## 6 Numerical Experiments
### Experiment Settings  
For the recipe tree, we adopt the basic structure of a user group and two alternative routes, e.g., the first route as the service shortcut route and the second route as the service chain route (with \(K\) different domains), as shown in Figure 2a. More complex structures will be considered in our future studies. The bandwidth amount requested by users is modeled with historical traffic data collected from the China Education and Research Network (CERNET). During this time period, the CERNET topology contained 14 nodes and 16 bi-directional links [56]. The historical traffic is recorded for each node pair every five minutes from 19 February 2013 to 26 March 2013, with a total number of 9999 time slots used in the experiments. After filtering the node pairs with only zero values, a total of 159 node pairs remain, out of which \(N\) node pairs are chosen at random and without replacement as the users (e.g., N = 10, 20, 50, 100, or 150). The historical traffic data distribution is shown in Figure 5, in which 300 Mbps is approximately the 90 th percentile value. Only the requested bandwidth from users is modeled as time-varying in the experiments. The available bandwidth amount provided by service providers is drawn from a uniform distribution \(U[0,300/\alpha]\), in which \(\alpha=M/N\) is the service provider/user ratio. When the number of users is equal to the number of service providers in a domain, the uniform distribution becomes \(U[0,300]\). With a lower service provider/user ratio (i.e., a smaller \(\alpha\)), the bandwidth resource provided by the remaining service provider increases accordingly to maintain the same expected total bandwidth for a fair comparison of the different service provider/user ratios in Section 6.3. The bid prices of users and the ask prices of service providers in the service shortcut route are drawn from a uniform distribution \(U[0,100]\), and the ask prices of service providers in the service chain route are drawn from a uniform distribution \(U[0,100/K]\), which is affected by the domain number in the service chain route. With a longer service chain (i.e., a larger \(K\)), the ask price from the growing domains decreases accordingly to maintain the same expected total cost of using the service chain route for a fair comparison of different domain numbers in Section 6.4. Otherwise, if the ask prices increase with the domain numbers linearly, then no users would prefer a longer service chain route and this comparison becomes trivial (and thus, the service chain route becomes economically prohibitive in practice). The economic intuition is that, if more service providers are meant to cooperate in the service chain route, the overall cost must be controlled to be competitive with the satellite service provider in the service shortcut route. The parameters used in the experiments as well as their value ranges are summarized in Table 7. Only the bandwidth information is derived from real-world historical traffic values and the user or price information is difficult to obtain, even from the existing terrestrial network service providers, as such information is usually their commercial secret. It is also impossible to obtain such information from the satellite network service provider, which is at the very early stage of providing commercial services. Instead, we set the similar parameters and the uniform distribution format following previous relevant studies [8,44,57]. In each time slot, \(N\) user requests are generated, and the market operator attempts to admit or reject these requests based on the bandwidth and price information. Both the optimal trade mechanism and the proposed ascending auction mechanism are implemented and compared. To evaluate the admission results and quantify the influence of different parameter values, different evaluation metrics are defined and used in the experiments. The first evaluation metric is the admission ratio within the range of 0-1, which calculates the ratio of the admitted requests to all the requests.