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8.00 Probability [%] 6.00 GOS 4.00 2.00 0.00 50 100 150 200 Pb
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Number of users
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FIGURE 12.3. [Pb] is traf c blocking without fading effect; [GOS] is traf c blocking with fading effect.
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The goal of our simulations presented in the next section is to demonstrate the decrease of traf c as an effect of fading or load balancing algorithm. 12.1.3. Traf c Computation in Wireless Channels with Fading For each single scenario, overlapped or contained, and an algorithm we have scattered various numbers of users that have a call statistics of Poisson distribution with an average arrival process of one hour and an average call time of four minutes in order to measure the probability of dropped calls (call blocking). It is possible to measure the same results with and without considering the fading effect. We now consider how the fading affects the results. In Figure 12.3, two graphs are presented showing the blocking rate (Pb) as a function of the number of users as well as the traf c loss when considering the fading effects (GOS). In this example, a system that has 2% blocking carried 180 users, while taking into account the fading, we get for a GOS of 2% with only 130 users. The fading therefore has an effect that reduces the system capacity by 50 users. Results of Simulations. Our test and simulation results measured three parameters the effect of fading on the average increase of the overlapping area; the increase of probability of call blocking when considering the fading effect; the effect of overlapping on the GOS. In the numerical experiment we checked the GOS for 128 users only. Figures 12.4 and 12.5 depict the results achieved by computing the problem concerning the last two scenarios. Mixed Residential Area. Figure 12.4 depicts situation when the GOS was computed taking into account fading phenomena. Without fading, the probability of blocking was not more than 3%. As can be seen, the effects of fading can increase
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By_ss 10 8 GOS loss [%] 6 4 2 0 2 10 30
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Overlapping [%]
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FIGURE 12.4. Mixed residential area: GOS versus overlapping (in %) for three load balancing algorithms.
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the probability of blocking (GOS) up to 5 7%, as well as an increase of the overlapping area for the same GOS. Urban Area. Figure 12.5 depicts situation when GOS was computed taking into account the fading phenomena. Here, without accounting for the fading effect we get not more than 5% of the blocking probability, whereas in the overlapping scenario in urban environments fading has tremendous effect on the GOS (up to 20 30%) and in low overlapping, it is so large that an unacceptable GOS was obtained (for overlapping of 50% it can achieve 50 70%). Some Speci c Example. Finally, we will present some speci c example of a cellular system arranged in the mixed residential area to show the loading effect on
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70 GOS loss [%] 60 50 40 30 40 60 80 Overlapping [%] 100
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FIGURE 12.5. Urban area: GoS versus overlapping.
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FIGURE 12.6. An example of two cells propagation map in an overlapping case.
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each cell constructed according to the overlapping scenario. We use the following testing area con guration: two cells located at a distance of 1 km; number of users is 128; average arrival time is 60 min; average holding time is 4 min; decision rule is random with decision probability P1 35%. After the corresponding simulation, we get the following overlapping map shown in Figure 12.6. The overlapping area (red area in the middle) is 53% of the entire service coverage area. Finally, we get two histograms that represent the load on each cell (see Fig. 12.7). These histograms show the percentage of time of occupancy for a certain number of channels. As it is seen, as we took the probability of decision of P1 35%, the common users had higher probability to be in Cell #2, because we decided more time of occupancy of eight channels being in Cell #2 compared to Cell #1. We also get from this simulation the following results: the probability of fading (Pf ) is 0.6%, that is it is low, for the high overlapping, and the probability of blocking (Pbl ) is 1.8%. Finally we get according to Reference [8] that GOS Pbl 1 Pf Pf 1 Pbl Substituting probabilities mentioned above, we get GOS 0:018 1 0:006 0:006 1 0:018 0:023 or 2:3% 12:1
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