Efficient Modeling and Demand Allocation for Differentiated Cloud Virtual-Network as-a Service Offerings Cloud clients (CCs) of current distributed cloud applications are still not assured of their service quality, in particular, in terms of the experienced latency. Unfortunately, this is mainly attributed to the unpredictability of the communication links among their hosting distributed data centers. To address this problem, this article introduces a novel virtual-network-as-a-service (VNaaS) model to host these applications. In contrast to existing randomly or statically provisioned inter-data centers bandwidth sharing models, the proposed model allows CCs to accurately express their varying network resources needs, demand constraints and tolerance to the cloud latency. In turn, the model maps these requirements to create inter-data centers virtual links hosting each multiple virtual pipes with differentiated service qualities to carry the CC’s various traffic flows. To aid the CCs in optimally determining their VNaaS demands, given the budget constraints of their hosted applications, we also develop a novel demand selection scheme based on a two stagebudget allocation mechanism. In the first budgeting stage, the CC calculates an optimal effective service rate for each of its virtual link along with a corresponding link budget and price index. In the second stage, the virtual link budget isdistributed to purchase bandwidth for the link’s virtual pipes, each with a given service quality and pricing. We then extend the proposed model to allow the CC to enforce any required virtual links’ capacity constraints on the effective service rates resulting from the traffic matrix on the VNaaS. Finally, we develop corresponding differentiated VNaaS pricing and service monitoring mechanisms that can be employed by the cloud service provider (CSP) to regulate the offerings and demands of thedistributed cloud services. Performance evaluation results demonstrate the significant improvement in the service quality, the higher utilization of the cloud resour- es and the increase in the CSP’s net profit.