This work studies the online electricity cost minimization problem at a co-location data center. A co-location data center serves multiple tenants who rent the physical infrastructure within the data center to run their respective cloud computing services. Consequently, the co-location operator has no direct control over power consumption of its tenants, and an efficient mechanism is desired for eliciting desirable consumption patterns from the co-location tenants. Electricity billing faced by a data center is nowadays based on both the total volume consumed and the peak consumption rate. This leads to an interesting new combinatorial optimization structure on the electricity cost optimization problem, which also exhibits an online nature due to the definition of peak consumption. We model and solve the problem through two approaches: the pricing approach and the auction approach. For the former, we design an offline 2-approximation algorithm as well as an online algorithm with a small competitive ratio in most practical settings. For the latter, we design an efficient (2+ c )-competitive online algorithm, where c is a system dependent parameter close to 1.49, and then convert it into an efficient mechanism that executes in an online fashion, runs in polynomial time, and guarantees truthful bidding and (2+2 c )-competitive in social cost.

We study online resource allocation in a cloud computing platform, through a posted pricing mechanism: e 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 the current resource utilization ratios, in a wide array of demandsupply relationships and resource occupation durations, and prove worst-case competitive ratios of the pricing functions in terms of social welfare. In the basic case of a single-type, non-recycled resource (i.e., allocated resources are not later released for reuse), we prove that our pricing function design is optimal, in that any other pricing function can only lead to a worse competitive ratio. Insights obtained from the basic cases 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 back to the cloud resource pool.