Section 3: Action Invariants Deduced From Cycles

In this section, we present results obtained from recognizing if a state is reached again.Which actions have to occur how often yields vectors that are considered invariants since they leave the state of the model unchanged.Traces often generate large numbers of such vectors such that we will only consider a subset of vectors that are linearly independent.Actions that do not contribute to invariants are likely to represent irregular or faulty behavior such that we list those actions separately and upfront.

List of actions that are not present in the set of invariants

Link connecting node 0 to node 1 went down(0L1_DOWN)
Link connecting node 0 to node 1 went online(0L1_UP)
Link connecting node 1 to node 2 went down(1L2_DOWN)
Link connecting node 1 to node 2 went online(1L2_UP)
Link connecting node 2 to node 3 went down(2L3_DOWN)
Link connecting node 2 to node 3 went online(2L3_UP)
Link connecting node 3 to node 4 went down(3L4_DOWN)
Link connecting node 3 to node 4 went online(3L4_UP)
Link connecting node 4 to node 5 went down(4L5_DOWN)
Link connecting node 4 to node 5 went online(4L5_UP)
Link connecting node 5 to node 6 went down(5L6_DOWN)
Link connecting node 5 to node 6 went online(5L6_UP)
Link connecting node 6 to node 0 went down(6L0_DOWN)
Link connecting node 6 to node 0 went online(6L0_UP)
Node 4 dropped packet to node 3(node4_d_node3)
Node 4 dropped packet to node 5(node4_d_node5)
Node 4 up(node4_UP)
Node 4 down(node4_DOWN)
Node 0 dropped packet to node 1(node0_d_node1)
Node 0 dropped packet to node 6(node0_d_node6)
Node 0 up(node0_UP)
Node 0 down(node0_DOWN)
Node 5 dropped packet to node 4(node5_d_node4)
Node 5 dropped packet to node 6(node5_d_node6)
Node 5 up(node5_UP)
Node 5 down(node5_DOWN)
Node 1 dropped packet to node 0(node1_d_node0)
Node 1 dropped packet to node 2(node1_d_node2)
Node 1 up(node1_UP)
Node 1 down(node1_DOWN)
Node 6 dropped packet to node 5(node6_d_node5)
Node 6 dropped packet to node 0(node6_d_node0)
Node 6 up(node6_UP)
Node 6 down(node6_DOWN)
Node 2 dropped packet to node 1(node2_d_node1)
Node 2 dropped packet to node 3(node2_d_node3)
Node 2 up(node2_UP)
Node 2 down(node2_DOWN)
Node 3 dropped packet to node 2(node3_d_node2)
Node 3 dropped packet to node 4(node3_d_node4)
Node 3 up(node3_UP)
Node 3 down(node3_DOWN)
Packet hopping from node 0 to node 1(node0_h_0L1)
Node 0 receiving packet from node 1(node0_r_0L1)
Packet hopping from node 1 to node 0(node1_h_0L1)
Node 1 receiving packet from node 0(node1_r_0L1)
Packet hopping from node 1 to node 2(node1_h_1L2)
Node 1 receiving packet from node 2(node1_r_1L2)
Packet hopping from node 2 to node 1(node2_h_1L2)
Node 2 receiving packet from node 1(node2_r_1L2)
Packet hopping from node 2 to node 3(node2_h_2L3)
Node 2 receiving packet from node 3(node2_r_2L3)
Packet hopping from node 3 to node 2(node3_h_2L3)
Node 3 receiving packet from node 2(node3_r_2L3)
Packet hopping from node 3 to node 4(node3_h_3L4)
Node 3 receiving packet from node 4(node3_r_3L4)
Packet hopping from node 4 to node 3(node4_h_3L4)
Node 4 receiving packet from node 3(node4_r_3L4)
Packet hopping from node 4 to node 5(node4_h_4L5)
Node 4 receiving packet from node 5(node4_r_4L5)
Packet hopping from node 5 to node 4(node5_h_4L5)
Node 5 receiving packet from node 4(node5_r_4L5)
Packet hopping from node 5 to node 6(node5_h_5L6)
Node 5 receiving packet from node 6(node5_r_5L6)
Packet hopping from node 6 to node 5(node6_h_5L6)
Node 6 receiving packet from node 5(node6_r_5L6)
Packet hopping from node 6 to node 0(node6_h_6L0)
Node 6 receiving packet from node 0(node6_r_6L0)
Packet hopping from node 0 to node 6(node0_h_6L0)
Node 0 receiving packet from node 6(node0_r_6L0)

Set of linearly independent action invariants

Invariant 1:

Action	Value
Node 0 enqueued packet to node 1(node0_+_node1)	1
Total	1

Invariant 2:

Action	Value
Node 0 dequeued packet to node 1(node0_-_node1)	1
Total	1

Invariant 3:

Action	Value
Node 0 enqueued packet to node 6(node0_+_node6)	1
Total	1

Invariant 4:

Action	Value
Node 0 dequeued packet to node 6(node0_-_node6)	1
Total	1

Invariant 5:

Action	Value
Node 2 enqueued packet to node 1(node2_+_node1)	1
Total	1

Invariant 6:

Action	Value
Node 2 dequeued packet to node 1(node2_-_node1)	1
Total	1

Invariant 7:

Action	Value
Node 2 enqueued packet to node 3(node2_+_node3)	1
Total	1

Invariant 8:

Action	Value
Node 2 dequeued packet to node 3(node2_-_node3)	1
Total	1

Invariant 9:

Action	Value
Node 1 enqueued packet to node 0(node1_+_node0)	1
Total	1

Invariant 10:

Action	Value
Node 1 dequeued packet to node 0(node1_-_node0)	1
Total	1

Invariant 11:

Action	Value
Node 1 enqueued packet to node 2(node1_+_node2)	1
Total	1

Invariant 12:

Action	Value
Node 1 dequeued packet to node 2(node1_-_node2)	1
Total	1

Invariant 13:

Action	Value
Node 6 enqueued packet to node 0(node6_+_node0)	1
Total	1

Invariant 14:

Action	Value
Node 6 dequeued packet to node 0(node6_-_node0)	1
Total	1

Invariant 15:

Action	Value
Node 6 enqueued packet to node 5(node6_+_node5)	1
Total	1

Invariant 16:

Action	Value
Node 6 dequeued packet to node 5(node6_-_node5)	1
Total	1

Invariant 17:

Action	Value
Node 3 enqueued packet to node 2(node3_+_node2)	1
Total	1

Invariant 18:

Action	Value
Node 3 dequeued packet to node 2(node3_-_node2)	1
Total	1

Invariant 19:

Action	Value
Node 3 enqueued packet to node 4(node3_+_node4)	1
Total	1

Invariant 20:

Action	Value
Node 3 dequeued packet to node 4(node3_-_node4)	1
Total	1

Invariant 21:

Action	Value
Node 5 enqueued packet to node 4(node5_+_node4)	1
Total	1

Invariant 22:

Action	Value
Node 5 dequeued packet to node 4(node5_-_node4)	1
Total	1

Invariant 23:

Action	Value
Node 5 enqueued packet to node 6(node5_+_node6)	1
Total	1

Invariant 24:

Action	Value
Node 5 dequeued packet to node 6(node5_-_node6)	1
Total	1

Invariant 25:

Action	Value
Node 4 enqueued packet to node 3(node4_+_node3)	1
Total	1

Invariant 26:

Action	Value
Node 4 dequeued packet to node 3(node4_-_node3)	1
Total	1

Invariant 27:

Action	Value
Node 4 enqueued packet to node 5(node4_+_node5)	1
Total	1

Invariant 28:

Action	Value
Node 4 dequeued packet to node 5(node4_-_node5)	1
Total	1