ECE428 Homework 2 FIFO channels solution


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Question 1: The only things guaranteed in life are FIFO channels [20 points]
Consider a system with pair-wise FIFO communication channels. Explain, which of the ordering
properties – FIFO, causal, and/or total ordering – will be satisfied in the following four scenarios. For
each ordering property, either explain (in one or two sentences) why it will be satisfied, or provide a
counter-example, for example, using a diagram. The same counter-example can be used for
different scenarios. For B-multicast over FIFO channels, explain whether and why it automatically
satisfies causal ordering, or provide a counterexample.
(a)B-multicast in a situation where there are no process failures;
(b)R-multicast in a situation where there are no process failures;
(c) R-multicast in a situation where process failures may occur;
(d)The sequence number-based FIFO multicast algorithm discussed in class.
Questions 2-4 are on the next pages.
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Question 2: You’re out of order! This whole trial is out of order! [18 points]
(6) (a) Consider the event diagram above. To assure the FIFO multicast delivery order, which
messages will have to be delayed in a holdback buffer? For these messages, what is
the earliest point at which they can be delivered? For simplicity, assume that messages
multicast are self-delivered at the sending process instantaneously.
(6) (b) Consider the same diagram, but now suppose we wanted to assure a causal multicast
delivery order. Which messages would have to be delayed?
(6) (c) Still considering the same diagram, assume ISIS total ordering has been used. For
every message and process, write down the process’s proposed priority for the
message, and what the final priority for the message will be. Assume that no other
messages have been seen, and the proposed priorities all start at 1. It can be also
assumed that reply messages with their proposed priorities get delivered after time 17.
Question 3: Trickle-up Multicast [7 points]
Consider an R-multicast algorithm running in a multicast group of 100 nodes.
(2) (a) How many copies of a message will be sent at each multicast?
(2) (b) The R-multicast was modified, so that upon receiving a multicast request, the remulticast is sent only to the higher-numbered processes, as indicated in this Python
implementation on the next page:
Page 3
How many messages will be sent using this modification at each multicast?
(3) (c) Change the Python code above to guarantee a reliable delivery. Assume that once the
call to unicast() returns, the message will always be delivered to the recipient, even if
the sender may later crash. The proposed code modification should send the same
number of messages as the original code given in part (b).
Question 4: There’s Only Room for One Sheriff in This Critical Section [15 points]
Consider the following table of processes, which lists at what time (since the system starts) the
processes request to enter a critical section by calling enter, and how long each process spends in
a critical section after it is admitted:
Process Time critical section Time spent in
is requested critical section
P3 10 ms 20 ms
P2 15 ms 10 ms
P1 20 ms 15 ms
P4 25 ms 30 ms
P5 40 ms 25 ms
(5) (a) Suppose that mutual exclusion is managed by a central server algorithm, with P1 being
the leader. In this system, assume a one-way delay of 8 ms between any pair of
processes. Note that P1’s messages to itself for requesting/granting/releasing critical
section access take a negligible time (0 ms). List what time each process enters the
critical section. You may want to include a diagram for a partial credit.
(5) (b) Suppose now that the processes are in a token ring, with the following structure:
P1 ž P4 ž P2 ž P3 ž P5 ž P1
Assume that at time 0 ms, the token is at P1, and one-way delay between any
processes is 8 ms. When would each process enter its critical section?
(5) (c) Assume now that the processes are using Ricart-Agrawala mutual exclusion. Assuming
again a one-way delay of 8 ms, when will each process enter the critical section? All
processes’ local Lamport timestamps are set to 0 at time 0 ms, and no messages other
than those used in the Ricart-Agrawala exclusion are sent between any processes.