Success probability over the number of nodes Nn for message interarrival time τ = 4 s. Circular markers are from APCMA simulations, black square markers are from the CSMA/CA simulations, and all lines are from the corresponding analyses results.

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... success probability plotted against the number of nodes is shown in Fig. 8. Our first observation is that all analytical models (solid lines) fit rather well with their respective simulated values (discrete markers) for both CSMA/CA and APCMA. We also see that the curve for CSMA/CA intersects with APCMA with N p = 5 pulses at about 8,000 nodes and with N p = 6 pulses at about 16,000 nodes. Note that the ...

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... compute the 95% confidence intervals over the success probability averaged over all nodes in each scenario. Since we are dealing with very large numbers of nodes and our metric takes values that are limited to the interval [0,1], the confidence intervals that we obtain are very small in size. Therefore, we do not include confidence intervals in Fig. 8, but instead illustrate the one-sided confidence interval lengths for each APCMA version and CSMA/CA separately in Fig. 9 as a function of the number of nodes. The largest confidence intervals for each APCMA variant occur when the corresponding success probability is close to 0.5 in Fig. 8. In all of the considered cases, the ...

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... Therefore, we do not include confidence intervals in Fig. 8, but instead illustrate the one-sided confidence interval lengths for each APCMA version and CSMA/CA separately in Fig. 9 as a function of the number of nodes. The largest confidence intervals for each APCMA variant occur when the corresponding success probability is close to 0.5 in Fig. 8. In all of the considered cases, the confidence intervals remain below ...

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... 10 are shown in Table 2 for all three values of τ = 1 s, 2 s and 4 s, where a consistent linear trend can be recognized. Figure 8 also shows that when the number of nodes N n increases, the APCMA success probability decreases. The which the analytical success probabilities for CSMA/CA and APCMA intersect for τ = 1 s, 2 s and 4 s, i.e., Nn at which ps A = ps C . ...

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... see is that the z-axis with the number of nodes scales down accordingly. Numerically inverting the curve of CSMA/CA success probability at τ = 4 s and N b = 10 yields N n = 933.58 at ps C = 0.95. This value also scales linearly with τ and stays at about the value of APCMA with N p = 4 pulses and N c = 1, 024 codewords as we could already see in Fig. ...

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... the shapes of Figs. 8 and 14 are basically similar for APCMA, the channel utilization variable aggregates the parameters C and N n into a single value, which we can arbitrarily scale up. In Fig. 8, we could not increase the codeword bits N b beyond a certain limit, since we would then have messages that become longer to transmit than the interarrival time τ . However, since the same utilization value can be reached by several different combinations of the parameters, we can now avoid this problem. The surface plots of the target ...