## 5 Case Studies on the OMF-Enabled Testbed
### Case Study 2: Available Bandwidth Estimations  
In this section, the estimation accuracies of various end-to-end avail-bw estimation tools, namely pathload [25], spruce [28], west [29], and pathchirp [30], are evaluated on two different testbed setups and cross-traffic scenarios. The avail-bw is defined mathematically as:  
\[\text{Avail-bw}=C-U \tag{3}\]  
In Equation (3), \(C\) represents the capacity of the link, and \(U\) denotes the utilization of the link over a particular time period. This equation provides the foundational metric for comparison between the tools under test and the MRTG derived ground truth. First, the estimation accuracies of pathload and spruce are validated through the results obtained by performing passive measurements using the Multi Router Traffic Grapher (MRTG). Pathload estimates the avail-bw by generating periodic probe packets and analyzing the one-way delay trends of these packets. The tool measures the difference in inter-arrival times of packets between the sender and receiver, expressed as:  
\[\Delta t_{\text{recv}}-\Delta t_{\text{send}}=\text{Delay Increase} \tag{4}\]  
where \(\Delta t_{\text{send}}\) and \(\Delta t_{\text{recv}}\) are the inter-packet time differences between the sender and receiver, respectively. When the delay increase becomes significant, it indicates that the probing rate exceeds the avail-bw, allowing pathload to converge on an accurate estimation of avail-bw. Spruce uses a packet pair dispersion model to estimate avail-bw. The dispersion of two packets, sent back-to-back, is used to calculate the estimate as:  
\[\text{Avail-bw}_{\text{spruce}}=\frac{s}{\Delta t_{\text{recv}}}-C \tag{5}\]  
In Equation (5), \(s\) is the size of the packets, \(\Delta t_{\text{recv}}\) is the time difference between the arrivals of the two packets at the receiver, and \(C\) is the known capacity of the link. Spruce relies on the assumption that cross-traffic does not fully utilize the link's capacity. Figure 4: Comparison of the passive TCP-based SA estimates with the average of ten active ICMP-based and UDP-based ping measurements just before the TCP connection establishment. MRTG estimates avail-bw based on the difference between the measured traffic utilization and the total link capacity over a 5 min period. The average avail-bw is calculated as:  
\[\text{Avail-bw}_{\text{MRTG}}=\frac{\sum_{i=1}^{N}\left(C-U_{i}\right)}{N} \tag{6}\]  
where \(N\) is the number of samples collected over the 5-minute period, \(C\) is the total link capacity, and \(U_{i}\) is the measured utilization at sample \(i\). MRTG provides a low-resolution, passive measurement that serves as a benchmark for evaluating active tools. MRTG is a widely used tool for monitoring and visualizing network traffic, providing detailed insights into bandwidth utilization across links. More specifically, assuming that MRTG is able to obtain the same available bandwidth (avail-bw) as the pathload and spruce tools under test, it can provide reference values (i.e., the ground truth avail-bw) against which estimates from both active tools are compared to indicate their consistency and accuracy. In the literature, MRTG data are considered one of the most accurate methods for verifying the output of active avail-bw estimation tools. The experiments of pathload, spruce, and MRTG have been specified in an experiment description file using the testbed setup and configuration illustrated in Figure 3b. Consider the end-to-end path consisting of four links between the research nodes S and R acting as the sender and receiver hosts. The pathload and spruce tools with their sender and receiver components are started along the path to estimate the end-to-end avail-bw. By assuming the previous knowledge of the capacity of all traversed links and running the MRTG on each node of the measurement path, avail-bw on each link segment can be measured separately. Concatenation of avail-bw measurements of different link segments enables us to estimate this metric at the end-to-end scope.