The problem of pricing the cloud has attracted much recent attention due to the widespread use of cloud computing and cloud services. From a theoretical perspective, several mechanisms that provide strong efficiency or fairness guarantees and desirable incentive properties have been designed. However, these mechanisms often rely on a rigid model, with several parameters needing to be precisely known in order for the guarantees to hold. In this paper, we consider a stochastic model and show that it is possible to obtain good welfare and revenue guarantees with simple mechanisms that do not make use of the information on some of these parameters. In particular, we prove that a mechanism that sets the same price per time step for jobs of any length achieves at least 50 of the welfare and revenue obtained by a mechanism that can set different prices for jobs of different lengths, and the ratio can be improved if we have more specific knowledge of some parameters. Similarly, a mechanism that sets the same price for all servers even though the servers may receive different kinds of jobs can provide a reasonable welfare and revenue approximation compared to a mechanism that is allowed to set different prices for different servers.
Other work in this space has dealt with comparing pricing mechanisms such as the on-demand market and the spot market @cite_15 @cite_3 @cite_8 , achieving fairness in job allocation @cite_13 , and studying models of real-time pricing with budget constraints @cite_1 . gave a survey of the current state of research in economics and computer science with respect to cloud pricing.
@cite_8 @cite_1 @cite_3 @cite_15 @cite_13
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In Amazon EC2, cloud resources are sold through a combination of an on-demand market, in which customers buy resources at a fixed price, and a spot market, in which customers bid for an uncertain supply of excess resources. Standard market environments suggest that an optimal design uses just one type of market. We show the prevalence of a dual market system can be explained by heterogeneous risk attitudes of customers. In our stylized model, we consider unit demand risk-averse bidders. We show the model admits a unique equilibrium, with higher revenue and higher welfare than using only spot markets. Furthermore, as risk aversion increases, the usage of the on-demand market increases. We conclude that risk attitudes are an important factor in cloud resource allocation and should be incorporated into models of cloud markets. We introduce a new model of user-based dynamic pricing in which decisions occur in real time and are strongly influenced by the budget constraints of users. This model captures the fundamental operation of many electronic markets that are used for allocating resources. In particular, we focus on those used in data centers and cloud computing where pricing is often an internal mechanism used to efficiently allocate virtual machines. We study the allocative properties and dynamic stability of this pricing model under a standard framework of cloud computing systems which leads to highly degenerate systems of prices. We show that as the size of the system grows the user-based budget-constrained dynamic pricing mechanism converges to the standard Walrasian prices. However, for finite systems, the prices can be non-degenerate and the allocations unfair, with large groups of users receiving allocations significantly below their fair share. In addition, we show that improper choice of price update parameters can lead to significant instabilities in prices, which could be problematic in real cloud computing systems, by inducing system instabilities and allowing manipulations by users. We construct scaling rules for parameters that reduce these instabilities. We study a model of congestible resources, where pricing and scheduling are intertwined. Motivated by the problem of pricing cloud instances, we model a cloud computing service as linked @math queuing systems where the provider chooses to offer a fixed pricing service, a dynamic market based service, or a hybrid of both, where jobs can be preempted in the market-based service. Users (jobs), who are heterogeneous in both the value they place on service and their cost for waiting, then choose between the services offered. Combining insights from auction theory with queuing theory we are able to characterize user equilibrium behavior, and show its insensitivity to the precise market design mechanism used. We then provide theoretical and simulation based evidence suggesting that a fixed price typically, though not always, generates a higher expected revenue than the hybrid system for the provider. We present a model for fair strategyproof allocations in a realistic model of cloud computing centers. This model has the standard Leontief preferences but also captures a key property of virtualization, the use of containers to isolate jobs. We first present several impossibility results for deterministic mechanisms in this setting. We then construct an extension of the well known dominant resource fairness mechanism (DRF), which somewhat surprisingly does not involve the notion of a dominant resource. Our mechanism relies on the connection between the DRF mechanism and the Kalai-Smorodinsky bargaining solution; by computing a weighted max-min over the convex hull of the feasible region we can obtain an ex-ante fair, efficient and strategyproof randomized allocation. This randomized mechanism can be used to construct other mechanisms which do not rely on users' being expected (ex-ante) utility maximizers, in several ways. First, for the case of @math identical machines one can use the convex structure of the mechanism to get a simple mechanism which is approximately ex-post fair, efficient and strategyproof. Second, we present a more subtle construction for an arbitrary set of machines, using the Shapley-Folkman-Starr theorem to show the existence of an allocation which is approximately ex-post fair, efficient and strategyproof. This paper provides both a rigorous foundation for developing protocols that explicitly utilize the detailed structure of the modern cloud computing hardware and software, and a general method for extending the dominant resource fairness mechanism to more complex settings.