Ambuj Goyal

A unified framework for simulating Markovian models of highly dependable systems

The authors present a unified framework for simulating Markovian models of highly dependable systems. It is shown that a variance reduction technique called importance sampling can be used to speed up the simulation by many orders of magnitude over standard simulation. This technique can be combined very effectively with regenerative simulation to estimate measures such as steady-state availability and mean time to failure. Moveover, it can be combined with conditional Monte Carlo methods to quickly estimate transient measures such as reliability, expected interval availability, and the distribution of interval availability. The authors show the effectiveness of these methods by using them to simulate large dependability models. They discuss how these methods can be implemented in a software package to compute both transient and steady-state measures simultaneously from the same sample run. >

DB2 parallel edition

The rate of increase in database size and response-time requirements has outpaced advancements in processor and mass storage technology. One way to satisfy the increasing demand for processing power and input/output bandwidth in database applications is to have a number of processors, loosely or tightly coupled, serving database requests concurrently. Technologies developed during the last decade have made commercial parallel database systems a reality, and these systems have made an inroad into the stronghold of traditionally mainframe-based large database applications. This paper describes the DB2® Parallel Edition product that evolved from a prototype developed at IBM Research in Hawthorne, New York, and now is being jointly developed with the IBM Toronto laboratory.

Probabilistic modeling of computer system availability

System availability is becoming an increasingly important factor in evaluating the behavior of commercial computer systems. This is due to the increased dependence of enterprises on continuously operating computer systems and to the emphasis on fault-tolerant designs. Thus, we expect availability modeling to be of increasing interest to computer system analysts and for performance models and availability models to be used to evaluate combined performance/availability (performability) measures. Since commercial computer systems are repairable, availability measures are of greater interest than reliability measures. Reliability measures are typically used to evaluate nonrepairable systems such as occur in military and aerospace applications. We will discuss system aspects which should be represented in an availability model; however, our main focus is a state of the art summary of analytical and numerical methods used to solve computer system availability models. We will consider both transient and steady-state availability measures and for transient measures, both expected values and distributions. We are developing a program package for system availability modeling and intend to incorporate the best solution methods.

Modeling of correlated failures and community error recovery in multiversion software

Three aspects of the modeling of multiversion software are considered. First, the beta-binomial distribution is proposed for modeling correlated failures in multiversion software. Second, a combinatorial model for predicting the reliability of a multiversion software configuration is presented. This model can take as inputs failure distributions either from measurements or from a selected distribution (e.g. beta-binomial). Various recovery methods can be incorporated in this model. Third, the effectiveness of the community error recovery method based on checkpointing is investigated. This method appears to be effective only when the failure behaviors of program versions are lightly correlated. Two different types of checkpoint failure are also considered: an omission failure where the correct output is recognized at a checkpoint but the checkpoint fails to correct the wrong outputs and a destructive failure where the good versions get corrupted at a checkpoint. >

A measure of guaranteed availability and its numerical evaluation

A success (risk) measure of guaranteed availability is proposed. Using a genetic system model, the authors describe the measure and study the effects of the guaranteed level and the observation period on it. Furthermore, they introduce a numerical approach for continuous-time Markov chain models which allows component-level modeling, Coxian failure and repair distributions, time-dependent failure and repair rates and deferred repair and nondeferred repair strategies to be handled. An example of a fault-tolerant database computer system is considered and the measure of guaranteed availability is evaluated for various guaranteed levels and observation periods. >

Measure specific dynamic importance sampling for availability simulations

This paper considers the application of importance sampling to simulations of highly available systems. By regenerative process theory, steady state performance measures of a Markov chain take the form of a ratio. Analysis of a simple three state Birth and Death process shows that the optimal (zero variance) importance sampling distributions for the numerator and denominator of this ratio are quite different and are both dynamic in that they do not correspond directly to time homogeneous Markov chains. Analysis of this three state example suggests heuristics for choosing effective importance sampling distributions for more complex models of highly available systems. These heuristics are applied to a large model of computer system availability. The example shows that additional variance reduction over that previously reported can be obtained by simulating the numerator and denominator independently with different dynamic importance sampling distributions.

Performance analysis of future shared storage systems

This paper deals with the analysis and design of two important classes of computer systems: BIP (Billion Instructions Per Second) systems consisting of a few very high performance processors and KMIP (K Million Instructions Per Second) systems with hundreds of low speed processors. Each system has large, shared semiconductor memories. Simpl analytic models are developed for estimating the performance of such systems. The models are validated using simulation. They can be utilized to quickly reduce the design space and study various trade-offs. The models are applied to BIP and KMIP systems and their use is illustrated using examples.

Likelihood Ratio Sensitivity Analysis for Markovian Models of Highly Dependable Systems

This paper discusses the application of the likelihood ratio gradient estimator to simulations of large Markovian models of highly dependable systems. Extensive empirical work, as well as some mathematical analysis of small dependability models, suggests that in this model setting the gradient estimators are not significantly more noisy than the estimates of the performance measures themselves. The paper also discusses implementation issues associated with likelihood ratio gradient estimation, as well as some theoretical complements associated with application of the technique to continuous-time Markov chains.

Fast simulation of highly dependable systems with general failure and repair processes

An approach for simulating models of highly dependable systems with general failure and repair time distribution is described. The approach combines importance sampling with event rescheduling in order to obtain variance reductions in such rare event simulations. The approach is general in nature and allows a variety of features commonly arising in dependability modeling to be simulated effectively. It is shown how the technique can be applied to systems with redundant components and/or periodic maintenance. For different failure time distributions, the effect of the maintenance period on the steady-state availability is explored. The amount of component redundancy needed to achieve a certain reliability level is determined. >

Fast simulation of dependability models with general failure, repair and maintenance processes

An approach to simulating models of highly dependable systems with general failure and repair time distributions is described. The approach combines importance sampling with event rescheduling in order to obtain variance reduction in such rare event simulations. The approach is general in nature and allows effective simulation of a variety of features commonly arising in dependability modeling. For example, it is shown how the technique can be applied to systems with periodic maintenance. The effects on the steady-state availability of the maintenance period and of different failure time distributions are explored. Some of the trade-offs involved in the design of specific rescheduling rules are described, and their potential effectiveness in simulations of systems with nonexponential failure and repair time distributions are demonstrated. It is found that an effective method for selecting the rescheduling distribution is to keep the probability of a failure transition in the range between 0.1 and 0.5.<<ETX>>