## Reference Scenario  
NFV is a new paradigm that employs cloud infrastructures to support telecommunication services. The service functions, also referred to as VNF are executed in VM hosted in geographically-distributed data-centers referred to as NFV Infrastructure-Point-of Presence (NFVI-PoP) and managed by different providers. To support high bandwidth service requests, we consider an Elastic Optical Networks (EON) to provide optical circuits interconnecting the VM located in different NFVI-PoPs.  
Due to the dynamic nature of the applications, the traffic flowing through VM can change over time. To reduce the costs in dynamic traffic scenario, we propose a solution to maintain as low as possible the processing and bandwidth costs, changing over time the NFVI-PoPs in which the VMs are executed. Given that the migration of the VMs across the network may lead to many optical circuit reconfigurations and consequently to bit loss and revenue loss of the Network Operator (NO), we also take into account the number of reconfigurations to be applied to the elastic optical network. A possible reconfiguration example from an high to a low traffic scenario is reported in Figure 1a, where two different NFVI-PoPs host a Firewall (FW) and an Intrusion Detection System (IDS) VMs exploited to satisfy the SFC request reported in Figure 1. The black circles represent the cores required from the VM.  
In particular, notice how in the low traffic interval, the FW VM can be moved from NFVI-PoP #1 to NFVI-PoP #2 because the cloud resources of NFVI-PoP #2 are less expensive than the ones of NFVI-PoP #1. This migration leads to tear down the two lightpaths between the access node E1 and the NFVI-PoP #1 and between NFVI-PoP #1 and NFVI-PoP #2, reported with dashed lines in Figure 1a. As shown in Figure 1b a new lightpath is then set up between access node E1 and NFVI-PoP #2, while the lightpath represented by the continuous line remains the same.  
The proposed solution is based on:  
* the application of a VM consolidation technique towards the less costly NFVI-PoPs;
* the agility of an elastic optical network in reconfiguring optical lightpaths between active NFVI-PoPs. The dynamic allocation problem of processing and bandwidth resource consists in determining:
* in each stationary traffic interval both the NFVI-PoPs to be held active and the processing core amount to be allocated to each VM;
* the lightpaths to be reconfigured, the more appropriate modulation index according to the optical path length and the maximum number of switch reconfigurations.  
The objective is to minimize the total cost given by the sum of the processing and bandwidth cost with the constraint of not exceeding the maximum number of switch reconfigurations. In some cases, this constraint may limit the number of VMs to be migrated in order to reduce the cost to be paid by the Network Operator because of QoS degradation occurring during the VM migrations.  
We assume a cycle-stationary traffic con \(T\) Stationary Intervals (SI). We have formulated the ILP problem. It was inherited from the one proposed in [16] with the addition of a constraint on the maximum number \(R\) of switch reconfigurations. The output of the ILP provides for each SI: (i) in which NFVI-PoPs the VMs are allocated; (ii) the cloud resources, in terms of number of cores, allocated to each VM; (iii) the optical paths connecting each tuple of VMs, as well as the modulation system (BPSK, QPSK, 16 QAM) used. The objective function to be minimized is characterized by the sum of cloud and bandwidth resource costs. Due to the high complexity of the optimization problem, we have defined a heuristic that allows us to achieve a low computational complexity reconfiguration policy.  
Figure 1: Interconnection of NFV Infrastructure-Points-of Presence (NFVI-PoPs) by means of an Elastic Optical Network (**a**); Migration of a Virtual Machine (VM) from NFVI-PoP-1 to NFVI-PoP-2 (**b**).