**3.1 Assumptions for E-Model**

80 Mobile Networks

B= η × (R� ×S� + R��� × S���)

+ μ × (R��� × S��� + R����� × S����� + R��� × S���) + (R��� × S��� + R��� × S���)

The IP Multimedia subsystem (IMS) is an overlay system that is serving the convergence of mobile, wireless and fixed broadband data networks into a common network architecture where all types of data communications are hosted in all IP environments using the session initiation protocol (SIP) protocols infrastructure (23.228 2009). IMS is logically divided into two main communication domains, one for data traffic, i.e., real time protocol packets consisting of audio, video and data and the second one is for SIP signaling traffic. This chapter focuses on the VoIP Quality of Service over IMS using SIP as a signaling protocol. Quality is a subjective factor, which makes it difficult to measure. Taking an end to end perspective of the network further complicates the QoS measurements. The reasons for low quality voice transmission are due to degrading parameters like delay, packet delay variation, codec related impairments like speech compression, echo and most importantly packet loss. Large research efforts have been made to solve the vital quality of service issues. There are some models were developed to measure the VoIP end to end QoS. The output of these models is generally a single quality rating correlated to the subjective Mean Opinion Score (MOS score) which represents the QoS for Voice calls. Many of the developed models for measuring VoIP quality of service are inappropriate for smaller, private networks. They may take too much process resource, are intrusive on the regular traffic or contain very complicated test algorithms. One of the best models used for measuring VoIP quality of

The E-Model, (ITU-T Rec. G.107 2005), is a model that allows users to relate Network impairments to voice quality. This model allows impairments to be introduced and voice quality to be assessed. Three cases are considered to demonstrate the effectiveness of optimizing the VoIP over IMS network using E-Model. New equations were also provided to enhance E-Model that can be used to relate packet loss to the level of Equipment Impairment (Ie) with different codecs. The objective function for all cases is to maximize the number of

calls that can be active on a link while maintaining a minimum level of voice quality.

1. Find voice coder given link bandwidth, packet loss level, and link utilization level. 2. Find voice coder and packet loss level given link bandwidth and background link

l : is the probability of losses between two hops (Assume l is the constant).

L : is the one way End to End Losses. L�: is the two ways End to End Losses.

r : is the number of Calls or Sessions per Second.

**3. VoIP quality optimization in IMS** 

B: The Bandwidth needed for IMS Sessions Establishment.

service is the E-model, which is a parameter-based model.

S: is the SIP Message Size. η : is the number of hops. μ: is the number of ringing.

The cases considered are:

utilization.

+( R��� × S��� + R����� × S����� + R��� × S���) + (R������ × S������ + R��� × S���) (42)

The E-Model, (ITU-T Rec. G.107 2005) is extremely complex with 18 inputs that feed interrelated components. These components feed each other and recombine to form an output (R). The recommendation (ITU-T Rec. G.108 1999) gives a thorough description on how to carry out an E-model QoS calculation within VoIP networks.

Due to the complexity of the E-Model, the approach used here is to try to identify which E-Model parameters are fixed and which parameters are not. In the context of this research the only parameters of the E-Model that are not fixed are:


Where (T) is the mean one way delay of the echo path, (Ta) is the absolute delay in echo free conditions. In addition, parameters that affect delay Id and Ie are introduced:


Next, the relationship between these parameters is identified. Since, we are making the assumption that the echo cancellers on the end are very good, we can say that T = Ta and Ie is directly related to a particular coding scheme and the packet loss ratio.

According to the above assumption, R-Factor equation can be reduced to the following expression (ITU-T Rec. G.107 2005):

$$\text{IR} = 93.2 - \text{Id (Ta)} - \text{le (code, packet loss)} \tag{43}$$
