Modeling of the resource allocation in cloud computing centers

Cloud computing offers on-demand network access to the computing resources through virtualization. This paradigm shifts the computer resources to the cloud, which results in cost savings as the users leasing instead of owning these resources. Clouds will also provide power constrained mobile users accessibility to the computing resources. In this paper, we develop performance models of these systems. We assume that jobs arrive to the system according to a Poisson process and they may have quite general service time distributions. Each job may consist of multiple numbers of tasks with each task requiring a virtual machine (VM) for its execution. The size of a job is determined by the number of its tasks, which may be a constant or a variable. The jobs with variable sizes may generate new tasks during their service times. In the case of constant job size, we allow different classes of jobs, with each class being determined through their arrival and service rates and number of tasks in a job. In the variable case a job generates randomly new tasks during its service time. The latter requires dynamic assignment of VMs to a job, which will be needed in providing service to mobile users. We model the systems with both constant and variable size jobs using birth-death processes. In the case of constant job size, we determined joint probability distribution of the number of jobs from each class in the system, job blocking probabilities and distribution of the utilization of resources for systems with both homogeneous and heterogeneous types of VMs. We have also analyzed tradeoffs for turning idle servers off for power saving. In the case of variable job sizes, we have determined distribution of the number of jobs in the system and average service time of a job for systems with both infinite and finite amount of resources. We have presented numerical results and any approximations are verified by simulation. The results of the paper may be used in the dimensioning of cloud computing centers.