Cloud Computing is a type of Internet-based computing, much used in recent years, that relies on sharing computer processing resources and data to computers and other devices on demand, from any location and at any time rather than having local servers or personal devices to handle applications. This shared IT infrastructure contains large pools of systems that are linked together. Often, virtualization techniques are used to maximize the power of cloud computing. In this paper we describe the global network of a cloud computing environment with five different layers, represented by hardware/datacenter, infrastructure, platform, application and end-users. Then, we present the mathematical model of the network and study the behavior of the typical IaaS provider in order to find the optimization problem. A computational procedure for the calculus of the optimal solutions is proposed, is applied to two numerical examples and is compared with a linearization.
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Anselmi J, Ardagna D, Passacantando M (2014) Generalized Nash equilibria for SaaS/PaaS Clouds. Eur J Oper Res 236:326–339
Calheiros RN, Ranjan R, Beloglazov A, De Rose CAF, Buyya R (2011) CloudSim: a toolkit for modeling and simulation of cloud computing environments and evaluation of resource provisioning algorithms. Software: Practice and Experience 411:23–50
Caruso V, Daniele P (2018) A network model for minimizing the total organ transplant costs. Eur J Oper Res 266:652–662
Chen D, Zhao H (2012) Data security and privacy protection issues in cloud computing. In: 2012 international conference on computer science and electronics engineering (ICCSEE). Vol 1. IEEE
Colajanni G, Daniele P (2017) A cloud computing network and an optimization algorithm for IaaS providers. Proceedings of the 2nd international conference on internet of things and cloud computing. ACM
Colajanni G, Daniele P (2018) A convex optimization model for business management. Journal of Convex Analysis 252:487–514
Colajanni G, Daniele P (2018) A financial model for a multi-period portfolio optimization problem with a variational formulation, variational analysis and set optimization: Developments and applications in decision making, A Khan, E Kbis, C Tammer, in press
Daniele P (2006) Dynamic networks and Evolutionary Variational Inequalities. Edward Elgar Publishing, Cheltenham
Daniele P (2010) Evolutionary variational inequalities and applications to complex dynamic multi-level models. Transp Res E 46:855–880
Gabriel SA, Shim Y, Llorca J, Milner S (2008) A multiobjective optimization model for dynamic reconfiguration of ring topologies with stochastic load. Networks and Spatial Economics 8:419– 441
Gao Y, Guan H, Qi Z, Hou Y, Liu L (2013) A multi objective ant colony system algorithm for virtual machine placement in cloud computing. J Comput Syst Sci 79:1230–1242
He X, Peeta S (2014) Dynamic Resource Allocation Problem for Transportation Network Evacuation. Networks and Spatial Economics 14:505–530
Litoiu M, Woodside M, Wong J, Ng J, Iszlai G (2010) A business driven cloud optimization architecture, ACM Symposium on Applied Computing (SAC ’10), pp 380–385
Manvi SS, Shyam GK (2014) Resource management for Infrastructure as a Service (IaaS) in cloud computing: A survey. J Netw Comput Appl 41:424–440
Mell P, Grance T (2011) The NIST definition of cloud computing
Moya-Gomez B, Salas-Olmedo MH, Garcia-Palomares JC, Gutierrez J (2017) Dynamic accessibility using big data: The role of the changing conditions of network congestion and destination attractiveness. Networks and Spatial Economics 18:273–290
Nagurney A (2015) A multiproduct network economic model of cybercrime in financial services. Ser Sci 7(1):70–81
Nagurney A, Daniele P, Shukla S (2017) A supply chain network game theory model of cybersecurity investments with nonlinear budget constraints. Ann Oper Res 248(1):405–427
Nagurney A, Dong J (2002) Supernetworks: Decision-making for the information age. Edward Elgar Publishers, Chelthenham
Passacantando M, Ardagna D, Savi A (2016) Service Provisioning Problem in Cloud and Multi-Cloud System. INFORMS J Comput 28(2):265–277
Pearson Siani, Shen Yun, Mowbray Miranda (2009) A privacy manager for cloud computing. In: IEEE international conference on cloud computing. Springer, Berlin
Pietri, Sakellariou R (2016) Mapping virtual machines onto physical machines in cloud computing: A survey. ACM Comput Surv 49:3
Qian H, Medhi D (2011) Server operational cost optimization for cloud computing service providers over a time horizon. In: Proceedings of the 11th USENIX conference on hot topics in management of internet, cloud, and enterprise networks and services (Hot-ICE’11) USENIX Association, Berkeley, CA, USA, pp 4–4
Shahabi M, Akbarinasaji S, Unnikrishnan A, James R (2013) Integrated inventory control and facility location decisions in a multi-echelon supply chain network with hubs. Networks and Spatial Economics 13:497–514
Usmani Z, Singh S (2016) A survey of virtual machine placement techniques in a cloud data center. Prog Comput Sci 78:491–498
Zhang Q, Cheng L, Boutaba R (2010) Cloud computing: state-of-the-art and research challenges. J Internet Serv Appl 1:7–18
Mann ZA (2015) Allocation of virtual machines in cloud data centers - a survey of problem models and optimization algorithms. ACM Comput Surv 48(1):11
The research of the authors was partially supported by the research project “Modelli Matematici nell’Insegnamento-Apprendimento della Matematica” DMI, University of Catania. This support is gratefully acknowledged.
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Colajanni, G., Daniele, P. A Mathematical Network Model and a Solution Algorithm for IaaS Cloud Computing. Netw Spat Econ 22, 267–287 (2022). https://doi.org/10.1007/s11067-019-09460-x
- Cloud computing
- Optimization problems
- Computational procedures