### Problem Definition  
Virtualized Network systems are usually deployed as a composite chain of Virtual Network Functions (VNF), often called a _service function chain_ (SFC). Every incoming request to a virtualized network system will be mapped to a corresponding deployed SFC. The problem of deploying a SFC inside a VNF infrastructure is called _VNF Placement_ or _SFC Deployment_[14]. Many service requests can share the same SFC deployment scheme, or the SFC deployments can vary. Given two service requests that share the same requested chain of VNFs, the SFC deployment will vary when at least one pair of same-type VNFs are deployed on different physical locations for each request. This work focuses on the particular case of Live-Video delivery, also referred to as _live-streaming_. In such a context, each service request is associated with a Live-Video streaming session. CDNs have proved essential to meet scalability, reliability, and security in Live-Video delivery scenarios. One important Quality of Experience (QoE) measure in live-video streaming is the _session startup delay_, which is the time the end-user waits since the content is requested and the video is displayed. One important factor that influences the startup delay is the round-trip-time (RTT) of the session request, which is the time between the content request is sent, and the response is received. In live-Streaming, the data requested by each session is determined only by the particular content provider or _channel_ requested. Notably, cache HIT and cache MISS events may result in very different request RTTs. Consequently, a realistic Live-Streaming vCDN model should keep track of the caching memory status of every cache-VNF module for fine-grain RTT simulation. Different SFC deployments may result in different round-trip times (RTT) for live-video sessions. The QoS/QoE goodness of a particular SFC deployment policy is generally measured by the mean acceptance ratio (AR) of client requests, where the acceptance ratio is defined as the percentage of requests whose RTT is below a maximum threshold [14; 15; 16]. Notice that RTT is different from the total delay, which is the total propagation time of the data stream from the origin server and the end-user. Another important factor that influences RTT computation is the request processing time. Such a processing time will notably depend on the current VNF utilization. To model VNF utilization in a video-delivery context, major video streaming companies [17] recommend to consider not only the _content-delivery_ tasks, but also the resource consumption associated with _content-ingestion_ processes. In other words, any VNF must ingest a particular data stream before being able to deliver it through its own client connections, and such ingestion will incur non-negligible resource usage. Further, a realistic vCDN delay model must incorporate VNF instantiation times, as they may notably augment the starting delay of any video-streaming session. Finally, both instantiation time and resource consumption may differ significantly depending on the specific characteristics of each VNF [3]. In this paper, we model a vCDN following the NFV Management and orchestration (NFV-MANO) framework published by the ETSI standard group specification [9; 18; 19; 20]. We propose elastic container-based virtualization of a CDN inspired by [5; 19]. One of the management software components of a vCDN in the ETSI standard is the Virtual Network Orchestrator (VNO), which is generally responsible for the dynamic scaling of the containers' resource provision [19]. The resource scaling is triggered when needed, for example, when traffic bursts occur. Such a resource scaling may influence the resource provision costs, also called _hosting costs_, especially if we consider a cloud-hosted vCDN context [20]. Also, data-transportation (DT) routes in the substrate network of a vCDN may be affected by different SFC deployment decisions.