Non-homogeneous Poisson processes (NHPPs) have gained much popularity in actual software testing phases to estimate the software reliability, the number of remaining faults in software and the software release timing. In this paper, we propose a new modeling approach for the NHPP-based software reliability models (SRMs) to describe the stochastic behavior of software fault-detection processes. The fundamental idea is to apply the equilibrium distribution to the fault-detection time distribution in NHPP-based modeling. We also develop efficient parameter estimation procedures for the proposed NHPP-based SRMs. Through numerical experiments, it can be concluded that the proposed NHPP-based SRMs outperform the existing ones in many data sets from the perspective of goodness-of-fit and prediction performance.

This paper considers a transaction-based multi-server system with rejuvenation, and derive the optimal software rejuvenation policies under some system dependability measures; the steady-state availability, the probability of transaction loss and the upper bound of mean response time on transactions. We compare the system configuration based on a single-server with that based on a multi-server in terms of the software rejuvenation scheme. In numerical examples, we calculate the optimal software rejuvenation timing and its associated dependability measure, and refer to the effect of preventive maintenance in the transaction-based multi-server software systems.

In this paper, we consider the similar software cost models with periodic rejuvenation to Garg, Puliafito, Telek and Trivedi (1995) under the cost effectiveness criteria. First, an alternative model as well as the original one are analyzed by Markov regenerative processes. We derive analytically the optimal periodic software rejuvenation policies which maximize the cost-effectiveness in the steady state for two models. Further, we develop statistical non-parametric algorithms to estimate the optimal software rejuvenation policies, provided that the sample data to characterize the system failure times are given. Then, the total time on test (TTT) concept is used. In numerical examples, we compare the periodic software rejuvenation policy with the non-periodic one, and investigate the asymptotic properties of the non-parametric estimators for the optimal software rejuvenation policies through a simulation experiment.

This paper proposes the test case prioritization in regression testing. The large size of a test suite to be executed in regression testing often causes large amount of testing cost. It is important to reduce the size of test cases according to prioritized test sequence. In this paper, we apply the Markov chain Monte Carlo random testing (MCMC-RT) scheme, which is a promising approach to effectively generate test cases in the framework of random testing. To apply MCMC-RT to the test case prioritization, we consider the coverage-based distance and develop the algorithm of the MCMC-RT test case prioritization using the coverage-based distance. Furthermore, the MCMC-RT test case prioritization technique is consistently comparable to coverage-based adaptive random testing (ART) prioritization techniques and involves much less time cost.

Software rejuvenation is a proactive fault management technique that has been extensively studied in the recent literature. In this paper, we focus on an example for a telecommunication billing application considered in Huang et al. (1995) and develop the discrete-time stochastic models to estimate the optimal software rejuvenation schedule. More precisely, two software availability models with rejuvenation are formulated via the discrete semi-Markov processes, and the optimal software rejuvenation schedules which maximize the steady-state availabilities are derived analytically. Further, we develop statistically non-parametric algorithms to estimate the optimal software rejuvenation schedules, provided that the complete sample data of failure times are given. Then, a new statistical device, called the discrete total time on test statistics, is introduced. Finally, we examine asymptotic properties for the statistical estimation algorithms proposed in this paper through a simulation experiment.

This paper discusses how to compute the parametric sensitivity function in continuous-time Markov chains (CTMC). The sensitivity function is the first derivative of the steady-state probability vector regarding a CTMC parameter. Since the sensitivity function is given as a solution of linear equations with a sparse matrix, several linear equation solvers are available to obtain it. In this paper, we consider Jacobi and successive-over relaxation as variants of the Gauss-Seidel algorithm. In addition, we develop an algorithm based on the Takahashi method for the sensitivity function. In numerical experiments, we comprehensively evaluate the performance of these algorithms from the viewpoint of computation time and accuracy.

Survivability is the capability of a system to provide its services in a timely manner even after intrusion and compromise occur. In this paper, we focus on the quantitative analysis of survivability of virtual machine (VM) based intrusion tolerant system in the presence of Byzantine failures due to malicious attacks. Intrusion tolerant system has the ability of a system to continuously provide correct services even if the system is intruded. This paper introduces a scheme of the intrusion tolerant system with virtualization, and derives the success probability for one request by a Markov chain under the environment where VMs have been intruded due to a security hole by malicious attacks. Finally, in numerical experiments, we evaluate the performance of VM-based intrusion tolerant system from the viewpoint of survivability.

This paper presents the opportunity-based software rejuvenation policy and the optimization problem of software rejuvenation trigger time maximizing the system performance index. Our model is based on a basic semi-Markov software rejuvenation model by Dohi et al. 2000 under the environment where possible time, called opportunity, to execute software rejuvenation is limited. In the paper, we consider two stochastic point processes; renewal process and Markovian arrival process to represent the opportunity process. In particular, we derive the existence condition of the optimal trigger time under the two point processes analytically. In numerical examples, we illustrate the optimal design of the rejuvenation trigger schedule based on empirical data.

This paper proposes a dynamic capture-recapture (DCR) model to estimate not only the total number of software faults but also quantitative software reliability from observed data. Compared to conventional static capture-recapture (SCR) model and usual software reliability models (SRMs) in the past literature, the DCR model can handle dynamic behavior of software fault-detection processes and can evaluate quantitative software reliability based on capture-recapture sampling of software fault data. This is regarded as a unified modeling framework of SCR and SRM with the Bayesian estimation. Simulation experiments under some plausible testing scenarios show that our models are superior to SCR and SRMs in terms of estimation accuracy.

In this paper, we present non-Markovian availability models for capturing the dynamics of system behavior of an operational software system that undergoes aperiodic time-based software rejuvenation and checkpointing. Two availability models with rejuvenation are considered taking account of the procedure after the completion of rollback recovery operation. We further proceed to investigate whether there exists the optimal rejuvenation schedule that maximizes the steady-state system availability, which is derived by means of the phase expansion technique, since the resulting models are not the trivial stochastic models such as semi-Markov process and Markov regenerative process, so that it is hard to solve them by using the common approaches like Laplace-Stieltjes transform and embedded Markov chain techniques. The numerical experiments are conducted to determine the optimal rejuvenation trigger timing maximizing the steady-state system availability for each availability model, and to compare both two models.

Long running software systems are known to experience an aging phenomenon called software aging, one in which the accumulation of errors during the execution of software leads to performance degradation and eventually results in failure. To counteract this phenomenon a proactive fault management approach, called software rejuvenation, is particularly useful. It essentially involves gracefully terminating an application or a system and restarting it in a clean internal state. In this paper, we evaluate dependability performance of a communication network system with the software rejuvenation under the assumption that the requests arrive according to a Markov modulated Poisson process (MMPP). Three dependability measures, steady-state availability, loss probability of requests and mean response time on tasks, are derived through the hidden Markovian analysis based on the time-based software rejuvenation scheme. In numerical examples, we investigate the sensitivity of some model parameters to the dependability measures.

The software rejuvenation is one of the most effective preventive maintenance technique for operational software systems with high assurance requirement. In this paper, we propose the workload-based software rejuvenation scheme for a server type of software system, and develop stochastic models to determine the optimal software rejuvenation schedules for some dependability measures. In numerical examples, we evaluate quantitatively the performance of workload-based software rejuvenation scheme and compare it with the time-based rejuvenation scheme.

This paper considers how to evaluate the resiliency for virtualized system with software rejuvenation. The software rejuvenation is a proactive technique to prevent the failure caused by aging phenomenon such as resource exhaustion. In particular, according to Gohsh et al. (2010), we compute a quantitative criterion to evaluate resiliency of system by using continuous-time Markov chains (CTMC). In addition, in order to convert general state-based models to CTMCs, we employ PH (phase-type) expansion technique. In numerical examples, we investigate the resiliency of virtualized system with software rejuvenation under two different rejuvenation policies.

The software rejuvenation is a proactive fault management technique for operational software systems which age due to the error conditions that accrue with time and/or load, and is important for high assurance systems design. In this paper, fine-grained shock models are developed to determine the optimal rejuvenation policies which maximize the system availability. We introduce three kinds of rejuvenation schemes and calculate the optimal software rejuvenation schedules maximizing the system availability for respective schemes. The stochastic models with three rejuvenation policies are extentions of Bobbio et al. (1998, 2001) and represent the failure phenomenon due to the exhaustion of the software resources caused by the memory leak, the fragmentation, etc. Numerical examples are devoted to compare three control schemes quantitatively.

Utilization data (a kind of incomplete data) is defined as the fraction of a fixed period in which the system is busy. In computer systems, utilization data is very common and easily observable, such as CPU utilization. Unlike inter-arrival times and waiting times, it is more significant to consider the parameter estimation of transaction-based systems with utilization data. In our previous work [7], a novel parameter estimation method using utilization data for an Mt/M/1/K queueing system was presented to estimate the parameters of a non-homogeneous Poisson process (NHPP). Since NHPP is classified as a simple counting process, it may not fit actual arrival streams very well. As a generalization of NHPP, Markovian arrival process (MAP) takes account of the dependency between consecutive arrivals and is often used to model complex, bursty, and correlated traffic streams. In this paper, we concentrate on the parameter estimation of an MAP/M/1/K queueing system using utilization data. In particular, the parameters are estimated by using maximum likelihood estimation (MLE) method. Numerical experiments on real utilization data validate the proposed approach and evaluate the effective traffic intensity of the arrival stream of MAP/M/1/K queueing system. Besides, three kinds of utilization datasets are created from a simulation to assess the effects of observed time intervals on both estimation accuracy and computational cost. The numerical results show that MAP-based approach outperforms the exiting method in terms of both the estimation accuracy and computational cost.