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.
Much recent work has focused on designing online scheduling mechanisms with good welfare guarantees and incentive properties. exhibited a truthful mechanism for batch jobs on cloud systems where jobs are allocated non-preemptively, and the same group of authors came up with mechanisms for deadline-sensitive jobs in large computing clusters @cite_12 . also considered the problem of scheduling deadline-sensitive jobs; they circumvented known lower bounds by assuming that jobs could be delayed and still finish by their deadline. developed a framework for truthful online cloud auctions where users with heterogeneous demands can come and leave on the fly. More recently, constructed a truthful mechanism that achieves a constant competitive ratio given that slackness is allowed, while assumed a stochastic model and developed a truthful mechanism that approximates the expected maximum welfare up to a constant factor. designed mechanisms for selling reserved instances where users are allowed to reserve resources of any length and from any time point in the future. Their mechanisms determine the acceptance and payment immediately when the job arrives, and achieve a competitive ratio that is optimal to within a constant factor with regard to welfare.
@cite_12
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We consider a market-based resource allocation model for batch jobs in cloud computing clusters. In our model, we incorporate the importance of the due date of a job rather than the number of servers allocated to it at any given time. Each batch job is characterized by the work volume of total computing units (e.g., CPU hours) along with a bound on maximum degree of parallelism. Users specify, along with these job characteristics, their desired due date and a value for finishing the job by its deadline. Given this specification, the primary goal is to determine the scheduling of cloud computing instances under capacity constraints in order to maximize the social welfare (i.e., sum of values gained by allocated users). Our main result is a new ( C (C-k) ⋅ s (s-1))-approximation algorithm for this objective, where C denotes cloud capacity, k is the maximal bound on parallelized execution (in practical settings, k l C) and s is the slackness on the job completion time i.e., the minimal ratio between a specified deadline and the earliest finish time of a job. Our algorithm is based on utilizing dual fitting arguments over a strengthened linear program to the problem. Based on the new approximation algorithm, we construct truthful allocation and pricing mechanisms, in which reporting the job true value and properties (deadline, work volume and the parallelism bound) is a dominant strategy for all users. To that end, we provide a general framework for transforming allocation algorithms into truthful mechanisms in domains of single-value and multi-properties. We then show that the basic mechanism can be extended under proper Bayesian assumptions to the objective of maximizing revenues, which is important for public clouds. We empirically evaluate the benefits of our approach through simulations on data-center job traces, and show that the revenues obtained under our mechanism are comparable with an ideal fixed-price mechanism, which sets an on-demand price using oracle knowledge of users' valuations. Finally, we discuss how our model can be extended to accommodate uncertainties in job work volumes, which is a practical challenge in cloud settings. In this paper, we study the problem of designing new mechanisms for selling reserved instances (also referred to as virtual machines) in cloud computing. Unlike the practice in today's clouds in which users only have a few predefined options to reserve instances (i.e., either 1-year reservation or 3-year reservation), we allow users to reserve resources for any length and from any time point in the future. Our goal is to maximize the social welfare. We propose two mechanisms, one for the case where all the jobs are tight (their lengths are exactly their reservation time intervals), and the other for the more general case where jobs are delayable and have some flexibility on their reservations. Both of the mechanisms are prompt in the sense that the acceptance and the payment for a job is determined at the very moment of its arrival. We use competitive analysis to evaluate the performance of our mechanisms, and show that both of the mechanisms have a competitive ratio of O(ln(kT)) under some mild assumption, where k (res. T) is the maximum ratio between per-instance-hour valuation (res. length) of any two jobs. We then prove that no algorithm can achieve a competitive ratio better than ln(2kT) under the same assumption. Therefore, our mechanisms are optimal within a constant factor. We introduce a novel pricing and resource allocation approach for batch jobs on cloud systems. In our economic model, users submit jobs with a value function that specifies willingness to pay as a function of job due dates. The cloud provider in response allocates a subset of these jobs, taking into advantage the flexibility of allocating resources to jobs in the cloud environment. Focusing on social-welfare as the system objective (especially relevant for private or in-house clouds), we construct a resource allocation algorithm which provides a small approximation factor that approaches 2 as the number of servers increases. An appealing property of our scheme is that jobs are allocated non-preemptively, i.e., jobs run in one shot without interruption. This property has practical significance, as it avoids significant network and storage resources for checkpointing. Based on this algorithm, we then design an efficient truthful-in-expectation mechanism, which significantly improves the running complexity of black-box reduction mechanisms that can be applied to the problem, thereby facilitating its implementation in real systems. We consider a task of scheduling with a common deadline on a single machine. Every player reports to a scheduler the length of his job and the scheduler needs to finish as many jobs as possible by the deadline. For this simple problem, there is a truthful mechanism that achieves maximum welfare in dominant strategies. The new aspect of our work is that in our setting players are uncertain about their own job lengths, and hence are incapable of providing truthful reports (in the strict sense of the word). For a probabilistic model for uncertainty we show that even with relatively little uncertainty, no mechanism can guarantee a constant fraction of the maximum welfare. To remedy this situation, we introduce a new measure of economic efficiency, based on a notion of a fair share of a player, and design mechanisms that are Ω(1)-fair. In addition to its intrinsic appeal, our notion of fairness implies good approximation of maximum welfare in several cases of interest. In our mechanisms the machine is sometimes left idle even though there are jobs that want to use it. We show that this unfavorable aspect is unavoidable, unless one gives up other favorable aspects (e.g., give up Ω(1)-fairness). We also consider a qualitative approach to uncertainty as an alternative to the probabilistic quantitative model. In the qualitative approach we break away from solution concepts such as dominant strategies (they are no longer well defined), and instead suggest an axiomatic approach, which amounts to listing desirable properties for mechanisms. We provide a mechanism that satisfies these properties.