Multi-installment scheduling (MIS) has been deemed as a promising paradigm that can sharply reduce the processing time of large-scale divisible workloads on various network-based compute platforms. Unfortunately, the practicality of MIS was crippled due to its overwhelming complexity for deriving optimal values for (n × m) + 2 related variables, i.e., we have to obtain an optimal number n of required computing resources, optimal number m of installments, and optimal load partition matrix A = (αij)n×m which determines the sizes of load fractions assigned to each computing unit in every installment. To circumvent this complexity, in this paper, we first derive explicit analytical expressions for optimal load partition matrix A of size n × m based on a given number of n and m. Then we propose a heuristic algorithm referred to as Time, Resource, and Energy Efficient MIS (TREE-MIS) to determine optimal values of n and m. The efficiency of our approach is shown to significantly improve since it can produce globally optimal solutions directly for (n × m) variables among (n × m) + 2 in total for MIS problems based on the derived analytical expressions within a short runtime. We conduct extensive simulations to demonstrate the effectiveness of the proposed algorithm. Simulation results show that our TREE-MIS can not only minimize the processing time of workloads as well as improve resource utilization of the compute platform but also drastically reduce the runtime compared to other state-of-art MIS strategies. Furthermore, while handling large-scale workloads in any large network infrastructures would inexorably result in significant amounts of energy wastage if the strategy is not prudently designed. As an offshoot of our analysis and design, we clearly demonstrate that the energy wastage in adopting our TREE-MIS is kept minimum when compared to other currently available strategies in practice.

Accelerated life tests (ALTs) are often used to make timely assessments of the lifetime distribution of materials and components. The goal of many ALTs is the estimation of a quantile of a log-location-scale failure time distribution. Much of the previous work on planning accelerated life tests has focused on deriving test-planning methods under a specific log-location-scale distribution. This paper presents a new approach for computing approximate large-sample variances of maximum likelihood estimators of a quantile of a general log-location-scale distribution with censoring, and time-varying stress. The approach is based on a cumulative exposure model. Using sample data from a published paper describing optimum ramp-stress test plans, we show that our approach and the one used in the previous work give the same variance-covariance matrix of the quantile estimator from the two different approaches. Then, as an application of this approach, we extend the previous work to a new optimum ramp-stress test plan obtained by simultaneously adjusting the ramp rate with the lower start level of stress. We find that the new optimum test plan can have a smaller variance than that of the optimum ramp-stress test plan previously obtained by adjusting only the ramp rate. We compare optimum ramp-stress test plans with the more commonly used constant-stress accelerated life test plans. We also conduct simulations to provide insight, and to check the adequacy of the large-sample approximate results obtained by the approach.

Previous work on planning accelerated life tests has been based on large-sample approximations to evaluate test plan properties. In this paper, we use more accurate simulation methods to investigate the properties of accelerated life tests with small sample sizes where large-sample approximations might not be expected to be adequate. These properties include the simulated -bias, and variance for quantiles of the failure-time distribution at use conditions. We focus on using these methods to find practical compromise test plans that use three levels of stress. We also study the effects of not having any failures at test conditions, and the effect of using incorrect planning values. We note that the large-sample approximate variance is far from adequate when the probability of zero failures at certain test conditions is not negligible. We suggest a strategy to develop useful test plans using a small number of test units while meeting constraints on the estimation precision, and on the probability that there will be zero failures at one or more of the test stress levels.