Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

Steiner Systems for Topology-Transparent Access Control in MANETs 255S(2,k,v) Minimum ThroughputS(2,k,v) Minimum Throughput vs. TDMAMinimum Throughput0.40.30.20.1Ratio to TDMA Throughput40302010010 20 30 40Size of Neighbourhood010 20 30 40Size of NeighbourhoodFig. 3. Minimum throughput for (a) S(2,k,v); and (b) versus TDMA, for k =3, 6, 9, 12.Minimum Frame Throughput0.140.120.10.080.060.040.020S(2,k,v) Minimum Frame Throughput10 20 30 40Size of NeighbourhoodRatio to TDMA Frame ThroughputS(2,k,v) Minimum Frame Throughput vs. TDMA4321010 20 30 40Size of NeighbourhoodFig. 4. Minimum frame throughput for (a) S(2,k,v); and (b) versus TDMA, for k =3, 6, 9, 12.Again, we look at frame throughput, this time the minimum value, in Fig. 4(for the same k’s and v’s). Not surprisingly, the minimum frame throughput islower than when using the more optimistic acknowledgement model. The maindifference between this figure and Fig. 2 is the x-intercepts. Here, they correspondto k, clearly showing that with minimum frame throughput, once theneighbourhood exceeds the design parameter, all guarantees are lost immediately.This is also true for the ratio of minimum frame throughput over TDMAwith the same frame length (b). This figure also shows that the minimum framethroughput is essentially constant for each k as long as the design parameter issatisfied.Figure 4 shows us something very important, in addition. Larger Steinersystems give us a minimum frame throughput substantially better than TDMAwhen the neighbourhood is within the bound. This is in stark constrast with theschemes in [2,10]; they never outperform TDMA on minimum frame throughputwhen orthogonal arrays of strength two are used.Figure 5 is different from all other figures in that it plots expected throughputversus density of the neighbourhood. That is, the x-axis is the percentage ofnodes that are neighbours — these are not absolute values, and represent much