Simulation results for evaluating the performance of fault-tolerant data broadcasting in FLTQn and FLTQn using three EDHCs

Three Edge-disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes


Figure 1 show three edge-disjoint Hamiltonian cycles in folded locally twisted cube FLTQ5. For ease of visual judgement, some complementary edges are omitted.

Figure 1.

Three Edge-disjoint Hamiltonian Cycles in Folded Crossed Cubes


Figure 2 show three edge-disjoint Hamiltonian cycles in folded crossed cube FCQ5. For ease of visual judgement, some complementary edges are omitted.

Figure 2.

Simulation on Folded Locally Twisted Cubes

Descriptions:
1. Let m be the number of faulty edges.
2. In FLTQ_n, 5 <= n <= 10, 1 <= m <= 10.
3. Randomly generate 1,000,000 instances of number-lists (source s, faulty edges f1, f2, ..., fm) and f1 != f2 != ... != fm
4. For each instances, source node s send the messages to the next nodes simultaneously in two directions through three Hamiltonian cycles.

Example 1,
While n=5, m=6 and instances (21, 56, 72, 59, 10, 83, 39),
Source = node 21, edge 56 = (12,28), edge 72 = (18,19), edge 59 = (13,21), edge 10 = (1, 25), edge 83 = (22,30), edge 39 = (8,12),
For source node 21,
Hamiltonian Cycle HC1 = 21-19-18-26-24-28-30-22-23-27-25-31-29-17-16-0-1-13-15-9-11-7-6-14-12-8-10-2-3-5-4-20-21,
Hamiltonian Cycle HC2 = 21-23-17-19-31-7-1-30-26-27-3-15-14-10-11-13-12-4-6-22-20-28-29-5-9-8-0-2-18-16-24-25-21,
Hamiltonian Cycle HC3 = 21-13-18-22-9-17-14-30-31-0-4-27-29-2-6-25-1-3-28-12-19-11-20-16-15-23-8-24-7-5-26-10-21

Node 21 send by HC1 in forward direction: 21 -> 19 -x- 18,
reachable node set S1 = {19}
Node 21 send by HC1 in backward direction: 21 -> 20 -> 4 -> 5 -> 3 -> 2 -> 10 -> 8 -x- 12,
reachable node set S2 = {20, 4, 5, 3, 2, 10, 8}
Node 21 send by HC2 in forward direction: 21 -> 23 -> 17 -> 19 -> 31 -> 7 -> 1 -> 30 -> 26 -> 27 -> 3 -> 15 -> 14 -> 10 -> 11 -> 13 -> 12 -> 4 -> 6 -> 22 -> 20 -> 28 -> 29 -> 5 -> 9 -> 8 -> 0 -> 2 -> 18 -> 16 -> 24 -> 25 -> 21,
reachable node set S3 = {23, 17, 19, 31, 7, 1, 30, 26, 27, 3, 15, 14, 10, 11, 13, 12, 4, 6, 22, 20, 28, 29, 5, 9, 8, 0, 2, 18, 16, 24, 25}
Node 21 send by HC2 in backward direction: 21 -> 25 -> 24 -> 16 -> 18 -> 2 -> 0 -> 8 -> 9 -> 5 -> 29 -> 28 -> 20 -> 22 -> 6 -> 4 -> 12 -> 13 -> 11 -> 10 -> 14 -> 15 -> 3 -> 27 -> 26 -> 30 -> 1 -> 7 -> 31 -> 19 -> 17 -> 23 -> 21,
reachable node set S4 = {25, 24, 16, 18, 2, 0, 8, 9, 5, 29, 28, 20, 22, 6, 4, 12, 13, 11, 10, 14, 15, 3, 27, 26, 30, 1, 7, 31, 19, 17, 23}
Node 21 send by HC3 in forward direction: 21 -x- 13
reachable node set S5 = {}
Node 21 send by HC3 in backward direction: 21 -> 10 -> 26 -> 5 -> 7 -> 24 -> 8 -> 23 -> 15 -> 16 -> 20 -> 11 -> 19 -> 12 -x- 28
reachable node set S6 = {21, 10, 26, 5, 7, 24, 8, 23, 15, 16, 20, 11, 19, 12}

unreachable node set = V(FLTQ5) - {s} - S1 - S2 - S3 - S4 - S5 - S6 = {},
data broadcast successful

Example 2,
While n=5, m=6 and instances (5, 42, 40, 77, 37, 59, 70),
Source = node 5, edge 42 = (9,11), edge 40 = (8,23), edge 77 = (20,21), edge 37 = (8,9), edge 59 = (13,21), edge 70 = (17,23)
For source node 5,
Hamiltonian Cycle HC1 = 5-4-20-21-19-18-26-24-28-30-22-23-27-25-31-29-17-16-0-1-13-15-9-11-7-6-14-12-8-10-2-3-5,
Hamiltonian Cycle HC2 = 5-9-8-0-2-18-16-24-25-21-23-17-19-31-7-1-30-26-27-3-15-14-10-11-13-12-4-6-22-20-28-29-5,
Hamiltonian Cycle HC3 = 5-26-10-21-13-18-22-9-17-14-30-31-0-4-27-29-2-6-25-1-3-28-12-19-11-20-16-15-23-8-24-7-5

Node 5 send by HC1 in forward direction: 5 -> 4 -> 20 -x- 21,
reachable node set S1 = {4, 20}
Node 5 send by HC1 in backward direction: 5 -> 3 -> 2 -> 10 -> 8 -> 12 -> 14 -> 6 -> 7 -> 11 -x- 9,
reachable node set S2 = {3, 2, 10, 8, 12, 14, 6, 7, 11}
Node 5 send by HC2 in forward direction: 5 -> 9 -x- 8,
reachable node set S3 = {9}
Node 5 send by HC2 in backward direction: 5 -> 29 -> 28 -> 20 -> 22 -> 6 -> 4 -> 12 -> 13 -> 11 -> 10 -> 14 -> 15 -> 3 -> 27 -> 26 -> 30 -> 1 -> 7 -> 31 -> 19 -> 17 -x- 23,
reachable node set S4 = {29, 28, 20, 22, 6, 4, 12, 13, 11, 10, 14, 15, 3, 27, 26, 30, 1, 7, 31, 19, 17}
Node 5 send by HC3 in forward direction: 5 -> 26 -> 10 -> 21 -x- 13,
reachable node set S5 = {26, 10, 21}
Node 5 send by HC3 in backward direction: 5 -> 7 -> 24 -> 8 -x- 23,
reachable node set S6 = {7, 24, 8}

unreachable node set = V(FLTQ5) - {s} - S1 - S2 - S3 - S4 - S5 - S6 = {0, 16, 18, 23, 25},
data broadcast failed

Simulation result:
Simulation 1. In FLTQ_5, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 2. In FLTQ_5, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 3. In FLTQ_5, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 4. In FLTQ_5, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 5. In FLTQ_5, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 6. In FLTQ_5, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 70382, unreachable nodes: mean = 2.501208, std = 2.704814, max. = 25
Simulation 7. In FLTQ_5, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 204025, unreachable nodes: mean = 3.01538, std = 3.152752, max. = 29
Simulation 8. In FLTQ_5, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 364468, unreachable nodes: mean = 3.59248, std = 3.542302, max. = 29
Simulation 9. In FLTQ_5, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 519204, unreachable nodes: mean = 4.252342, std = 4.001215, max. = 30
Simulation 10. In FLTQ_5, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 651935, unreachable nodes: mean = 4.966418, std = 4.372772, max. = 30
Simulation 11. In FLTQ_6, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 12. In FLTQ_6, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 13. In FLTQ_6, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 14. In FLTQ_6, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 15. In FLTQ_6, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 16. In FLTQ_6, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 30221, unreachable nodes: mean = 4.607591, std = 5.319708, max. = 50
Simulation 17. In FLTQ_6, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 103015, unreachable nodes: mean = 5.373227, std = 5.928557, max. = 55
Simulation 18. In FLTQ_6, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 209751, unreachable nodes: mean = 6.277429, std = 6.607425, max. = 56
Simulation 19. In FLTQ_6, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 332432, unreachable nodes: mean = 7.276742, std = 7.287308, max. = 55
Simulation 20. In FLTQ_6, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 455486, unreachable nodes: mean = 8.369261, std = 7.973092, max. = 59
Simulation 21. In FLTQ_7, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 22. In FLTQ_7, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 23. In FLTQ_7, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 24. In FLTQ_7, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 25. In FLTQ_7, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 26. In FLTQ_7, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 11388, unreachable nodes: mean = 9.052424, std = 10.380866, max. = 88
Simulation 27. In FLTQ_7, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 44706, unreachable nodes: mean = 10.207601, std = 11.268898, max. = 95
Simulation 28. In FLTQ_7, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 102720, unreachable nodes: mean = 11.445084, std = 12.141096, max. = 105
Simulation 29. In FLTQ_7, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 179573, unreachable nodes: mean = 12.775996, std = 13.061086, max. = 106
Simulation 30. In FLTQ_7, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 270438, unreachable nodes: mean = 14.201163, std = 13.955794, max. = 111
Simulation 31. In FLTQ_8, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 32. In FLTQ_8, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 33. In FLTQ_8, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 34. In FLTQ_8, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 35. In FLTQ_8, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 36. In FLTQ_8, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 5728, unreachable nodes: mean = 25.348638, std = 27.392142, max. = 166
Simulation 37. In FLTQ_8, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 24285, unreachable nodes: mean = 28.186082, std = 29.444123, max. = 193
Simulation 38. In FLTQ_8, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 59665, unreachable nodes: mean = 31.086667, std = 31.514909, max. = 206
Simulation 39. In FLTQ_8, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 112515, unreachable nodes: mean = 34.120491, std = 33.29434, max. = 219
Simulation 40. In FLTQ_8, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 178019, unreachable nodes: mean = 37.433594, std = 35.08539, max. = 211
Simulation 41. In FLTQ_9, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 42. In FLTQ_9, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 43. In FLTQ_9, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 44. In FLTQ_9, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 45. In FLTQ_9, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 46. In FLTQ_9, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 2792, unreachable nodes: mean = 58.874284, std = 61.362436, max. = 398
Simulation 47. In FLTQ_9, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 12524, unreachable nodes: mean = 65.921431, std = 65.69756, max. = 373
Simulation 48. In FLTQ_9, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 32954, unreachable nodes: mean = 70.076592, std = 67.844103, max. = 389
Simulation 49. In FLTQ_9, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 65882, unreachable nodes: mean = 74.755366, std = 70.453844, max. = 417
Simulation 50. In FLTQ_9, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 110943, unreachable nodes: mean = 81.084647, std = 73.723329, max. = 420
Simulation 51. In FLTQ_10, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 52. In FLTQ_10, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 53. In FLTQ_10, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 54. In FLTQ_10, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 55. In FLTQ_10, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 56. In FLTQ_10, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 1464, unreachable nodes: mean = 135.026639, std = 130.524593, max. = 837
Simulation 57. In FLTQ_10, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 7008, unreachable nodes: mean = 139.681221, std = 132.648822, max. = 817
Simulation 58. In FLTQ_10, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 18962, unreachable nodes: mean = 148.232465, std = 137.317424, max. = 872
Simulation 59. In FLTQ_10, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 39582, unreachable nodes: mean = 156.741398, std = 141.611604, max. = 859
Simulation 60. In FLTQ_10, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 69710, unreachable nodes: mean = 167.073921, std = 147.403842, max. = 914

Simulation on Folded Crossed Cubes

Descriptions:
1. Let m be the number of faulty edges.
2. In FCQ_n, 5 <= n <= 10, 1 <= m <= 10.
3. Randomly generate 1,000,000 instances of number-lists (source s, faulty edges f1, f2, ..., fm) and f1 != f2 != ... != fm
4. For each instances, source node s send the messages to the next nodes simultaneously in two directions through three Hamiltonian cycles.

Simulation result:
Simulation 61. In FCQ_5, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 62. In FCQ_5, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 63. In FCQ_5, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 64. In FCQ_5, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 65. In FCQ_5, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 66. In FCQ_5, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 66978, unreachable nodes: mean = 2.576503, std = 2.703212, max. = 24
Simulation 67. In FCQ_5, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 197690, unreachable nodes: mean = 3.072983, std = 3.136592, max. = 27
Simulation 68. In FCQ_5, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 354502, unreachable nodes: mean = 3.648112, std = 3.555571, max. = 29
Simulation 69. In FCQ_5, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 507802, unreachable nodes: mean = 4.281533, std = 3.946938, max. = 30
Simulation 70. In FCQ_5, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 639659, unreachable nodes: mean = 4.973026, std = 4.326895, max. = 30
Simulation 71. In FCQ_6, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 72. In FCQ_6, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 73. In FCQ_6, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 74. In FCQ_6, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 75. In FCQ_6, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 76. In FCQ_6, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 29781, unreachable nodes: mean = 4.392431, std = 5.03028, max. = 44
Simulation 77. In FCQ_6, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 101762, unreachable nodes: mean = 5.170722, std = 5.731939, max. = 55
Simulation 78. In FCQ_6, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 208297, unreachable nodes: mean = 6.041014, std = 6.398268, max. = 55
Simulation 79. In FCQ_6, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 329718, unreachable nodes: mean = 7.004182, std = 7.066707, max. = 54
Simulation 80. In FCQ_6, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 452615, unreachable nodes: mean = 8.075952, std = 7.731268, max. = 56
Simulation 81. In FCQ_7, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 82. In FCQ_7, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 83. In FCQ_7, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 84. In FCQ_7, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 85. In FCQ_7, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 86. In FCQ_7, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 11455, unreachable nodes: mean = 9.289481, std = 10.612614, max. = 83
Simulation 87. In FCQ_7, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 45234, unreachable nodes: mean = 10.293761, std = 11.423996, max. = 102
Simulation 88. In FCQ_7, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 104209, unreachable nodes: mean = 11.589527, std = 12.394696, max. = 107
Simulation 89. In FCQ_7, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 182297, unreachable nodes: mean = 12.936817, std = 13.265848, max. = 105
Simulation 90. In FCQ_7, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 273228, unreachable nodes: mean = 14.442546, std = 14.25681, max. = 112
Simulation 91. In FCQ_8, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 92. In FCQ_8, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 93. In FCQ_8, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 94. In FCQ_8, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 95. In FCQ_8, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 96. In FCQ_8, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 5606, unreachable nodes: mean = 25.329112, std = 27.594944, max. = 174
Simulation 97. In FCQ_8, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 60203, unreachable nodes: mean = 31.030646, std = 31.490845, max. = 194
Simulation 98. In FCQ_8, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 60203, unreachable nodes: mean = 31.030646, std = 31.490845, max. = 194
Simulation 99. In FCQ_8, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 112375, unreachable nodes: mean = 33.938607, std = 33.330429, max. = 221
Simulation 100. In FCQ_8, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 179055, unreachable nodes: mean = 37.328972, std = 35.15072, max. = 217
Simulation 101. In FCQ_9, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 102. In FCQ_9, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 103. In FCQ_9, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 104. In FCQ_9, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 105. In FCQ_9, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 106. In FCQ_9, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 2840, unreachable nodes: mean = 59.961268, std = 62.647367, max. = 364
Simulation 107. In FCQ_9, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 12507, unreachable nodes: mean = 64.938834, std = 64.306362, max. = 366
Simulation 108. In FCQ_9, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 32693, unreachable nodes: mean = 70.232863, std = 67.523311, max. = 413
Simulation 109. In FCQ_9, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 65642, unreachable nodes: mean = 75.456826, std = 70.805765, max. = 427
Simulation 110. In FCQ_9, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 110595, unreachable nodes: mean = 80.824305, std = 73.846062, max. = 442
Simulation 111. In FCQ_10, m = 1, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 112. In FCQ_10, m = 2, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 113. In FCQ_10, m = 3, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 114. In FCQ_10, m = 4, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 115. In FCQ_10, m = 5, randomly generate 1,000,000 instances, number of data broadcast failures = 0, unreachable nodes: mean = 0, std = 0, max. = 0
Simulation 116. In FCQ_10, m = 6, randomly generate 1,000,000 instances, number of data broadcast failures = 1435, unreachable nodes: mean = 134.480836, std = 129.202952, max. = 818
Simulation 117. In FCQ_10, m = 7, randomly generate 1,000,000 instances, number of data broadcast failures = 6901, unreachable nodes: mean = 138.185191, std = 131.173356, max. = 810
Simulation 118. In FCQ_10, m = 8, randomly generate 1,000,000 instances, number of data broadcast failures = 19040, unreachable nodes: mean = 149.028256, std = 136.725477, max. = 840
Simulation 119. In FCQ_10, m = 9, randomly generate 1,000,000 instances, number of data broadcast failures = 40060, unreachable nodes: mean = 157.587544, std = 142.856002, max. = 864
Simulation 120. In FCQ_10, m = 10, randomly generate 1,000,000 instances, number of data broadcast failures = 70071, unreachable nodes: mean = 168.24371, std = 148.278211, max. = 899

Table 1. BSR of fault-tolerant data broadcasting in FLTQn using three EDHCs while 1 <= m <= 10
m 1 2 3 4 5 6 7 8 9 10
FLTQ5       1.000       1.000       1.000       1.000       1.000       0.930       0.796       0.636       0.481       0.348
FLTQ6       1.000       1.000       1.000       1.000       1.000       0.970       0.897       0.790       0.668       0.545
FLTQ7       1.000       1.000       1.000       1.000       1.000       0.989       0.955       0.897       0.820       0.730
FLTQ8       1.000       1.000       1.000       1.000       1.000       0.994       0.976       0.940       0.887       0.822
FLTQ9       1.000       1.000       1.000       1.000       1.000       0.997       0.987       0.967       0.934       0.889
FLTQ10       1.000       1.000       1.000       1.000       1.000       0.999       0.993       0.981       0.960       0.930

Table 2. In FLTQn while 1 <= m <= 10, simulation results of three statistical quantities related to the number of unreachable nodes: means, std and max.

 FLTQ_5 FLTQ_6 FLTQ_7 FLTQ_8 FLTQ_9 FLTQ_10
m Mean Std Max. Mean Std Max. Mean Std Max. Mean Std Max. Mean Std Max. Mean Std Max.
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 2.501208 2.704814 25 4.607591 5.319708 50 9.052424 10.38087 88 25.34864 27.39214 166 58.87428 61.36244 398 135.0266 130.5246 837
7 3.01538 3.152752 29 5.373227 5.928557 55 10.2076 11.2689 95 28.18608 29.44412 193 65.92143 65.69756 373 139.6812 132.6488 817
8 3.59248 3.542302 29 6.277429 6.607425 56 11.44508 12.1411 105 31.08667 31.51491 206 70.07659 67.8441 389 148.2325 137.3174 872
9 4.252342 4.001215 30 7.276742 7.287308 55 12.776 13.06109 106 34.12049 33.29434 219 74.75537 70.45384 417 156.7414 141.6116 859
10 4.966418 4.372772 30 8.369261 7.973092 59 14.20116 13.95579 111 37.43359 35.08539 211 81.08465 73.72333 420 167.0739 147.4038 914

Table 3. BSR of fault-tolerant data broadcasting in FCQn using three EDHCs while 1 <= m <= 10
m 1 2 3 4 5 6 7 8 9 10
FCQ5       1.000       1.000       1.000       1.000       1.000       0.933       0.802       0.645       0.492       0.360
FCQ6       1.000       1.000       1.000       1.000       1.000       0.970       0.898       0.792       0.670       0.547
FCQ7       1.000       1.000       1.000       1.000       1.000       0.989       0.955       0.896       0.818       0.727
FCQ8       1.000       1.000       1.000       1.000       1.000       0.994       0.940       0.940       0.888       0.821
FCQ9       1.000       1.000       1.000       1.000       1.000       0.997       0.987       0.967       0.934       0.889
FCQ10       1.000       1.000       1.000       1.000       1.000       0.999       0.993       0.981       0.960       0.930

Table 4. In FCQn while 1 <= m <= 10, simulation results of three statistical quantities related to the number of unreachable nodes: means, std and max.

 FCQ_5 FCQ_6 FCQ_7 FCQ_8 FCQ_9 FCQ_10
m Mean Std Max. Mean Std Max. Mean Std Max. Mean Std Max. Mean Std Max. Mean Std Max.
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 2.576503 2.703212 24 4.392431 5.03028 44 9.289481 10.61261 83 25.32911 27.59494 174 59.96127 62.64737 364 134.4808 129.203 818
7 3.072983 3.136592 27 5.170722 5.731939 55 10.29376 11.424 102 31.03065 31.49085 194 64.93883 64.30636 366 138.1852 131.1734 810
8 3.648112 3.555571 29 6.041014 6.398268 55 11.58953 12.3947 107 31.03065 31.49085 194 70.23286 67.52331 413 149.0283 136.7255 840
9 4.281533 3.946938 30 7.004182 7.066707 54 12.93682 13.26585 105 33.93861 33.33043 221 75.45683 70.80577 427 157.5875 142.856 864
10 4.973026 4.326895 30 8.075952 7.731268 56 14.44255 14.25681 112 37.32897 35.15072 217 80.82431 73.84606 442 168.2437 148.2782 899