Selling reserved instances (or virtual machines) is a basic service in cloud computing. In this paper, we consider a more flexible pricing model for instance reservation, in which a customer can propose the time length and number of resources of her request, while in today's industry, customers can only choose from several predefined reservation packages. Under this model, we design randomized mechanisms for customers coming online to optimize social welfare and providers' revenue. We first consider a simple case, where the requests from the customers do not vary too much in terms of both length and value density. We design a randomized mechanism that achieves a competitive ratio @math for both and , which is a improvement as there is usually no revenue guarantee in previous works such as azar2015ec,wang2015selling . This ratio can be improved up to @math when we impose a realistic constraint on the maximum number of resources used by each request. On the hardness side, we show an upper bound @math on competitive ratio for any randomized mechanism. We then extend our mechanism to the general case and achieve a competitive ratio @math for both social welfare and revenue, where @math is the ratio of the maximum request length to the minimum request length and @math is the ratio of the maximum request value density to the minimum request value density. This result outperforms the previous upper bound @math for deterministic mechanisms wang2015selling . We also prove an upper bound @math for any randomized mechanism. All the mechanisms we provide are in a greedy style. They are truthful and easy to be integrated into practical cloud systems.
There are many works that concern online resource allocation for cloud computing @cite_18 @cite_24 @cite_1 @cite_13 @cite_16 @cite_21 . Among these works, the pay-as-you-go model is considered in @cite_13 , and authors in @cite_24 propose a framework for cloud resource allocation when agents' value functions are continuous and concave. In @cite_16 , a more general scheduling problem is studied. The authors also take both social welfare and revenue into consideration. However, the their competitive ratios are related to the total amount of resources. In @cite_21 , the authors propose online strategies to reserve instances without any a priori knowledge of future demands. Those strategies are optimal when considering cost management.
@cite_18 @cite_21 @cite_1 @cite_24 @cite_16 @cite_13
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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. 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. There is an increasing need for cloud service performance that can be tailored to customer requirements. In the context of jobs submitted to cloud computing clusters, a crucial requirement is the specification of job completion-times. A natural way to model this specification, is through client job utility functions that are dependent on job completion-times. We present a method to allocate and schedule heterogeneous resources to jointly optimize the utilities of jobs in a cloud. Specifically: (i) we formulate a completion-time optimal resource allocation (CORA) problem to apportion cluster resources across the jobs that enforces max-min fairness among job utilities, and (ii) starting with an integer programming problem, we perform a series of steps to transform it into an equivalent linear programming problem, and (iii) we implement the proposed framework as a utility-aware resource scheduler in the widely used Hadoop data processing framework, and finally (iv) through extensive experiments with real-world datasets, we show that our prototype achieves significant performance improvement over existing resource-allocation policies. 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.