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Cloud computing coupled with Internet of Things technology provides a wide range of cloud services such as memory, storage, computational processing, network bandwidth, and database application to the end users on demand over the Internet. More specifically, cloud computing provides efficient services such as " pay as per usage ". However, Utility providers in Smart Grid are facing challenges in the design and implementation of such architecture in order to minimize the cost of underlying hardware, software, and network services. In Smart Grid, smart meters generate a large volume of different traffics, due to which efficient utilization of available resources such as buffer, storage, limited processing, and bandwidth is required in a cost-effective manner in the underlying network infrastructure. In such context, this article introduces a QoS-aware Hybrid Queue Scheduling (HQS) model that can be seen over the IoT-based network integrated with cloud environment for different advanced metering infrastructure (AMI) application traffic, which have different QoS levels in the Smart Grid network. The proposed optimization model supports, classifies, and prioritizes the AMI application traffic. The main objective is to reduce the cost of buffer, processing power, and network bandwidth utilized by AMI applications in the cloud environment. For this, we developed a simulation model in the CloudSim simulator that uses a simple mathematical model in order to achieve the objective function. During the simulations, the effects of various numbers of cloudlets on the cost of virtual machine resources such as RAM, CPU processing, and available bandwidth have been investigated in cloud computing. The obtained simulation results exhibited that our proposed model successfully competes with the previous schemes in terms of minimizing the processing, memory, and bandwidth cost by a significant margin. Moreover, the simulation results confirmed that the proposed optimization model behaves as expected and is realistic for AMI application traffic in the Smart Grid network using cloud computing.