A new general-purpose method for the computation of the interval availability distribution

We develop a new randomization-based general-purpose method for the computation of the interval availability distribution of systems modeled by continuous-time Markov chains (CTMCs). The basic idea of the new method is the use of a randomization construct with different randomization rates for up and down states. The new method is numerically stable and computes the measure with well-controlled truncation error. In addition, for large CTMC models, when the maximum output rates from up and down states are significantly different, and when the interval availability has to be guaranteed to have a level close to one, the new method is significantly or moderately less costly in terms of CPU time than a previous randomization-based state-of-the-art method, depending on whether the maximum output rate from down states is larger than the maximum output rate from up states, or vice versa. Otherwise, the new method can be more costly, but a relatively inexpensive for large models switch of reasonable quality can be easily developed to choose the fastest method. Along the way, we show the correctness of a generalized randomization construct, in which arbitrarily different randomization rates can be associated with different states, for both finite CTMCs with infinitesimal generator and uniformizable CTMCs with denumerable state space.Preprin

An efficient and numerically stable method for computing bounds for the interval availability distribution

This paper is concerned with the computation of the interval availability (proportion of time in a time interval in which the system is up) distribution of a fault-tolerant system modeled by a finite (homogeneous) continuous-time Markov chain (CTMC). General-purpose methods for performing that computation tend to be very expensive when the CTMC and the time interval are large. Based on a previously available method (regenerative transformation) for computing the interval availability complementary distribution, we develop a method called bounding regenerative transformation for the computation of bounds for that measure. Similar to regenerative transformation, bounding regenerative transformation requires the selection of a regenerative state. The method is targeted at a certain class of models, including both exact and bounding failure/repair models of fault-tolerant systems with increasing structure function, with exponential failure and repair time distributions and repair in every state with failed components having failure rates much smaller than repair rates (F/R models), with a “natural” selection for the regenerative state. The method is numerically stable and computes the bounds with well-controlled error. For models in the targeted class and the natural selection for the regenerative state, computational cost should be traded off with bounds tightness through a control parameter. For large models in the class, the version of the method that should have the smallest computational cost should have small computational cost relative to the model size if the value above which the interval availability has to be guaranteed to be is close to 1. In addition, under additional conditions satisfied by F/R models, the bounds obtained with the natural selection for the regenerative state by the version that should have the smallest computational cost seem to be tight for all time intervals or not small time intervals, depending on whether the initial probability distribution of the CTMC is concentrated in the regenerative state or not.Postprint (published version

Solving large interval availability models using a model transformation approach

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.Postprint (published version

An efficient and numerically stable method for computing interval availability distribution bounds

The paper develops a method, called bounding regenerative transformation, for the computation with numerical stability and well-controlled error of bounds for the interval availability distribution of systems modeled by finite (homogeneous) continuous-time Markov chain models with a particular structure. The method requires the selection of a regenerative state and is targeted at a class of models, class C'_1, with a “natural” selection for the regenerative state. For class C'_1 models, bounds tightness can be traded-off with computational cost through a control parameter D_C, with the option D_C = 1 yielding the smallest computational cost. For large class C'_1 models and the selection D_C = 1, the method will often have a small computational cost relative to the model size and, with additional conditions, seems to yield tight bounds for any time interval or not small time intervals, depending on the initial probability distribution of the model. Class C'_1 models with those additional conditions include both exact and bounding failure/repair models of coherent fault-tolerant systems with exponential failure and repair time distributions and repair in every state with failed components with failure rates much smaller than repair rates.Preprin

An optimal approach for the joint problem of level of repair analysis and spare parts stocking

We propose a method that can be used when deciding on how to maintain capital goods, given a product design and the layout of a repair network. Capital goods are physical systems that are used to produce products or services. They are expensive and technically complex and have high downtime costs. Examples are manufacturing equipment, defense systems, and medical devices

Energy-Aware Cloud Management through Progressive SLA Specification

Novel energy-aware cloud management methods dynamically reallocate computation across geographically distributed data centers to leverage regional electricity price and temperature differences. As a result, a managed VM may suffer occasional downtimes. Current cloud providers only offer high availability VMs, without enough flexibility to apply such energy-aware management. In this paper we show how to analyse past traces of dynamic cloud management actions based on electricity prices and temperatures to estimate VM availability and price values. We propose a novel SLA specification approach for offering VMs with different availability and price values guaranteed over multiple SLAs to enable flexible energy-aware cloud management. We determine the optimal number of such SLAs as well as their availability and price guaranteed values. We evaluate our approach in a user SLA selection simulation using Wikipedia and Grid'5000 workloads. The results show higher customer conversion and 39% average energy savings per VM.Comment: 14 pages, conferenc

Uncertain Price Competition in a Duopoly with Heterogeneous Availability

We study the price competition in a duopoly with an arbitrary number of buyers. Each seller can offer multiple units of a commodity depending on the availability of the commodity which is random and may be different for different sellers. Sellers seek to select a price that will be attractive to the buyers and also fetch adequate profits. The selection will in general depend on the number of units available with the seller and also that of its competitor - the seller may only know the statistics of the latter. The setting captures a secondary spectrum access network, a non-neutral Internet, or a microgrid network in which unused spectrum bands, resources of ISPs, and excess power units constitute the respective commodities of sale. We analyze this price competition as a game, and identify a set of necessary and sufficient properties for the Nash Equilibrium (NE). The properties reveal that sellers randomize their price using probability distributions whose support sets are mutually disjoint and in decreasing order of the number of availability. We prove the uniqueness of a symmetric NE in a symmetric market, and explicitly compute the price distribution in the symmetric NE.Comment: 45 pages, Accepted for publication in IEEE Transaction on Automatic Contro

A Framework for Trusted Services

An existing challenge when selecting services to be used in a service- based system is to be able to distinguish between good and bad services. In this paper we present a trust-based service selection framework. The framework uses a trust model that calculates the level of trust a user may have with a service based on past experience of the user with the service and feedback about the service received from other users. The model takes into account different levels of trust among users, different relationships between users, and different levels of importance that a user may have for certain quality aspects of a service. A prototype tool has been implemented to illustrate and evaluate the work. The trust model has been evaluated in terms of its capacity to adjust itself due to changes in user ratings and its robustness