es. This is shown in Figure 17.9. To compute the queueing delay we have assumed an M/M/1 queueing model for MH as well as CSCF servers, and a priority based M/G/1 model for the destination server. The rationale behind these assumptions is that while the MH and the CSCF servers perform dedicated jobs, the destination server may be busy with a variety of jobs other than serving the SIP messages and thus, may have arbitrary service time distribution. Table 17.2 lists the parameters used in the analysis and their meanings. Although, it has been shown that the Internet delay varies between 100 ms to 1 S [29], emerging high-speed technologies like Generalized Multiprotocol Label Switching (GMPLS) [30] provide efficient traffic engineering to reduce this Internet delay to a nominal fraction of the minimum allowed end-to-end delay (on the order of few ms). Hence, the major concern is with the delay introduced by the wireless links in the access networks. Let us now determine the queueing delay of a SIP message at the MH, the intermediate CSCF servers, the destination and the transport delay over the wireless access. We assume that multiple MHs are served by the CSCF servers that also support load balancing functions. Hence < l or is a fraction of 1. The SIP message transmission delay, DSIP-UMTS, for GPRS radio access of a UMTS network can be computed as: DSIP-UMTS = DMH + DRLP + DP-CSCF + DI-CSCF + DS-CSCF + I + Dest (17.4) Using the results from queuing theory [31] and the parameters presented in Table 17.2, the delay components are estimated as follows. (17.5) DP-CSCF (17.6) (17.7) where R = while XI and X2 are the second moments of and Us, respectively. The expression for DDest is obtained by using the result of C 2009 by Taylor & Francis Group, LLC Internet I-CSCF S-CSCF Destination P-CSCF delay M/M/1 M/M/1 M/M/1 M/M/1 M/G/1 2M - SIP message arrival rate at a Mobile Terminal a - SIP message arrival rate at the Base Station a - SIP message arrival rate at the Server or CH No - Other application level messages arrival 