigl, Georg
Abstract: In this paper we present a new scan-path structure for improving the security of systems including a scan path, which normally introduces a security critical information channel into a design. The structure, named differential scan path (DiSP), divides the internal state of the scan path into two sections.
During shift-out operation, only subtraction of the two sections is provided. The discovery of the internal state from this subtraction requires guesswork that increases exponentially with scan path length. Subtraction does not preserve parity, a property sometimes used during attacks. Output subtraction cannot be reversed and hence it is not possible to restore the internal state of the chip from the output. The structure is simple, requires little area and no unlocking keys.Thu, 02 Jan 2014 16:38:55 GMThttp://hdl.handle.net/2117/211362014-01-02T16:38:55ZManich Bou, Salvador; S. Wamser, Markus; Sigl, Georgnosecurity, testability, scan path, attack, smart-card, bilbo.In this paper we present a new scan-path structure for improving the security of systems including a scan path, which normally introduces a security critical information channel into a design. The structure, named differential scan path (DiSP), divides the internal state of the scan path into two sections.
During shift-out operation, only subtraction of the two sections is provided. The discovery of the internal state from this subtraction requires guesswork that increases exponentially with scan path length. Subtraction does not preserve parity, a property sometimes used during attacks. Output subtraction cannot be reversed and hence it is not possible to restore the internal state of the chip from the output. The structure is simple, requires little area and no unlocking keys.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 López, Juan Antonio; 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 López, Juan Antonio; 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 López, Juan Antonio; Suñé Socías, Víctor Manuel
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 López, Juan Antonio; Suñé Socías, Víctor ManuelnoIn 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 López, Juan Antonio
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 López, Juan AntonionoDegradable 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 Socías, Víctor Manuel; Domingo Fuster, José Luis; Carrasco López, Juan Antonio
Abstract: In this paper we deal with iterative numericalmethods 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 Socías, Víctor Manuel; Domingo Fuster, José Luis; Carrasco López, Juan AntonionoIn this paper we deal with iterative numericalmethods 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.Tight steady-state availability bounds using the failure distance concept
http://hdl.handle.net/2117/21067
Title: Tight steady-state availability bounds using the failure distance concept
Authors: Carrasco López, Juan Antonio
Abstract: Continuous-timeMarkov chains are commonly used for dependabilitymodeling of repairable
fault-tolerant computer systems. Realistic models of non-trivial fault-tolerant systems often have very large state spaces. An attractive approach for dealing with the largeness problem is the use of pruningmethods with error bounds. Several such methods for computing steady-state
availability bounds have been proposed recently. This paper presents a new method which exploits the failure distance concept to bound more efficiently the behavior in the non-generated state space. It is proved that the bounding method gives tighter bounds than previous methods.
Numerical analysis shows that the new bounds can be significantly tighter.Fri, 20 Dec 2013 08:05:25 GMThttp://hdl.handle.net/2117/210672013-12-20T08:05:25ZCarrasco López, Juan AntonionoContinuous-timeMarkov chains are commonly used for dependabilitymodeling of repairable
fault-tolerant computer systems. Realistic models of non-trivial fault-tolerant systems often have very large state spaces. An attractive approach for dealing with the largeness problem is the use of pruningmethods with error bounds. Several such methods for computing steady-state
availability bounds have been proposed recently. This paper presents a new method which exploits the failure distance concept to bound more efficiently the behavior in the non-generated state space. It is proved that the bounding method gives tighter bounds than previous methods.
Numerical analysis shows that the new bounds can be significantly tighter.Efficient implementations of the randomization method with control of the relative error
http://hdl.handle.net/2117/20936
Title: Efficient implementations of the randomization method with control of the relative error
Authors: Suñé Socías, Víctor Manuel; Carrasco López, Juan Antonio
Abstract: Randomization is a well-known numerical method for the transient analysis of continuous-time Markov chains. The main advantages of the method are numerical stability, well-controlled computation error and ability to specify the computation error in advance. Typical implementations of the method control the truncation error in absolute value, which is not completely satisfactory in some cases. Based on a theoretical result regarding the dependence on the parameter of the Poisson distribution of the relative error introduced when a weighted sum of Poisson probabilities is truncated by the right, in this paper we develop efficient and numerically stable implementations of the randomization method for the computation of two measures on rewarded continuous-time Markovchains with control of the relative error. The numerical stability of those implementations is analyzed using a small example. We also discuss the computational efficiency of the implementations with respect to simpler alternatives.Mon, 09 Dec 2013 10:15:29 GMThttp://hdl.handle.net/2117/209362013-12-09T10:15:29ZSuñé Socías, Víctor Manuel; Carrasco López, Juan AntonionoRandomization is a well-known numerical method for the transient analysis of continuous-time Markov chains. The main advantages of the method are numerical stability, well-controlled computation error and ability to specify the computation error in advance. Typical implementations of the method control the truncation error in absolute value, which is not completely satisfactory in some cases. Based on a theoretical result regarding the dependence on the parameter of the Poisson distribution of the relative error introduced when a weighted sum of Poisson probabilities is truncated by the right, in this paper we develop efficient and numerically stable implementations of the randomization method for the computation of two measures on rewarded continuous-time Markovchains with control of the relative error. The numerical stability of those implementations is analyzed using a small example. We also discuss the computational efficiency of the implementations with respect to simpler alternatives.Solving large interval availability models using a model transformation approach
http://hdl.handle.net/2117/20935
Title: Solving large interval availability models using a model transformation approach
Authors: Carrasco López, Juan Antonio
Abstract: Fault-tolerant systems are often modeled using (homogeneous) continuous time Markovchains (CTMCs).
Computation of the distribution of the interval availability, i.e. of the distribution of the fraction of time in
a time interval in which the system is operational, of a fault-tolerant system modeled by a CTMC is an important problem which has received attention recently. However, currently available methods to perform that computation are very expensive for large models and large time intervals. In this paper, we develop a new method to compute the distribution of the interval availability which, for large enough models and large enough time intervals, is significantly faster than previous methods. In the method, a truncated transformed model,
which has with some arbitrarily small error the same interval availability distribution as the original model, is obtained from the original model and the truncated transformed model is solved using a previous state-of-the-art method. The method requires the selection of a “regenerative” state and its performance depends on that selection. For a class of models, including typical failure/repair models of coherent fault-tolerant systems with exponential failure and repair time distributions and repair in every state with failed components, a natural
selection for the regenerative state exists and theoretical results are available assessing the performance of the method for that natural selection in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive for models in that class. Numerical results are presented showing that the new method can indeed be significantly faster than a previous state-of-the-art method and is able to deal with some large models and large time intervals in reasonable CPU times.Mon, 09 Dec 2013 10:10:01 GMThttp://hdl.handle.net/2117/209352013-12-09T10:10:01ZCarrasco López, Juan AntonionoFault-tolerant systems are often modeled using (homogeneous) continuous time Markovchains (CTMCs).
Computation of the distribution of the interval availability, i.e. of the distribution of the fraction of time in
a time interval in which the system is operational, of a fault-tolerant system modeled by a CTMC is an important problem which has received attention recently. However, currently available methods to perform that computation are very expensive for large models and large time intervals. In this paper, we develop a new method to compute the distribution of the interval availability which, for large enough models and large enough time intervals, is significantly faster than previous methods. In the method, a truncated transformed model,
which has with some arbitrarily small error the same interval availability distribution as the original model, is obtained from the original model and the truncated transformed model is solved using a previous state-of-the-art method. The method requires the selection of a “regenerative” state and its performance depends on that selection. For a class of models, including typical failure/repair models of coherent fault-tolerant systems with exponential failure and repair time distributions and repair in every state with failed components, a natural
selection for the regenerative state exists and theoretical results are available assessing the performance of the method for that natural selection in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be competitive for models in that class. Numerical results are presented showing that the new method can indeed be significantly faster than a previous state-of-the-art method and is able to deal with some large models and large time intervals in reasonable CPU times.Computation of Bounds for Transient Measures of Large Rewarded Markov Models using Regenerative Randomization
http://hdl.handle.net/2117/20934
Title: Computation of Bounds for Transient Measures of Large Rewarded Markov Models using Regenerative Randomization
Authors: Carrasco López, Juan Antonio
Abstract: In this paper we generalize a method (called regenerative randomization) for the transient solution of continuous time Markov models. The generalized method allows to compute two transient measures (the
expected transient reward rate and the expected averaged reward rate) for rewarded continuous time Markov models with a structure covering bounding models which are useful when a complete, exact model has
unmanageable size. The method has the same good properties as the well-known (standard) randomization method: numerical stability, well-controlled computation error, and ability to specify the computation error
in advance, and, for large enough models and long enough times, is significantly faster than the standard randomization method. The method requires the selection of a regenerative state and its performance depends on that selection. For a class ofmodels, class C , including typical failure=repair models with exponential
failure and repair time distributions and repair in every state with failed components, a natural selection for
the regenerative state exists, and results are available assessing approximately the performance of the method for that natural selection in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be significantly faster than standard randomization for models in that
class. The potentially superior e6ciency ofthe regenerative randomization method compared to standard randomization for models not in class C' is illustrated using a large performability model of a fault-tolerant multiprocessor system.Mon, 09 Dec 2013 10:00:17 GMThttp://hdl.handle.net/2117/209342013-12-09T10:00:17ZCarrasco López, Juan AntonionoIn this paper we generalize a method (called regenerative randomization) for the transient solution of continuous time Markov models. The generalized method allows to compute two transient measures (the
expected transient reward rate and the expected averaged reward rate) for rewarded continuous time Markov models with a structure covering bounding models which are useful when a complete, exact model has
unmanageable size. The method has the same good properties as the well-known (standard) randomization method: numerical stability, well-controlled computation error, and ability to specify the computation error
in advance, and, for large enough models and long enough times, is significantly faster than the standard randomization method. The method requires the selection of a regenerative state and its performance depends on that selection. For a class ofmodels, class C , including typical failure=repair models with exponential
failure and repair time distributions and repair in every state with failed components, a natural selection for
the regenerative state exists, and results are available assessing approximately the performance of the method for that natural selection in terms of “visible” model characteristics. Those results can be used to anticipate when the method can be expected to be significantly faster than standard randomization for models in that
class. The potentially superior e6ciency ofthe regenerative randomization method compared to standard randomization for models not in class C' is illustrated using a large performability model of a fault-tolerant multiprocessor system.