## 3 Traffic Model

Table 1: Call scenarios in the modeled IMS/NGN network. To conform to ITU-T standards [9, 10] defining CPP parameters, the delays introduced by UE 1 and UE 2 (Figure 1) are not considered in calculations of these parameters. Figure 3: Model of CSCF servers, RACF C1, RACF C2 (**left**) and links (**right**). Figure 2: Message flow for the \(\ell\)2 call scenario (black arrows—communications using SIP protocol; red arrows—Diameter protocol; blue arrows—dedicated MPLS resource control protocol). The output variables of our traffic model are mean values of Call Set-up Delay (\(E(CSD)\)) and Call Disengagement Delay (\(E(CDD)\)) evaluated individually for all successful call scenarios presented in Table 1 (scenarios b1, b2, d1, d2, f1 and f2). To distinguish between the evaluated CPP parameters, the names of scenarios are used in their indexes--e.g., \(E(CSD)_{\text{b1}}\) represents mean \(CSD\) for scenario b1. The calculations of the output parameters are based on the input variables of the traffic model, which can be divided into the following groups:  
* Intensities of requests generated in both domains:
* UE registration request intensity (**lambdaR** vector);
* Intra-operator call set-up request intensity (**lambda1d** vector);
* Inter-operator call set-up request intensity (**lambda2d** vector). * Processing times for network elements containing message queues (CSCF servers, RACF C1 and RACF C2):
* Times of processing SIP INVITE message by CSCF servers in both domains (**TINV** vector);
* Time of message authorization and request type determination by RACF C1 and RACF C2 (**TA** vector);
* Time of performing elementary database operations by RACF C1 and RACF C2 (**Tproc** vector);
* Time of processing a response from LER by RACF C1 and RACF C2 (**Tresp** vector). * Response times of network elements modeled as random variables (MPLS domains, RACF A1, RACF A2, SUP-FE 1/SAA-FE 1 and SUP-FE 2/SAA-FE 2):
* Mean response time of \"MPLS core 1\" and \"MPLS core 2 (**ETR** vector);
* Mean time of processing requests by RACF A1 and RACF A2 (**EXA** vector);
* Mean time of processing requests by SUP-FE 1/SAA-FE 1 and SUP-FE 2/SAA-FE 2 (**EY** vector). * Parameters of the transport stratum:
* Ratio of calls involving multiple access areas to all intra-operator calls generated in domains 1 and 2 (**rC** vector);
* Probability of transport resource unavailability in all access and core networks (**pb** vector);
* Probability of a successful bandwidth reservation or increase without the necessity of increasing LSP bandwidth in MPLS core networks of operators 1 and 2 (**p11** vector);
* Probability of a bandwidth release or decrease without the necessity of decreasing LSP bandwidth in MPLS core networks of operators 1 and 2 (**p21** vector). * Link parameters:
* Lengths (**d** vector);
* Bandwidths (**b** vector). * Types of queuing models for CSCF servers, RACF C1, RACF C2 and links (M/M/1 or M/G/1). In our analytical model of a multidomain IMS/NGN network with an MPLS-based transport stratum, the \(E(CSD)\) and \(E(CDD)\) times for successful call scenarios are calculated based on the definitions given by ITU-T [9; 10]. The calculations are performed by summation of mean values of component delays, which correspond to sending messages through links and message sojourn in different network elements. These delays result from the set of messages exchanged in a particular call scenario as well as network elements \"visited\" by these messages. For \(m\) \"visited\" links and \(n\) \"visited\" network elements:  
\[CPP_{x}=\sum_{i=1}^{m}T_{link-i}+\sum_{j=1}^{n}T_{NE-j}, \tag{1}\]  
where:* \(CPP_{x}\) is the \(E(CSD)\) or \(E(CDD)\) for the scenario \(x\) = b1, b2, d1, d2, f1 or f2;
* \(T_{link-i}\) is a delay corresponding to sending a message through the \(i\)-th link;
* \(T_{NE-j}\) is a delay corresponding to message sojourn in the \(j\)-th network element.