Static Worksharing Strategies for Heterogeneous Computers with Unrecoverable Failures

Overview & Synopsis

One has a large workload that is "divisible" (its constituent work's granularity can be adjusted arbitrarily) and one has access to p remote computers that can assist in computing the workload. How can one best utilize the computers? Two features complicate this question. First, the remote computers may differ from one another in speed. Second, each remote computer is subject to interruptions of known likelihood that kill all work in progress on it. One wishes to orchestrate sharing the workload with the remote computers in a way that maximizes the expected amount of work completed. We deal with three distinct problem instances. The simplest problem ignores communication costs, but considers a heterogeneous set of resources that may differ in speed. The other two problems account for communication costs, first with identical remote computers, and then with computers that may differ in speed. We provide exact expressions for the optimal work expectation for all three problems. For the first two problems we provide explicit, closed-form expressions; for the last (and most general) problem, we provide a recurrence for computing this optimal value.