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.
In @cite_8 @cite_19 @cite_5 , mechanisms design for scheduling problem with commitments is studied. Those mechanisms proposed either complete a reservation or reject it when there is enough time for this reservation to be completed before deadline. In @cite_19 , the authors study offline settings and design a near-optimal mechanism with commitments. In @cite_8 , a heuristic truthful mechanism for online scheduling is proposed, but no formal bound of competitive ratio is given. In @cite_5 , the authors follow @cite_8 and design truthful online mechanisms with a constant competitive when reservations are enough.
@cite_19 @cite_5 @cite_8
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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. The proliferation of high-volume time-critical Web services such as online trading calls for a scalable server design that allows meeting individual response-time guarantees of real time transactions. A main challenge is to honor these guarantees despite unpredictability in incoming server load. The extremely high volume of real-time service requests mandates constant-time scheduling and schedulability analysis algorithms (as opposed to polynomial or logarithmic ones in the number of current requests). The paper makes two major contributions towards developing an architecture and theoretical foundations for scalable real-time servers operating in dynamic environments. First, we derive a tight utilization bound for schedulability of aperiodic tasks (requests) that allows implementing a constant time schedulability test on the server. We demonstrate that Liu and Layland's schedulable utilization bound of ln 2 does not apply to aperiodic tasks, and prove that an optimal arrival-time independent scheduling policy will meet all aperiodic task deadlines if utilization is maintained below 1 1+ spl radic (1 2). Second, we show that aperiodic deadline-monotonic scheduling is the optimal arrival-time-independent scheduling policy for aperiodic tasks. This result is used to optimally prioritize server requests. Evaluation of a utilization control loop that maintains server utilization below the bound shows that the approach is effective in meeting all individual deadlines in a high performance real-time server. The authors show how to design truthful (dominant strategy) mechanisms for several combinatorial problems where each agent's secret data is naturally expressed by a single positive real number. The goal of the mechanisms we consider is to allocate loads placed on the agents, and an agent's secret data is the cost she incurs per unit load. We give an exact characterization for the algorithms that can be used to design truthful mechanisms for such load balancing problems using appropriate side payments. We use our characterization to design polynomial time truthful mechanisms for several problems in combinatorial optimization to which the celebrated VCG mechanism does not apply. For scheduling related parallel machines (Q spl par C sub max ), we give a 3-approximation mechanism based on randomized rounding of the optimal fractional solution. This problem is NP-complete, and the standard approximation algorithms (greedy load-balancing or the PTAS) cannot be used in truthful mechanisms. We show our mechanism to be frugal, in that the total payment needed is only a logarithmic factor more than the actual costs incurred by the machines, unless one machine dominates the total processing power. We also give truthful mechanisms for maximum flow, Q spl par spl Sigma C sub j (scheduling related machines to minimize the sum of completion times), optimizing an affine function over a fixed set, and special cases of uncapacitated facility location. In addition, for Q spl par spl Sigma w sub j C sub j (minimizing the weighted sum of completion times), we prove a lower bound of 2 spl radic 3 for the best approximation ratio achievable by truthful mechanism. For the problem of online real-time scheduling of jobs on a single processor, previous work presents matching upper and lower bounds on the competitive ratio that can be achieved by a deterministic algorithm. However, these results only apply to the non-strategic setting in which the jobs are released directly to the algorithm. Motivated by emerging areas such as grid computing, we instead consider this problem in an economic setting, in which each job is released to a separate, self-interested agent. The agent can then delay releasing the job to the algorithm, inflate its length, and declare an arbitrary value and deadline for the job, while the center determines not only the schedule, but the payment of each agent. For the resulting mechanism design problem (in which we also slightly strengthen an assumption from the non-strategic setting), we present a mechanism that addresses each incentive issue, while only increasing the competitive ratio by one. We then show a matching lower bound for deterministic mechanisms that never pay the agents.