Optimizing a Divisible Load Nonlinear Cost Function

Conference on Information Sciences and Systems, 2004

In this paper divisible load scheduling theory is used to examine monetary cost and energy use optimization in a single level tree network. The problem is to flnd an optimal sequence for the distri- bution of the load to each processor that will mini- mize the monetary cost or energy consumption of the network. Optimization results from four difierent al-

IEEE Transactions on Parallel and Distributed Systems, 1998

A bus oriented network where there is a charge for the amount of divisible load processed on each processor is investigated. A cost optimal processor sequencing result is found which involves assigning load to processors in nondecreasing order of the cost per load characteristic of each processor. More generally, one can trade cost against solution time. Algorithms are presented to minimize computing cost with an upper bound on solution time and to minimize solution time with an upper bound on cost. As an example of the use of this type of analysis, the effect of replacing one fast but expensive processor with a number of cheap but slow processors is also discussed. The type of questions investigated here are important for future computer utilities that perform distributed computation for some charge.

IEEE Transactions on Computers, 2016

This work investigates the problem of a non-linear divisible load distribution on a homogeneous linear network. A novel computational model of non-linear loads that includes complete steps for processing them, is proposed. This model solves the problem of the classical model, whose performance degrades by separating the load. This work also presents an algorithm S (Single-installment) that uses single-installment processing to distribute a non-linear divisible load on a homogeneous linear network. An algorithm M (Multi-installment) that applies multi-installment processing to reduce the initial distribution time for load is also proposed. Closed-form expressions for the parallel processing time and speed-up of the proposed algorithms are derived. The speed-up of algorithm S is much better than that of the classical algorithm that is based on the classical model. Algorithm M outperforms algorithm S in terms of speed-up when the load to be processed is very large or when the start-up costs are small.

h i g h l i g h t s

Electric Power Systems Research, 2009

This work is devoted to study and discuss the main methods to solve the network cost allocation problem both for generators and demands. From the presented, compared and discussed methods, the first one is based on power injections, the second deals with proportional sharing factors, the third is based upon Equivalent Bilateral Exchanges, the fourth analyzes the power flow sensitivity in relation to the power injected, and the last one is based on Z bus network matrix. All the methods are initially illustrated using a 4-bus system. In addition, the IEEE 24-bus RTS system is presented for further comparisons and analysis. Appropriate conclusions are finally drawn.

2007

Ordonnancement de tâches divisibles sur un réseau linéaire de processeurs Résumé : Min, Veeravalli, and Barlas ont proposé [18, 19] des stratégies pour minimiser le temps d'exécution d'une ou de plusieurs tâches divisibles sur un réseau linéaire de processeurs hétérogènes, en distribuant le travail en une ou plusieurs tournées. Sur un exemple très simple nous montrons que l'approche proposée dans [19] ne produit pas toujours une solution et que, quand elle le fait, la solution est souvent sous-optimale. Nous montronségalement comment trouver un ordonnancement optimal pour toute instance, quand le nombre de tournées par tâches est spécifié. Ensuuite, nous montrons formellement que lorsque les fonctions de coûts sont linéaires, comme c'est le cas dans [18, 19], un ordonnancement optimal a un nombre infini de tournées. Un tel modèle de coût ne peut donc pasêtre utilisé pour définir des stratégies en multi-tournées utilisables en pratique. Finalement, au moyen de simulations exhaustives, nous montrons que la meilleure solution est toujours produite par l'approche par programmation linéaire, tandis que les solutions de [19] peuventêtre trèś eloignées de l'optimal.

The Annals of Applied Probability, 2010

We analyze the asymptotic properties of an Euclidean optimization problem on the plane. Specifically, we consider a network with 3 bins and n objects spatially uniformly distributed, each object being allocated to a bin at a cost depending on its position. Two allocations are considered: the allocation minimizing the bin loads and the allocation allocating each object to its less costly bin. We analyze the asymptotic properties of these allocations as the number of objects grows to infinity. Using the symmetries of the problem, we derive a law of large numbers, a central limit theorem and a large deviation principle for both loads with explicit expressions. In particular, we prove that the two allocations satisfy the same law of large numbers, but they do not have the same asymptotic fluctuations and rate functions.

European Journal of Operational Research, 2002

A network design problem in which every pair of nodes can communicate directly is discussed. However, there is an incentive to combine¯ow from dierent sources, namely, if the total¯ow through a link exceeds the prescribed threshold, then the cost of this¯ow is discounted by a factor a. Alternative mixed integer linear formulations for this problem are presented. Computational results comparing the models on a set of benchmark problems are also presented. The results show the eectiveness of the formulations: for discounts of 5±10%, the gaps between linear and integer solutions are within few percent. Such a model oers economic incentives in building and utilizing communication networks. Ó

Journal of Parallel and Distributed …, 2005

In this paper, we consider the problem of scheduling multiple divisible loads on heterogeneous linear daisy chain networks. Our objective is to design a load distribution strategy such that the total processing time of a set of loads is minimized. We assume that the set of loads are resident in one of the farthest end processors, which has a scheduler that will distribute the load to the other processors in the network. When distributing a load from the set, the distribution pattern of the previous load has to be taken into consideration to ensure that no processors are left idle and there are no collisions in the communication links. We design single and multi-installments strategies to achieve the above objective. We derive certain important conditions to determine whether an optimum solution exists. We propose two heuristic strategies when an optimum solution is unattainable. Using all the above strategies, we conduct four different simulation experiments to track the performance of strategies under several real-life situations. We conducted four different simulation experiments based on the two heuristic strategies to identify the best combination suitable for our multiple-loads distribution strategy. We also run simulations for a homogeneous system to quantify the performance under 3 different policies, that is, when the loads are (a) unsorted, (b) sorted with smallest load first (SLF) and (c) sorted with largest load first (LLF). A detailed analysis of the simulation results is presented and based on these, recommendations are made for the choice of strategies. Finally, we compare the performance of a single-load distribution strategy against the multiple-loads distribution strategy designed in this paper to quantify the exact performance gain that can be achieved. Illustrative examples are also provided for ease of understanding.

Journal of Applied Mathematics and Decision Sciences, 2003

We present a genetic algorithm for heuristically solving a cost minimization problem applied to communication networks with threshold based discounting. The network model assumes that every two nodes can communicate and offers incentives to combine flow from different sources. Namely, there is a prescribed threshold on every link, and if the total flow on a link is greater than the threshold, the cost of this flow is discounted by a factor α. A heuristic algorithm based on genetic strategy is developed and applied to a benchmark set of problems. The results are compared with former branch and bound results using the CPLEX e R solver. For larger data instances we were able to obtain improved solutions using less CPU time, confirming the effectiveness of our heuristic approach.