g (MIP) model that explicitly captures the effect of network traffic on latency while maintaining a linear model; we minimize the maximum utilization over resources in the network. Minimizing the 3.6 VNF Placement worst-case utilization avoids the situation in which a small number of congested resources induce outsized delays on network traffic. While MIP can compute optimal solution, it cannot scale to a large size of network. We overcome this challenge by having a two-step process. As illustrated in Figure 3.10, we first propose a fast, scalable round-robin heuristic for VNF placement, which generates an initial VNF placement solution. This initial result is then fed to the MIP to help speed up the search process. Secondly, our MIP algorithm balances the competing objectives of minimizing congestion-induced latency and minimizing the number of servers used. It minimizes a weighted combination of two metrics: (1) the number of servers used to host VNF instances and (2) the maximum utilization over network resources, which we use as an approximation for latency. The optimization method generates multiple VNF placement solutions for different relative weightings of the two objectives, thereby gener- ating solutions along the efficient frontier of number of servers and maximum resource utilization. We present the model and the optimization formulation as follows: Model parameters: - N: The set of all nodes in the network (servers and switches) - L C N: The set of servers, which are leaves in the tree network - V: The set of VNF types. Instances of these VNF types must to be assigned to servers in the physical network in order to accom- modate service chains C: The set of service chains to be mapped to the network B E [0, 1]: A parameter representing the relative weight between two metrics, number of servers used and maximum utilization, in the objective function. Expected utilization latency # Nodes # Nodes Series of solutions along Series of solutions along efficient frontier of max efficient frontier of Heuristic