Competition and Peak-Demand Pricing in Clouds under Tenants' Demand Response

A significant fraction of the operational expenditures incurred by cloud service providers relates to their networking (Internet access) and electricity consumption. Both depend on the peak-demand over the billing interval. In the future, cloud services providers may in turn recoup these costs from their long-term customers through peak-based pricing. We explore two different methods for the cloud provider to recoup this charge: (i) equal allocation and (ii) proportional to usage allocation. Furthermore, we consider multiple strategic tenants whose active demand response to cloud price settings jointly depends on job responsiveness (modeled as queueing delay of admitted jobs) and lost/shed workload (due to excessive delay). Under certain conditions, we prove existence and uniqueness of Nash equilibria for regimes (i) and (ii). Due to nonconvexity in the utility (or cost) functions, existence statements require leveraging potentiality arguments while uniqueness statements rely on imposing further convexityrequirements. The resulting Nash equilibrium is parametrized by the price per unit demand, which may be strategically set by the cloud to maximize its revenue subject to tenants reaching a Nash equilibrium. We model the resulting interactions as a Stackelberg game between the cloud and a set of tenants. A relatively general existence statement is provided for the Stackelberg equilibrium under regime (i). For a special case of regime (ii), the unique Stackelberg equilibrium is characterized. Finally, we provide a numerical study for such a framework using real-world peak-based prices from an electric utility and demands given by Google workload traces.'