**2.5 Modeling IMS session establishment**

In this section we will provide a theoretical model for SIP retransmission techniques in lossy network, bandwidth calculation for IMS session set up and estimation of IMS session set up delay. Figure.2. shows that the calls traverse five SIP proxies. Each link of the depicted network has a loss rate of (l) and has a propagation delay of (D) seconds.

Design and Analysis of IP-Multimedia Subsystem (IMS) 73

For the case of INVITE requests, the exponential retransmission behavior is used up to a timer called TimerB. That is a request is retransmitted at time points T1, 3T1, 7T1, 15T1 and

With (2�� − 1)T1 = TimerB . Thereby the maximum number of retransmitted INVITE

TimerB

With a loss rate of l, out of r issued INVITE requests per T1 seconds (r x l) packets would be lost on average. These would be retransmitted T1 seconds later. The retransmitted packets would also suffer from a loss and will have to be retransmitted later. Hence, the call

N� = �l���(

Time *Ri* Lost 0 *r lr*  1 T1 *r + lr lr + l2r*  2 T1 *r + lr lr + l2r*  3 T1 *r + lr + l2r lr + l2r + l3r*  4 T1 *r + lr + l2r lr + l2r + l3r*  5 T1 *r + lr + l2r lr + l2r + l3r*  …. *…. ….*  7 T1 *r + lr + l2r + l3r lr + l2r + l3r + l4r*  8 T1 *r + lr + l2r + l3r lr + l2r + l3r + l4r*  …. *…. ….* 

Table 1. Retransmission Behavior of Invite Requests Due To Network Losses in IMS

sent by the sender at any time point (n) can, hence, be determined as:

R�(l, n) = r � �1 � � l�

At time point 0, r requests are sent per T1 seconds. After T1 seconds the senders will continue generating r new INVITE requests per T1 second and will retransmit the lost (l x r) requests, e.g, (r + (l x r)) will be sent. Out of those (l x (r + (l x r)) will be lost. These would be retransmitted at time 3T1.At time 2T1 r new requests will be sent plus the requests that were lost T1 seconds ago, e.g., (l x r) requests. Out of the sent request (l x (r + (l x r)) will be lost. These would be retransmitted at time 4T1 and so on.The number of INVITE requests (Ri)

���

��� �=r��l�

���

(3)

���

(2� − 1)T1, (2� − 1)T1, (2� − 1)T1 … … . (2�� − 1)T1 (1)

T1 � 1)� (2)

**2.5.1 Modeling the retransmission of the INVITE request** 

up to TimerB. This can be represented as a series in the form of:

generation rate (Ri) can be depicted is shown in Table 1.

requests (N�) is

Network (Sisalem et al. 2008)

Fig. 2. Basic session establishment scenario (Sisalem et al. 2009)

72 Mobile Networks

Fig. 2. Basic session establishment scenario (Sisalem et al. 2009)
