Overcommitment in Cloud Services -- Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance

Performance-oriented Cloud Provisioning: Taxonomy and Survey

Cloud computing is being viewed as the technology of today and the future. Through this paradigm, the customers gain access to shared computing resources located in remote data centers that are hosted by cloud providers (CP). This technology allows for provisioning of various resources such as virtual machines (VM), physical machines, processors, memory, network, storage and software as per the needs of customers. Application providers (AP), who are customers of the CP, deploy applications on the cloud infrastructure and then these applications are used by the end-users. To meet the fluctuating application workload demands, dynamic provisioning is essential and this article provides a detailed literature survey of dynamic provisioning within cloud systems with focus on application performance. The well-known types of provisioning and the associated problems are clearly and pictorially explained and the provisioning terminology is clarified. A very detailed and general cloud provisioning classification is presented, which views provisioning from different perspectives, aiding in understanding the process inside-out. Cloud dynamic provisioning is explained by considering resources, stakeholders, techniques, technologies, algorithms, problems, goals and more.Comment: 14 pages, 3 figures, 3 table

The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.Comment: 33 pages. A preliminary (4-page) version of this paper was presented at CTW 2016 (Cologne-Twente Workshop on Graphs and Combinatorial Optimization), with proceedings on Electronic Notes in Discrete Mathematic

Mathematical optimization for packing problems

During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques involved, concentrating on geometric packing problems such as the sphere-packing problem or the problem of packing regular tetrahedra in R^3.Comment: 17 pages, written for the SIAG/OPT Views-and-News, (v2) some updates and correction