Stochastic load balancing and related problems

Abstract

We study the problems of makespan minimization (load balancing), knapsack, and bin packing when the jobs have stochastic processing requirements or sizes. If the jobs are all Poisson, we present a two approximation for the first problem using Graham's rule, and observe that polynomial time approximation schemes can be obtained for the last two problems. If the jobs are all exponential, we present polynomial time approximation schemes for all three problems. We also obtain quasi-polynomial time approximation schemes for the last two problems if the jobs are Bernoulli variables.