tilization over offered traffic Erlang-B Erlang-B Simulations Simulations offered voice traffic [kbps] offered voice traffic [kbps] Figure 6.8: Validation of Erlang-B formula for the voice scenario: CAC reject ratio and link utilization over offered voice traffic Figure 6.9 depicts the state probability (i.e. the probability for the number of busy connections) derived with equation (6.5) and validated with simulations. The left figure plots the probability density function of the number of busy connections and the right one plots its cumulative distribution function. In this example, the total bandwidth on lub link is still 1 Mbps and the offered voice traffic is 0.427 Mbps. As each voice call reserves 12.4 kbps bandwidth, therefore the 1-Mbps lub link allows maximum 80 simultaneous calls in the system according to equation (6.17). Figure 6.9 shows the probability of the number of busy channels from 1 to 80. It is clearly seen that the calculated probability of each state with equation (6.5) matches well with the probability obtained from the simulations. 6.2 Dimensioning for Circuit-Switched Traffic probability density function cumulative distribution function Erlang-B Erlang-B Simulations Simulations number of connections number of connections Figure 6.9: Validation of Erlang-B formula for the voice scenario: state probabilities As mentioned in section 6.2.1, an important property of Erlang-B formula is the insensitivity property, which means that the state probabilities are fully insensitive to the form of the holding time distribution but depends only on the first moment of the holding time [Coh79, Ive04]. Here the holding time of a voice call corresponds to a voice session. This property is presented in Figure 6.10. It gives the probabilities of different states, i.e. the number of busy connections, under various holding time distributions with the same mean holding time. probability density function normal uniform constant exponential Erlang-B number of connections Figure 6.10: Insensitivity of Erlang-B mod