Allocating capacity to private cloud computing services is challenging because demand is time-varying, there are often no buffers, and customers can re-submit jobs a finite number of times. We model this setting using a multi-station queueing network where servers represent CPU cores and jobs not immediately processed retry several times. Assuming retrial rates are stationary and that there is a maximum number of retrial attempts, we determine an optimal service capacity and retrial interval under an admission control policy employed by our partner institution — the server informs customers when they should next attempt service without enforcement. We introduce a recursive representation of the offered load which approximates the fluid dynamics of the system. We then use this representation to develop a solution technique that minimizes the total variation in the constructed offered load. We prove this approach is linked to maximizing system throughput and that in certain settings, the optimal stationary and time-varying retrial intervals are equivalent. Utilizing a data set of cloud computing requests spanning a 24-hour period, our analysis indicates that the optimal policy prescribes a 10% reduction in capacity. We also investigate the fidelity of the fluid model and the sensitivity of our recommendations to the behavior of retrial jobs. We find that retrial-time announcements allow a provider to satisfy service level agreements while encouraging retrial jobs to be processed during off-peak periods. Further, the policy is suitably robust to a customer’s willingness to comply with the suggested retrial times.

中文翻译：

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为具有周期性、时间变化需求的云服务提供商进行最佳容量规划


为私有云计算服务分配容量具有挑战性，因为需求是随时间变化的，通常没有缓冲区，并且客户可以有限次数地重新提交作业。我们使用多站排队网络对此设置进行建模，其中服务器代表 CPU 内核，而未立即处理的作业会重试多次。假设重试率是固定的，并且有最大重试次数，我们会根据合作机构采用的准入控制政策确定最佳服务容量和重试间隔 — 服务器会通知客户何时应该下次尝试服务而不执行。我们引入了所提供载荷的递归表示，它近似于系统的流体动力学。然后，我们使用此表示来开发一种求解技术，以最小化构造的提供载荷的总变化。我们证明这种方法与最大化系统通量有关，并且在某些情况下，最佳稳态和时变重试间隔是等效的。利用跨越 24 小时的云计算请求数据集，我们的分析表明，最佳策略规定将容量减少 10%。我们还调查了流体模型的保真度以及我们的建议对重试作业行为的敏感性。我们发现，重试时间通知允许提供商满足服务级别协议，同时鼓励在非高峰时段处理重试作业。此外，该政策对客户遵守建议的重审时间的意愿具有适当的稳健性。