## 5 Performance Evaluation
### Simulation Environment  
The proposed schemes are evaluated based on real world telecom topologies and synthetic topologies, where real topologies have been obtained from Internet Topology Zoo [52] and they are: (1) the BT Europe (24 nodes and 37 edges) and (2) Interoute (110 nodes and 148 edges). An additional edges were generated for each of them to study the impact of increasing physical links, which results in: (1) BT\({}^{+}\) (24 nodes and 65 edges) and (2) Int\({}^{+}\) (110 nodes and 180 edges). Due to the high average execution-time of the ILP-A in long simulation run, twelve synthetic topologies are generated in order to compare the execution times of all schemes in short simulation run. Specifically, six of the synthetic topologies are generated with maximum 3 edges (denoted by \(E_{3}\)) attached to each node, while the remaining six are generated with maximum 4 edges (denoted by \(E_{4}\)) attached to each node. This configuration is selected to mimic real world networks, where high volume servers are usually equipped with 4 network adapters in average. More details about the used topologies in this work are shown in Table 3. \begin{table}
\begin{tabular}{l l} \hline \hline
**Notation** & **Description** \\ \hline _ILP-A_ & ILP-based scheme of the benchmark. \\ _DSBM_ & Heuristic scheme of the benchmark. \\ _ILP-P_ & Proposed optimal implementation of path mapping, which is ILP-based scheme. \\ _DcPSM_ & Proposed heuristic implementation of path mapping approach. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Compared schemes. Figure 3: Experiment frame work design. While many works in the literature have studied the placement problem considering the number of nodes in service requests, this work focuses only on the impact of multi-paths service requests. Thus, five types of service requests are generated to be mapped in these experiments: (1) Simple, (2) Multiple, (3) \(P_{5}\), (4) \(P_{10}\), and (5) \(P_{20}\). Simple indicates to service requests with simple/forking path in each decomposition in the request, while Multiple have multi-paths with multi-starting nodes (Ingress) and multi-ending nodes (Egress), both with a random number of end-to-end paths. \(P_{5}\), \(P_{10}\), and \(P_{20}\) are multiple paths service graphs with specific number of paths equal to 5, 10, and 20 paths, respectively. These experimental scenarios represent pairs of request type and physical network. Twenty-two experiments are conducted to evaluate the studied schemes, where six experiments with short simulation runs are used to evaluate all schemes in terms of execution time. See Table 4 for more details about the experimental scenarios. The resources of physical nodes, such as CPU, memory, and storage, and the bandwidth of physical links, are uniformly distributed between 100 and 150 capacity units. The embedding costs of physical nodes and links are set to 1 cost unit for each. Links between any pair of physical nodes are generated randomly with a chance of (0.5) in the synthetic topologies and additional links are generated for BT\({}^{+}\) and Int\({}^{+}\). The Propagation delay of a physical link is proportional to the real geographical distance between nodes based on the real telecom topologies, which varies from 1 to 30 time units, while it is calculated randomly from the same range for the synthetic topologies. Four virtualization technique types are used in these experiments, which are (1) Virtual Machine (VM), (2) process in a container (PRC), (3) input/output driver (I/O), and (4) hardware appliance (HW). The virtualization