## 4 Results and Discussion
### Results
Figure 5: Selected results for data set 2 from Table 1.  
Figure 6: Selected results for data set 3 from Table 1.  
For network elements whose response times are specified by random variables, larger mean values of these random variables (**ETR**, **EXA** and **EY**) result in proportionally higher \(E(CSD)\) and \(E(CDD)\) times (Figures 7 and 8). The set of affected CPP parameters is, however, dependent on the parameter modified in domain 1. Changes in the mean time of processing requests by RACF A1 (**EXA**) have an impact on the \(E(CSD)\) and \(E(CDD)\) times for all scenarios with resource reservation in the access network of operator 1 (scenarios b1, d1, f1 and f2). The mean response time of the operator 1 MPLS network (**ETR**) influences only CPP parameters for call scenarios with resource allocation in this network (scenarios d1, f1 and f2). A very interesting case is that of modifying the mean time of processing  
Figure 8: Selected results for data set 5 from Table 1.  
Figure 7: Selected results for data set 4 from Table 1.  
requests by SUP-FE 1/SAA-FE 1 **(EY)**. This network element is only used during the set-up of inter-operator calls originated in domain 2, so increasing its processing time increases only \(E(CSD)_{I2}\) and has no impact on other CPP parameters. Figure 10: Selected results for data set 7 from Figure 5:0  
Figure 5:1 Selected results for data set 6 from Figure 5:2  
Modification of the **rC** and **pb** parameters in domain 1 (Figure 9) has a very small influence on CPP parameters. Increasing the ratio of calls involving multiple access areas to all intra-operator calls generated in domain 1 (**rC**) makes resource reservations in the MPLS core network of operator 1 more common, which results in more messages exchanged in domain 1 and, consequently, a higher load of network elements. As a result, the \(E(CSD)\) and \(E(CDD)\) times for scenarios b1, d1, f1 and f2 are slightly increased. A higher probability of transport resource unavailability in the access and core networks of operator 1 (**pb**) leads to more unsuccessful call scenarios, which involves sending and processing less messages compared to successful ones. This results in a slightly lower load of all network elements and links in both domains and lower values of all CPP parameters. Higher values of the **p11** and **p21** probabilities describing the operation of the MPLS core network of operator 1 (Figure 10) result in more resource operations (bandwidth reservation or increase--**p11**; bandwidth release or decrease--**p21**) performed only by updating the resource state in the RACF C1 database (without communication with LERs). This decreases mean \(CSD\) and \(CDD\) times for scenarios d1 and f1, in which resource operations in the core network of operator 1 are necessary. A similar decrease can be observed in the values of \(E(CDD)_{\text{f2}}\). Interestingly, the values of \(E(CSD)_{\text{f2}}\) are not affected by modifications of the **p11** and **p21** probabilities. It results from the fact that during the set-up of inter-operator calls generated in domain 2 (scenario f2), there are two concurrent processes (Figure 2):  
1. Resource reservation in the destination domain 1 (messages 14-15);
2. Communication from domain 1 to domain 2 (messages 13 and 16-18), resource reservation in the originating domain 2 (messages 19-20) and communication from domain 2 to domain 1 (confirmation of resource reservation; messages 29-32). Typically, the second process is much more time-consuming and has a decisive influence on \(E(CSD)_{\text{f2}}\). Such a situation took place for the examined sets of input variables. The time necessary for resource reservation in the core network of operator 1 does not have an impact on \(E(CSD)_{\text{f2}}\), independently of the applied values of the **p11** and **p21** parameters. The last data set (Figure 11) examines the influence of link parameters in domain 1 on the analyzed CPP parameters.