Cloud applications heavily use resources and generate more traffic specifically during specific events. In order to achieve quality in service provisioning, the elasticity of resources is a major requirement. With the use of a hybrid cloud model, organizations combine the private and public cloud services to deploy applications for the elasticity of resources. For elasticity, a traditional adaptive policy implements threshold-based auto-scaling approaches that are adaptive and simple to follow. However, during a high dynamic and unpredictable workload, such a static threshold policy may not be effective. An efficient auto-scaling technique that predicts the system load is highly necessary. Balancing a dynamism of load through the best auto-scale policy is still a challenging issue. In this paper, we suggest an algorithm using Deep learning and queuing theory concepts that proactively indicate an appropriate number of future computing resources for short term resource demand. Experiment results show that the proposed model predicts SLA violation with higher accuracy 5% than the baseline model. The suggested model enhances the elasticity of resources with performance metrics.