Optimal Posted Prices for Online Cloud Resource Allocation

We study online resource allocation in a cloud computing platform through posted pricing: The cloud provider publishes a unit price for each resource type, which may vary over time; upon arrival at the cloud system, a cloud user either takes the current prices, renting resources to execute its job, or refuses the prices without running its job there. We design pricing functions based on current resource utilization ratios, in a wide array of demand-supply relationships and resource occupation durations, and prove worst-case competitive ratios in social welfare. In the basic case of a single-type, non-recycled resource (allocated resources are not later released for reuse), we prove that our pricing function design is optimal, in that it achieves the smallest competitive ratio among all possible pricing functions. Insights obtained from the basic case are then used to generalize the pricing functions to more realistic cloud systems with multiple types of resources, where a job occupies allocated resources for a number of time slots till completion, upon which time the resources are returned to the cloud resource pool.