Pranab K. Muhuri

Real-time task scheduling with fuzzy uncertainty in processing times and deadlines

In real-time systems, scheduling algorithms play the vital role of devising a feasible schedule of the tasks. The scheduling algorithm designer faces uncertainty associated with the timing constrains of the real-time tasks. This paper considers fuzzy timing constraints by modeling the real-time tasks with fuzzy deadlines and fuzzy processing times with different membership functions. Comparative studies and some interesting findings based on simulation experiments are reported.

Real-time scheduling of periodic tasks with processing times and deadlines as parametric fuzzy numbers

Task scheduling is very important in real-time systems as it accomplishes the crucial goal of devising a feasible schedule of the tasks. However, the uncertainty associated with the timing constrains of the real-time tasks makes the scheduling problem difficult to formulate. This motivates the use of fuzzy numbers to model task deadlines and completion times. In this paper a method for intuitively defining smooth membership functions (MFs) for deadlines and execution times has been proposed using mixed cubic-exponential Hermite interpolation parametric curves. The effect of changes in parameterized MFs on the task schedulability and task priorities are also reported. A new technique is proposed based on the concept of dynamic slack calculation to make the existing model more practical and realistic. Examples are given to demonstrate the more satisfactory performance of the new technique.

Particle swam optimization based reliability-redundancy allocation in a type-2 fuzzy environment

In this paper, we have addressed the reliability-redundancy allocation problem with a particle swam optimization based technique. The parameters of the system components are actually imprecise or uncertain quantity since those are generally guessed by the designers during the design-time. Thus, important features of the designed system, viz. reliability, costs, weight etc very suitably qualifies to be considered as fuzzy quantity. Our problem formulation considers these parameters as type-2 fuzzy quantity. There are few reports where the problem has been studied under type-1 fuzzy uncertainty. As far as we know, no research has been reported where the problem has been addressed with a particle swam optimization based approach in a type-2 fuzzy environment. Suitable examples are included to demonstrate our approach. Results are compared showing that the type-2 fuzzy uncertainty based approach outperforms other recently reported results.

Fuzzy multi-objective reliability-redundancy allocation problem

Reliability is the measure of the result of the quality of the system over a long run. The reliability-redundancy allocation problem (RRAP) aims to ensure high systems reliability in the presence of optimally redundant systems components. This is one of the most important design considerations for the systems designers. Several researchers have addressed this important issue during last few decades. However, due to the embedded uncertainty in the parameters of the system components, reliability as well as the costs of the whole system fits very well to be modeled as fuzzy quantity. We therefore modeled this problem as a fuzzy multi-objective optimization problem (MORRAP) that is addressed using the popular multi-objective evolutionary algorithm, NSGA-II (non-dominated sorting genetic algorithm-II). We have considered the based MORRAP with fuzzy type-2 uncertainty. As far as we know, no research has been reported where MORRAP was considered under type-2 fuzzy uncertainty. A typical numerical example is included and results are compared showing that our approach outperforms other recently reported results.

Real-time power aware scheduling for tasks with type-2 fuzzy timing constraints

The timing constraint of tasks in the mobile real-time computing systems plays the central role in deciding the task schedule as timely completion of the task is very important in such systems. These timing constraints are however completely unquantifiable during the time of system modeling and designing. Thus we consider type-2 fuzzy sets for modeling the timing constraints in mobile and time-critical computing systems and propose a new algorithm FT2EDF (Fuzzy Type-2 Earliest Deadline First) for task scheduling. On the other hand, because of the limitation of the storage power, power efficiency is another foremost design objective for designing mobile real-time computing systems. However, reduction of processor power pulls down the system performance. Timely task completion and power efficiency are therefore two mutually conflicting criteria. In this paper, we propose a heuristic based solution approach that with a modified version of the non-dominated sorting genetic algorithm-II (NSGA-II). Our approach allows that a processor dynamically switches between different voltage levels to ensure optimum reduction in the power requirements without compromising the timeliness of the task completion. The efficacy of our approach is demonstrated with two numerical examples. Comparison with the previous results show that our solution ensures approximately 44% of energy saving as compared to the around 25% of the earlier results.

Semi-elliptic membership function

A potentially important, yet under-stated membership function (MF) shape viz. semi-elliptic membership function (SEMF) has been elaborated in this paper so that researchers are able to see its true potential for realistic modelling of the decision variables in real-life applications. The concept of semi-elliptic membership function has the practical significance since it can nicely remove the drawbacks associated with the Gaussian membership function shape regarding its long tail with non-zero membership values. A semi-elliptic membership function can be mathematically expressed in terms of only two parameters. It is shown that, with the representation considered here, prominent arithmetic operations such as addition, subtraction, multiplication etc. can be applied on the semi-elliptic fuzzy numbers. As an extension, a novel membership function generation technique for interval type-2 semi-elliptic (IT2SE) MF has also been proposed. Then the applicability of the arithmetic operations on the IT2SE fuzzy numbers is shown. It is illustrated that semi-elliptic fuzzy numbers can suitably be ranked by existing distance measures. We have shown that the well-known INT (Improved Nie-Tans) defuzzification technique can be applied to the interval type-2 semi-elliptic fuzzy sets for producing defuzzified outputs. Finally, with application point of view, semi-elliptic fuzzy numbers has been applied to the real-time task scheduling problem. Results are compared with triangular fuzzy numbers. Suitable numerical examples are considered for demonstration purposes.

Energy efficient task scheduling with Type-2 fuzzy uncertainty

In this paper, we have reported a new approach for employing the non dominated sorting genetic algorithm-II (NSGA-II) with the type-2 fuzzy sets in optimizing energy in real-time embedded systems. The multi-objective problem of energy efficiency and timeliness of tasks has been extensively studied. Little variations in the task timing parameters produce considerable variations in the results of the critical real-time computations. Importantly, at the system designing phase these timing parameters are completely unquantifiable. We therefore propose here a new algorithm for real-time scheduling in type-2 fuzzy uncertain domains. We have included comparative results obtained from models with crisp timing parameters and their fuzzy type-1 and type-2 counterparts. From the observations of the outcome, it is found that model with crisp timing parameters gives the worst result as energy consumption in the system is maximum at a constant earliness. The crisp model is outperformed by both fuzzy type-1 and type-2 models and ensures significant reductions in energy consumption. Whereas fuzzy type-2 model overwhelms both fuzzy type-1 and crisp model in ensuring task completions with maximum earliness. Suitable numerical examples are included to demonstrate our proposed approach.

Multiobjective Reliability Redundancy Allocation Problem With Interval Type-2 Fuzzy Uncertainty

The multiobjective reliability redundancy allocation problem (MORRAP) aims to ensure high system reliability in the presence of optimally redundant components. This is one of the most important design considerations for system designers. Due to the associated uncertainty in component parameters, precise computations of overall system reliability, cost, and weight, etc., are difficult during design time. Hence, these parameters are befitting to be modeled as fuzzy quantities. As type-1 fuzzy numbers have limitations in representing higher order uncertainties, so this paper models the component parameters viz., reliability, cost, and weight with interval type-2 fuzzy numbers. Thus, we propose a novel formulation of MORRAP, termed as interval type-2 fuzzy multiobjective optimization problem (IT2FMORRAP). A popular multiobjective evolutionary algorithm, viz., nondominated sorting genetic algorithm II, is used to solve the proposed IT2FMORRAP, for which we have developed two novel algorithms in this paper. Numerical examples are included to demonstrate the solution approach. On comparing the outcomes with earlier results, we have found that the proposed IT2FMORRAP outperforms classical as well as other type-1 fuzzy-number-based approaches.

A novel clustering algorithm based on a new similarity measure over Intuitionistic fuzzy sets

In Intuitionistic fuzzy sets(IFSs), experts assign both membership value and non-membership value to each fuzzy element x with a certain degree of hesitation. The hesitancy in the opinion of the experts appear due to incomplete information available regarding x. Therefore, precise estimation of its both membership value and non-membership value becomes highly difficult. Hence, there is a high chance that both membership value and the non-membership value assigned to x by the expert may not be absolutely correct. So, whenever we try to measure similarity between the IFSs using the various distance measures involving all the components of IFSs like membership value, non-membership value together with hesitation, then we often notice that all of them fails to describe the underlying situation completely. Therefore, the similarity measures derived from these distance measures also fails to produce good results. So, we introduce a new similarity measure by properly defining a similarity degree through the result established in this paper. The similarity measure has a central role in developing a modified λ-cutting algorithm for clustering. Here we also establish the efficacy of our modified λ-cutting algorithm while implementing it on a real world data set.

User-Satisfaction-Aware Power Management in Mobile Devices Based on Perceptual Computing

Present day portable devices such as laptops, smartphones, etc., offer their users fastest processors, advanced operating systems, and numerous applications. However, a large section of the users are critical to the available battery capacity and its lifetime. This is because performance of the battery and its lifetime as perceived by the users are quite subjective in nature. It depends directly on user satisfactions, which are usually expressed in terms of words. So, in this paper, we propose a user-satisfaction-aware energy management approach, called “perceptual computer power management approach (Per-C PMA),” based on the technique of perceptual computing. At the heart of our technique is the perceptual computer that processes the linguistic input of the users to aid in the selection of a suitable processor frequency, which plays a significant role in the overall energy consumption of the systems. The Per-C PMA minimizes the energy consumption, while still keeping the user satisfied with the perceived system performance. The Per-C PMA achieves 1) reductions of 42.26% and 10.84% in power consumption, and 2) improvements in the overall satisfaction ratings of 16% and 10%, when compared to other existing power-saving schemes such as ON-DEMAND and human and application-driven frequency scaling for processor power efficiency, respectively. Per-C PMA is the first such application of Per-C on any hardware platform. It is implemented as Ubuntu scripts for end users and can be downloaded from: http://sau.ac.in/∼cilab/. We have also provided the MATLAB files so that interested researchers can use it in their research. For the ease of the users, the Ubuntu scripts and the MATLAB codes are given in the graphical user interface mode; a demo video on how to use the software is also provided on the webpage.