e website. Subscriber Traffic Modeling Subscriber Traffic Modeling this 95 percent confidence interval down to a range of 48 to 52 percent, it takes 20,000 tosses. Once we observe the fraction of heads and tails, we have to apply statistical con- fidence bands to the observation because we do not know the true probability, so the confidence interval on the fairness of the coin is about twice as wide as the probability range of its performance. This means that in 19 times out of 20 trials, 20,000 tosses of a truly fair coin is enough to give us 95 percent confidence that the coin is within 4 per- cent of fair. Consider simulating a 500-cell system engineered for 2 percent blocking during the busy hour, and let us suppose that the system actually meets the universal 2 percent blocking objective. We want to simulate the system to verify that the blocking is less than 3 percent, a comfortable margin over 2 percent. Suppose that we have a system with universal 2 percent blocking, and we want to simulate it for a long enough period of time to be 99 confident that the blocking rate is less than 3 percent. This means that each base station has to experience thousands of calls for that base station to give us that 99 percent confidence. By the time each base station has accumulated a few thousand calls, the simulation has performed millions of calls. And this still only gives us 99 percent assurance on a cell-by-cell basis, for an expected 495 of 500 cells. If we want comfort that all 500 cells are delivering adequate blocking, then we would have to let the simulation run a lot longer. Analytical tools are better for this kind of analysis, calculation of small probabilities at the tail of the probability distribution curves. We can do the mathematical compu- tations at the tail of the curve without dragging the computer through simulation of millions of perfectly fine calls. 48.4 Analytical Models An analytical performance tool for a wireless telephone system looks directly at the sta- tistical distributions themselves ra