## 2 Related Work
A capacity planning and admission control model is proposed in [12] to maximize revenue and optimize capacity allocation. The authors proposed a stochastic dynamic programming algorithm with two heuristic objectives that can tradeoff between computation complexity and the optimal solution. Workload modeling, evaluation and forecasting are investigated in [7, 16, 18, 19, 20]. Both [7, 16] used a stochastic queuing scheme to model cloud data center workload as a time variable and dynamic behavior. A Platform as a Service (PaaS) elastic model (AutoElastic) is proposed in [18] for HPC clusters in a cloud environment. The authors of this work contribute in two ways: (a) making an aging technique for cloud elasticity actions instead of using static threshold values on VM provisioning and de-provisioning, and (b) applying an asynchronous approach in VM management (create/delete/modify VM instances) that can achieve parallel execution in cloud management actions. This allows parallelization in VM allocation for parallel applications. Our concern in [18] is the asynchronous model might cause conflicts in management actions and may violate elastic conditions. This is because the asynchronous model type does not consider all application performance parameters concerning resource provisioned values. Prediction, consolidation and migration modules are proposed in [19]. In this work, the authors used the ARIMA forecasting method to predict the workload and estimate the allocated cloud storage resources. A combination is proposed between the prediction of resource demands (Resource Demand Estimator) and server consolidation to minimize the data migration time. The ARIMA forecasting method is used to predict the workload in [20] for SaaS cloud providers. Using the proposed predictive resource allocation method, the authors analyzed the system accuracy by an enhancement factor in QoS conditions and resource utilization. An auction-based provisioning model for cloud laaS instead of a \"pay as you go\" scheme (elastic scheme) is proposed in [21]. The authors of this work proposed a geographically distributed cloud data center to scale IaaS resources. Their work is based on a classic optimization method with a cost function subjected to maximizing the revenue of the cloud owner with respect to the cost of provisioned resources (resource allocation). [PERSON] et al. in [18, 22] worked on an auction-based resource allocation model for efficient resource allocation and the best cost and pricing scheme. In [22], an auction-based resource provisioning via geographical data centers is proposed. The authors of this work proposed a randomized auction method for dynamic VM provision, using smoothed analysis in their algorithm to reduce its NP-hard problem complexity of resource allocation. In [18], the researchers proposed efficient VM provisioning and pricing using an online auction for VM scaling. With this auction, model users can continually bid for needed VM using both scaling methods (vertical scale-up and horizontal scale-out). The limitation of [18, 22] is that the auction model might reduce the cost on the cloud consumer side but does not utilize resource allocation efficiently, especially in a geographical data center. It will waste a small amount of available resources for each data center member, which can be consolidated and rebalanced to accommodate a larger size of jobs. Cloud elasticity has been modeled and analyzed in a quantitative approach in [23] for predicting elasticity in a cloud environment. The author proposed a probabilistic approach of computing provisioned resources matching the demand workload by modeling elasticity as a queuing system using a continuous Markov chain (CTMC). The parameters considered in the queuing model are task arrival rate, service rate, VM spanning time (VM start-up and service running time) and VM shutdown. The quantitative predicted elastic attributesare task response time, system throughput (tasks finished), QoS (performance), number of provisioned VMs, cost and scaling.