**3.1.1 Calculation of the delay impairment Id**

The factor Id is the delay impairment factor that can be calculated as follow (ITU-T Rec. G.107 2005):

$$\text{Id} = 25 \left[ \left( 1 + \chi^6 \right)^{\bigvee\_6} - \left( 1 + \left[ \frac{\chi}{3} \right]^6 \right)^{\bigvee\_6} + 2 \right] \tag{44}$$

With:

$$\chi = \frac{\log\left(\frac{\text{Ta}}{100}\right)}{\log 2}$$

Design and Analysis of IP-Multimedia Subsystem (IMS) 83

unacceptable below 50. It is recommended for most networks to arrive at a score above 70 when measuring. A user should therefore always reach for an R value as high as possible for all possible connections. Table 5 describes the various quality and satisfaction categories

**Quality Category User Satisfaction** 

related to the E-model factor R (ITU-T Rec. G.107 2005).

**3.2 Project setup** 

link utilization level.

Fig. 3. Network Topology

**Range of E-Model Rating R Speech Transmission** 

90 < R < 100 Best Very Satisfied 80 < R < 90 High Satisfied

NOTE - Connection with E-Model Rating R Below 50 are not Recommended

70 < R < 80 Medium Some Users Dissatisfied 60 < R < 70 Low Many Users Dissatisfied 50 < R < 60 Poor Nearly All Users Dissatisfied

Table 5. E-model related quality and satisfaction categories (ITU-T Rec. G.107 2005).

maintaining a minimum level of voice quality (R). The cases considered are:

The simulation is done using OPNET simulation tool IT Guru Academic Edition 9.1 for VoIP in IMS network using SIP Protocol. The network consists of IP-Telephones (VoIP or IMS Clients) connected to the Internet by routers which act as IP gateway, the network is managed by the SIP proxy server (act as P-CSCF) which uses the SIP protocol to establish the voice calls (VoIP) on the IMS network as shown in figure 3. The links between the routers and the Internet are T1 with link speed 1.544 Mbps and the links between the dialer, dialed, Proxy Server and the routers are 1000 Base-x. The idea is to configure the network with a certain parameters and run the simulation then getting from the tool the result values which used in E-Model equations to measure the Quality of service Factor R. The objective function for all cases is to maximize the number of calls that can be active on a link while

1. Find the optimal voice coder given link bandwidth, packet loss level, and background
