We start with the basic concepts of cloud computing and then in section 2 describes the mathematical approaches that helps in formulation of cloud models. These cloud models aims to identify cloud’s configuration settings to optimize QOS, efficiency in terms of performance and energy under available conditions.
In section 3 simulators, their architecture and features are discussed. Basically there are 2 types of simulators, i.e simulators based on software and simulators based on both software and hardware. These simulators are used in validation of those models
Section 2 (modeling) and section 3 (simulation) technology is a suitable tool for evaluating cloud performance and concerned security issues but for evaluating QOS , cloud based web applications are tested by stimulated real world web traffic. Cloud testing termed as testing as a service, which is reviewed in section 4. Some common benchmarks are also reviewed in cloud computing testing as a service aspect.
2. Mathematical modeling approaches
Mathematical modeling and analysis helps in interdependencies of the cloud computing research approach. Islam et al.  developed an elastic (in terms of cost and time) model for cloud instances. There are two costs involved which are cost of overprovision (provisioned but unutilized) and underprovision (performance degradation). Calculation of former cost through difference between chargeable demand and supply, while latter cost through percentage of rejected requests, and then geometric mean of these two costs gives elasticity metric.
 have developed a metric to evaluate elasticity (database) of cloud for both consumer (to compare data services of cloud to choose the best accordingly) and provider (to meet the Service-Level Agreement (SLA) with the minimum amount of resources and cost) perspective. They used two penalty (overprovision and underprovision) approaches to measure imperfections in the elasticity for database system.
 have discussed the optimization problem by analyzing the mathematical relationship between the SLA which specifies service and number of servers with their running frequencies to optimize power usage. Basically this problem is NP-Hard.
 optimization problem of virtual machines allotment (developed a utility function for power saving and SLA satisfaction) and placement in actual cloud (multiple knapsack with capacity constrains ).they also discussed the management of allotment and placement using mathematical model.
There are many optimizations problems such as minimizing the energy and bandwidth cost or minimizing total carbon footprint in order to govern QoS constraints. With their solution different questions can be answered like suitable location to built data center, number of servers required, routing mechanism of service requests from different servers to the data center and many more.
 then they discussed...