Agapios N. Platis

A generalized formulation for the performability indicator

The main objective of this paper is to propose a generalized form of the performability measure, which has been initially defined for the purpose of studying the performance and reliability analysis of fault tolerant systems. This generalized form takes into account more detailed rewards and can be used in general for maintenance cost analysis as well as in the modeling of the website users behavior. We give different formulations by means of a homogeneous Markov chain and a cyclic nonhomogeneous Markov chain and their asymptotic expression.

On the optimization of free resources using non-homogeneous Markov chain software rejuvenation model

Software rejuvenation is an important way to counteract the phenomenon of software aging and system failures. It is a preventive and proactive technique, which consists of periodically restarting an application at a clean internal state. Starting an application generally means that an amount of memory is captured and closing an application engenders the release of an amount of memory. In general, when an application is initiated an amount of memory is captured and when terminated an amount of memory is released. In this paper a model describing the amount of free memory on a system is presented. The modelling is formulated under a continuous time Markov chain framework. Additionally the cost of performing rejuvenation is also taken into consideration, a cost function for the model is produced and a rejuvenation policy is proposed. The contribution of this paper consists of using a cyclic non-homogeneous Markov chain in order to study the overall behaviour of the system capturing time dependence of the rejuvenation rates and deriving an optimal rejuvenation policy. Finally, a case study is presented in order to illustrate the results of the cost analysis.

Semi-Markov Availability Modeling of a Redundant System with Partial and Full Rejuvenation Actions

Software rejuvenation is a preventive maintenance technique to prevent failures in continuously running systems that experience software aging. In this paper, rejuvenation is modeled in a redundant computer system via a semi-Markov process in order to counteract software aging. The system can be switched into the standby unit automatically or manually in the case of a failure at the switching mechanism. Depending on the degradation of the system resources, the running node is either rejuvenated or continues serving and systempsilas steady-state availability is studied along with the optimal time to perform rejuvenation, which increases systempsilas availability. Moreover, an alternative rejuvenation modeling is introduced, in which two different actions; partial and full rejuvenation are performed according to the degradation level. The optimal rejuvenation policies for this case are also derived, leading the system to higher levels of availability.

Performability indicators for the traffic analysis of wide area networks

Abstract In connecting computing networks, reliability term is strongly related to the availability of connections of Wide Area networks (WANs) or Local Area networks (LANs). In this paper we will examine the network connections activity of a Greek University in order to provide two sources of information: The Quantity of Information Not Delivered (QIND) and the Information Flow Interruption (IFI). These indicators will provide us with the inference of information from observable characteristics of data flow(s), even when the data is encrypted or otherwise not directly available (traffic), which is lost due to failures or upgrades inside this network. The reliability analysis is obtained by collecting the network failures data (duration and frequency) and traffic (total and average) for a specified period of 1 year. It is assumed that the numerical analysis is based on the fact that the lifetime follows and exponential distribution (here as we are working on discrete time the distribution must be the geometric distribution). Hence a Markov chain model seems suitable for modelling the functioning of this system. An algorithm concentrates the results in a transition probability matrix and calculates the reward functions for the QIND/IFI indicators with the use of the power method. Finally, the application part provides an example of how final results can be used to evaluate the observed network.

VoIP Availability and Service Reliability through Software Rejuvenation Policies

Nowadays voice over Internet protocol (VoIP) is becoming an evolutionary technology in telecommunications. In this paper the study is focused on the resources that are allocated for VoIP calls. Resource allocation in a VoIP system and resource degradation when new demands for resources arrive at the system are modeled. To counteract resource degradation and improve availability and service reliability, we propose to perform software rejuvenation.. Moreover, the rate of resource allocation in such a system can be importantly affected by the time that an amount of resources is allocated in order to serve VoIP calls. Hence, we model software rejuvenation in a VoIP system with a semi-Markov process in order to capture the effects of time spent at resource degraded states of the system. Through the stochastic analysis of the system an optimal rejuvenation policy that maximizes systems availability is proposed and furthermore the corresponding reliability levels in means of Mean Time To Failure are derived.

Semi-Markov performance modelling of a redundant system with partial, full and failed rejuvenation

Software rejuvenation is a preventive maintenance technique to prevent failures in continuously running systems that experience software aging. In this paper, rejuvenation is modelled in a redundant computer system via a Semi-Markov process in order to counteract software aging. An alternative rejuvenation modelling is also introduced, in which two different actions, partial and full rejuvenation, are performed according to the degradation level. Moreover, the case where software rejuvenation fails to fulfil its purpose leading to a failure is considered. Systems asymptotic availability is studied with respect to the optimal time to perform rejuvenation. Additionally, the expected downtime cost, along with some dependability measures, is also studied. The main purpose of our work is to provide the appropriate framework for finding the optimal rejuvenation interval that will improve not only systems asymptotic availability but also the downtime cost and its performance.

Using birth-and-death theory for container terminal strategic investment decisions

The present study uses birth-and-death modelling in order to examine the improvement of container terminal operations in two stages of the container transportation process. The first stage is the loading/unloading process and the second is the stacking of containers in the container yard. The data has been provided by a central container terminal station located in the Eastern Mediterranean encapsulating information on infrastructure, arrivals of vessels and service times for a period of three years. A number of scenarios are estimated based on changes in the number available servers (s) and the rate of service level (μ). Results show that both the increase in the number of servers (berth/slots) and the improvement in the rate of the service levels to users contribute decisively to the optimisation of container terminal operations benefiting not only the terminal but its users as well. However, the ability of Markov theory to estimate with the use of probabilities the economic consequences that strategic investment decisions could have on terminal efficiency is also of significance.

Coverage Modeling and Optimal Maintenance Frequency of an Automated Restoration Mechanism

In this paper, the coverage modeling of an automated restoration mechanism with two components is studied, and optimal maintenance frequencies are determined. Failures and repairs are exponentially distributed for the two components, while the failures of the automated mechanism follow a Weibull distribution. A corrective maintenance policy is considered for each component whereas, for the automated restoration mechanism, an additional preventive maintenance is taken into account. The system is modeled with a continuous time Markov chain and two performability indicators: one performability indicator modeling the downtime, and a second one modeling the overall operational cost. Consequently, two optimal maintenance frequencies are derived: first by minimizing the downtime, and second by minimizing the overall operational cost. A numerical example is used to evaluate the applicability of the proposed method.

Availability and reliability estimation for a system undergoing minimal, perfect and failed rejuvenation

In this paper, a software rejuvenation model is presented in which two different rejuvenation actions are considered, perfect and minimal. The concept of a failed rejuvenation action which leads the system to failure is also introduced. The presented model is studied under a Continuous Time Markov Chain (CTMC) framework and a maximum likelihood estimator of the generator matrix is presented. Based on this, estimators for instantaneous availability and reliability function are also presented. Moreover, the behavior of the above estimators is studied under various rejuvenation policies. A numerical example based on simulation results is finally presented.

A Two-Phase Cyclic Nonhomogeneous Markov Chain Performability Evaluation by Explicit Approximate Inverses Applied to a Replicated Database System

The need for a more accurate modeling of the performance of systems whose functioning mainly dependant on external time parameters such as the number of requests during a particular time phase, led us to a novel approach, taking into account the time parameters involved. This is achieved through the evaluation of a performability indicator modeled by means of a two-phase cyclic nonhomogenous Markov chain considering periodical time-dependant arrival request probabilities and applied to a replicated database system. The computation of the performability indicator modeled by cyclic nonhomogeneous Markov chain requires the use of efficient computational methods by using explicit approximate inverse preconditioning methods.