We study the cloud resource auction problem where users can bid for resource bundle containing heterogeneous types of virtual machines, and providers allocate virtual machines to their users through group price model. Compared with fixed price model, which is not always the best approach for trading resources as its economically inefficient and inflexible nature, the group price model possess the better flexibility and monetary benefits for auction participants (e.g., cloud providers and users). The proposed auction mechanism strategy-proof group buying-based auction mechanism, which formulates the problem of virtual machine allocation in clouds as a combinatorial auction problem, and holds some important property such as individual rationality, ex-post budget balance, and truthfulness, meanwhile guaranteeing efficiency in both the provider's revenue and system efficiency. Extensive simulation results show that the proposed mechanism yields the allocation efficiency and computational tractability compared with the mechanism with fixed price model. This enables bidders to express their valuations (i.e., private type) for requested bundle in a more meaningful way.There exist many challenges in designing a practical auction-based mechanism for the VM allocation in clouds. We list three major challenges as follows:Strategy-proofness: Because the participants are normally rational and selfish in the auction, they always tend to strategically manipulate the auction, if doing so can increase their utilities. Such strategic behaviors may hurt the other participant's utility. Therefore, designing an auction mechanism, which can prevent the participants from having an incentive to lie about their valuation of the requested bundle, is a critical issue in auction market. Such a mechanism is called strategy-proof mechanism (refer to Section 2 for the definition), simply submitting truthful valuation for the requested bundle maximizes each participant's utility. Allocative efficiency: The objective of an allocative efficient mechanism is to maximize social welfare, which is the sum of the winners' valuations of the allocated instances. Low execution time: Cloud computing is a large-scale and dynamic environment. The auction mechanism for cloud resources has to have a low computation complexity for deciding the winners and the payment in order to be feasible in real cloud market.
System modelThe cloud provider (i.e., seller) sets different configurations of physical resources that she wishes to sell to the cloud users (i.e., buyers) in the form of VM instances.We assume that the cloud provider offers K different instance types, K D ¹1; : : : ; Kº, and specifies the amounts q k of supplied VMs of type k.2 K/. Besides, the provider declares the discrete price curve p k .m/ W Z C ! R C for the instance of type k, which indicates the minimum unit price of the supplied instance that the provider wishes to sell, and is a decreasing step function of m, the number of units sold together, that is, f or m 1 < m 2 and m 1 ; m 2 > 0; p k ....