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Example

The following is a simple example of the analysis using the same parameters as the simulation in the next section. The parameters required are:

From the equations in the previous section, we can develop an analytical solution for the remaining parameters. Using basic probability the integral of Equation 5 should be one. Also, tex2html_wrap_inline902 is an exponential approximation of Equation 4, which can be found by taking the integral of the difference of tex2html_wrap_inline904 from Equation 4 and tex2html_wrap_inline902 and setting the result to zero,

equation482

equation485

This provides two equations and two unknowns which provide the solution for tex2html_wrap_inline908 and tex2html_wrap_inline910 . These values can be used to determine the tex2html_wrap_inline912 which can then be used in our extension of [1] as discussed previously. In the graph of tex2html_wrap_inline912 shown in Figures 4, it appears that there will be a high probability of blocking, since tex2html_wrap_inline916 . This is compared with an arrival rate of 0.01 calls/sec/unit area in Figure 5, which has a maximum at one channel per station, and a lower blocking probability.

   figure499
Figure 4: Channel Usage Prob. Density Function for 0.6 Call/Sec.

   figure504
Figure 5: Channel Usage Prob. Density Function for 0.01 Call/Sec.

Figures 4 and 5 are in agreement with the simulation results in Figures 7 and 8 as additional verification.



Steve Bush
Sun Aug 25 17:38:45 CDT 1996