11. Suppose a multicast group currently is participated by two processes: P1 and P2. Suppose P1 multicasts m11 then m12, P2 multicasts m21 then m22.

a. How many different orders can all the messages be delivered to each process?

For both P1 , and P2 since there is no relation between all messages, we have 4! = 24 possible orders. However if e consider that each process has knowledge of the order of its own messages then P1 will always get m11 before m12, thus the delivery order will be reduced by 2! 4!/2! = 12 and the same argument applies to P2.

b. How many different orders can all four messages be delivered to each process if the messages are causally related as m11 -> m21 -> m12 -> m22

Now we are reduced to 1 order: m11, m21, m12, m22

c. What are the possible orders of message delivery to each process if the multicast is (i) FIFO, (ii) causal, and (iii) atomic?

The two partial orders (i) m11 then m12 and (ii) m21 then m22 must be preserved for FIFO, and the messages must be delivered to each process in the same order, which can be any one of the 4!/ (2! * 2!) = 24/4 = 6. Another way to think about this: m11 must be delivered before m12, and m21 must be delivered before m22. The two series can interleave with each other, however. Hence the possible orders are:

m11, m12, m21, m21 m11, m21, m12, m21 m11, m21, m21, m12 m21, m11, m12, m21, m21, m11, m21, m12 m21, m21, m11, m12

d. What are the possible orders of message delivery to each process if the messages are causally related as m11 -> m21 -> m12 -> m22 and the multicast is (i) FIFO, (ii) causal, and (iii) atomic?

Please answer this question.