Vandy Berten

On the distribution of sequential jobs in random brokering for heterogeneous computational grids

Scheduling stochastic workloads is a difficult task. In order to design efficient scheduling algorithms for such workloads, it is required to have a good in-depth knowledge of basic random scheduling strategies. This paper analyzes the distribution of sequential jobs and the system behavior in heterogeneous computational grid environments where the brokering is done in such a way that each computing element has a probability to be chosen proportional to its number of CPUs and (new from the previous paper) its relative speed. We provide the asymptotic behavior for several metrics (queue-sizes, slowdowns, etc.) or, in some cases, an approximation of this behavior. We study these metrics for a variety of workload configurations (load, distribution, etc.). We compare our probabilistic analysis to simulations in order to validate our results. These results provide a good understanding of the system behavior for each metric proposed. This enables us to design advanced and efficient algorithms for more complex cases.

Brokering strategies in computational grids using stochastic prediction models

In this paper we propose a new routing policy to route jobs to clusters in computational grids. This routing policy is based on index tables computed at each cluster. These tables can be computed off-line or on-line. Their computations use predictions about the average future behavior of the grid. We show how can be used in practice for task allocations in computational grids. We also report numerous simulations providing numerical evidence of the efficiency of our index routing policy compared with the classical brokers used in most production grids today.

A probabilistic approach for fault tolerant multiprocessor real-time scheduling

In this paper we tackle the problem of scheduling a periodic real time system on identical multiprocessor platforms, moreover the tasks considered may fail with a given probability. For each task we compute its duplication rate in order to (1) given a maximum tolerated probability of failure, minimize the size of the platform such at least one replica of each job meets its deadline (and does not fail) using a variant of EDF namely EDF(k) or (2) given the size of the platform, achieve the best possible reliability with the same constraints. Thanks to our probabilistic approach, no assumption is made on the number of failures which can occur. We propose several approaches to duplicate tasks and we show that we are able to find solutions always very close to the optimal one

A global optimal scheduling algorithm for multiprocessor low-power platforms

This paper presents a real-time scheduling algorithm which globally schedules any feasible periodic task set --- i.e., is optimal --- on a multiprocessor platform. Beside respecting the deadlines, our algorithm, based on DP-Wrap algorithm, drastically reduces the power consumption of the device by slowing down the processors as much as possible. We present our algorithm in two versions (if frequency changes are allowed at any time, or if there are some restrictions about it), prove its (schedulability) correctness, and provide several simulations attesting its low-power efficiency.

Modeling resubmission in unreliable grids: the bottom-up approach

Failure is an ordinary characteristic of large-scale distributed environments. Resubmission is a general strategy employed to cope with failures in grids. Here, we analytically and experimentally study resubmission in the case of random brokering (jobs are dispatched to a computing elements with a probability proportional to its computing power). We compare two cases when jobs are resubmitted to the broker or to the computing element. Results show that resubmit to the broker is a better strategy. Our approach is different from most existing race-based one as it is a bottom-up one: we start from a simple model of a grid and derive its characteristics.

Grid brokering for batch allocation using indexes

In this paper we show how dynamic brokering for batch allocation in grids based on bi-dimensional indices can be used in practice in computational grids, with or without knowing the sizes of the jobs. We provide a fast algorithm (with a quadratic complexity) which can be used off-line or even on-line to compute the index tables. We also report numerous simulations providing numerical evidence of the great efficiency of our index routing policy as well as its robustness with respect to parameter changes. The value of information is also assessed by comparing the performance of indexes when the sizes of the jobs are known and when they are not known.

On the job distribution in random brokering for computational grids

This paper analyses the way jobs are distributed in a computational grid environment where the brokering is done in such a way that each Computing Element has a probability to be chosen proportional to its number of CPUs. We give the asymptotic behaviour for several metrics (queue sizes, slowdown...), or, in some case, an approximation of this behaviour. We study the unsaturated case as well as the saturated case, in several stochastic distributions.