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The confluence of advanced networking (5G/6G) and distributed cloud technologies (edge/fog computing) are rapidly transforming next-generation networks into highly distributed computation platforms, especially suited to host emerging resource-intensive and latency-sensitive services (e.g., smart transportation/city/factory, real-time computer vision, augmented reality). In this paper, we leverage the recently proposed Cloud Network Flow (CNF) modeling and optimization framework to design a novel two-timescale orchestration system for the joint control of communication and computation resources in cloud-integrated networks. The Long-Term Controller solves a properly constructed CNF optimization problem at a longer timescale that determines i) the end-to-end CNF routes (defining data paths and processing locations) for each service chain and ii) the associated allocation of communication and computation resources. The Short-Term Controller uses a local control policy to adjust the allocation of communication and computation resources based on queue state observations at a shorter timescale. Driven by the lack of proper simulation tools, we also develop new ns-3 features that allow modeling and simulation of cloud-integrated networks equipped with both communication and computation resources hosting arbitrary service chains. Finally, we integrate the proposed orchestration system into ns-3 to evaluate and analyze the dynamic orchestration of a set of representative service chains over a hierarchical cloud-integrated network.