This article analyzes the completion time of a job running on a virtualized server subject to software aging and rejuvenation in a virtual machine monitor (VMM). A job running on the server may be interrupted by virtual machine (VM) failure, VMM failure or VMM rejuvenation. The job interruption is categorized as either preemptive-repeat ( prt ), in which case the interrupted job needs to restart from the beginning, or preemptive-resume ( prs ), in which case the job resumes execution from the point of interruption. Using a semi-Markov process (SMP) to model the server behavior, the steady-state server availability is computed and the theory developed in Kulkarni et al. [1987] is used to obtain the Laplace-Stieltjes transform (LST) of the job completion time. In the numerical experiments, we introduce four types of aging behavior of VMM. The effectiveness of VMM rejuvenation on job completion time is discussed in association with the type of interruption it causes and the VMM aging type. With our parameter settings, VMM rejuvenation with prs job interruption improves the performance of job execution regardless of the aging type, with performance degradation is taken into account.

With the ever-increasing complexity and requirements of highly dependable systems, their evaluation during design and operation is becoming more crucial. Realistic models of such systems are often not amenable to analysis using conventional analytic or numerical methods. Therefore, analysts and designers turn to simulation to evaluate these models. However, accurate estimation of dependability measures of these models requires that the simulation frequently observes system failures, which are rare events in highly dependable systems. This renders ordinary Simulation impractical for evaluating such systems. To overcome this problem, simulation techniques based on importance sampling have been developed, and are very effective in certain settings. When importance sampling works well, simulation run lengths can be reduced by several orders of magnitude when estimating transient as well as steady-state dependability measures. This paper reviews some of the importance-sampling techniques that have been developed in recent years to estimate dependability measures efficiently in Markov and nonMarkov models of highly dependable systems.

We present new adaptive importance sampling techniques based on stochastic Newton recursions. Their applicability to the performance evaluation of communication systems is studied. Besides bit-error rate (BER) estimation, the techniques are used for system parameter optimization. Two system models that are analytically tractable are employed to demonstrate the validity of the techniques. As an application to situations that are analytically intractable and numerically intensive, the influence of crosstalk in a wavelength-division multiplexing (WDM) crossconnect is assessed. In order to consider a realistic system model, optimal setting of thresholds in the detector is carried out while estimating error rate performances. Resulting BER estimates indicate that the tolerable crosstalk levels are significantly higher than predicted in the literature. This finding has a strong impact on the design of WDM networks. Power penalties induced by the addition of channels can also be accurately predicted in short run-times.

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.>

An analysis of a threshold policy for scheduling readers and writers in a multiserver system and a comparison of its performance with the first-come, first-served (FCFS) policy are presented. The threshold fastest emptying (FTE) policy is analyzed in a system with writer arrivals and an infinite backlog of readers using a Markovian model as well as a vacationing server model to yield closed-form expressions for the mean writer response time and the reader throughput. The maximum throughput achieved by the TFE policy is shown to be an increasing function of K, the threshold on the number of writers in the system, which even at K=1 exceeds the maximum throughput achieved by FCFS. In a system with reader and writer arrivals (nonsaturated system), simulation is used to study and compare the mean response time for the FCFS and the TFE policies.>

The CLOCK algorithm is a popular buffer replacement algorithm because of its simplicity and its ability to approximate the performance of the Least Recently Used (LRU) replacement policy. The Generalized Clock (GCLOCK) buffer replacement policy uses a circular buffer and a weight associated with each page brought in buffer to decide on which page to replace. We develop an approximate analysis for the GCLOCK policy under the Independent Reference Model (IRM) that applies to many database transaction processing workloads. We validate the analysis for various workloads with data access skew. Comparison with simulations shows that in all cases examined the error is extremely small (less than 1%). To show the usefulness of the model we apply it to a Transaction Processing Council benchmark A (TPC-A) like workload. If knowledge of the different data partitions in this workload is assumed, the analysis shows that, with appropriate choice of weights, the performance of the GCLOCK algorithm can be better than the LRU policy. Performance very close to that for optimal (static) buffer allocation can be achieved by assigning sufficiently high weights, and can be implemented with a reasonably low overhead. Finally, we outline how the model can be extended to capture the effect of page invalidation in a multinode system.

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.>

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.>

Different checkpointing strategies are combined with recovery models of different refinement levels in the database systems. The complexity of the resulting model increases with its accuracy in representing a realistic system. Three different analytic approaches are used depending on the complexity of the model: analytic, numerical and simulation. A Markovian queuing model is developed, resulting in a combined Poisson and load-dependent checkpointing strategy with stochastic recovery. A state-space analysis approach is used to derive semianalytic expressions for the performance variables in terms of a set of unknown boundary state probabilities. An efficient numerical algorithm for evaluating unknown probabilities is outlined. The validity of the numerical solution is checked against simulation results and shown to be of acceptable accuracy, particularly in the stable operating range. Simulations have shown that realistic load-dependent checkpointing results in performance close to the optimal deterministic checkpointing. Furthermore, the stochastic recovery model is an accurate representation of a realistic recovery.>

In this paper we consider the queueing analysis of a fault-tolerant computer system. The failure/repair behavior of the server is modeled by an irreducible continuous-time Markov chain. Jobs arrive in a Poisson fashion to the system and are serviced according to FCFS discipline. A failure may cause the loss of the work already done on the job in service, if any; in this case the interrupted job is repeated as soon as the server is ready to deliver service. In addition to the delays due to failures and repairs, jobs suffer delays due to queueing. We present an exact queueing analysig of the system and study the steady-state behavior of the number of jobs in the system. As a numerical example, we consider a system with two processors subject to failures and repairs.

Queueing models provide a useful tool for predicting the performance of many service systems including computer systems, telecommunication systems, computer/communication networks and flexible manufacturing systems. Traditional queueing models predict system performance under the assumption that all service facilities provide failure-free service. It must, however, be acknowledged that service facilities do experience failures and that they get repaired. In recent years, it has been increasingly recognized that this separation of performance and reliability/availability models is no longer adequate.