Nowadays, as the need for capacity continues to grow, entirely novel services are emerging. A solid cloudnetwork integrated infrastructure is necessary to supply these services in a real-time responsive, and scalable way. Due to their diverse characteristics and limited capacity, communication and computing resources must be collaboratively managed to unleash their full potential. Although several innovative methods have been proposed to orchestrate the resources, most ignored network resources or relaxed the network as a simple graph, focusing only on cloud resources. This paper fills the gap by studying the joint problem of communication and computing resource allocation, dubbed CCRA, including function placement and assignment, traffic prioritization, and path selection considering capacity constraints and quality requirements, to minimize total cost. We formulate the problem as a non-linear programming model and propose two approaches, dubbed B&B-CCRA and WF-CCRA, based on the Branch & Bound and Water-Filling algorithms to solve it when the system is fully known. Then, for partially known systems, a Double Deep Q-Learning (DDQL) architecture is designed. Numerical simulations show that B&B-CCRA optimally solves the problem, whereas WF-CCRA delivers near-optimal solutions in a substantially shorter time. Furthermore, it is demonstrated that DDQL-CCRA obtains near-optimal solutions in the absence of request-specific information.