principle, the EM algorithm is divided into E-step (Expectation) and M-step (Maximization). The E-step is to compute the expectation of likelihood function for the observed data; the M-step is to estimate the parameter by maximizing the expectation of the likelihood function from the E-step. These two steps are repeated until a predefined maximum number of iterations is reached or until a convergence criteria holds. In this thesis, the BMAP results are generated using a software package IP2BMAP [LL03]. Figure 6.57 compares the CDF of the FP PDU inter-arrival time from the measured trace data, from BMAP using the EM algorithm and the Poisson process. It can be obviously seen in this figure that the CDF of the BMAP model accurately matches the CDF of the measured traffic; while the CDF of the Poisson process behave much more smoothly than the measured traffic, which means the Poisson process conceals the bursty property of the traffic. This figure demonstrates the advantages of using the BMAP model compared with Poisson process to analyze the aggregated UMTS traffic. 6 Dimensioning for Single ATM-Based lub FP PDU interarrival time (s) Measured traffic Poisson process Figure 6.57: CDF of FP PDU inter-arrival time - single RAB scenario Figure 6.58 plots sample paths of the aggregated UMTS traffic stream taken from the simulations (left) and sample paths of the aggregated traffic stream applying the parameterized BMAP model (right). The figure shows that the customized BMAP captures the average transferred data rate in packet per second. The burstiness of the measured FP PDU rate and the analytical FP PDU rate obtained by the BMAP are similar. The mean arrival FP PDU rate of the measured traffic is 703.90 packets/second, while the mean arrival FP PDU rate of BMAP is 722 packets/second. The standard deviation of arrival FP PDU rate of the measured traffic is 7657.9 packets/second and from BMAP is 7520.5 packets/second. 250000 250000 200000 200000 150000 150000 100000 100000 50000 50000 time (second) time (second) measu