1. IS 651: Distributed Systems HW3
Sisi Duan
Assistant Professor
Information Systems

2. HW3 Q1. Why E1->E10 and E8||E9?
Definition (->): We define e->e’ if…
Logical ordering: e->e’ if e->e’ for any process I
Messages: send (m) -> receive (m) for any message m
Transitivity: e->e’‘ if e->e’ and e’->e’’

3. HW3 Three rules: At process i, increment Li before each event
To send a message m at process i, apply rule 1 and then include the current local time in the message: i.e., send(m,Li)
To receive a message (m,t) at process j, set Lj = max(Lj,t) and then apply rule 1 before time-stamping the receive event
Alice sends sync request to Bob
Bob receives sync request from Alice
Alice sends sync request to Carol
Bob sends sync acknowledgment to Alice
Bob sends sync request to Carol
Carol receives sync request from Bob
Alice receives sync acknowledgment from Bob
Carol sends sync acknowledgment to Bob
Carol receives sync request from Alice
Bob receives sync acknowledgment from Carol
Carol sends sync acknowledgment to Alice
Alice receives sync acknowledgment from Carol
Alice combines the results and sends the final report to Bob
Alice sends final report to Carol
Carol receives final report from Alice
Bob receives final report from Alice

4. HW3
Q3.B. Sequential consistency does not admit a scalable implementation because it requires a total ordering of all operations in the system. 
Q3.E. Sequential consistency is sufficient to guarantee that an airline never overbooks its seats when multiple clients reserve seats on the same airplane.

5. HW3
Q3.C. Obeying all causal orderings is sufficient to guarantee convergence of state maintained by multiple replicas. 
Q3.D. Causal consistency is sufficient to guarantee that an airline never overbooks its seats when multiple clients reserve seats on the same airplane. 
Q3.A. Sequential consistency guarantees causal ordering. 
In shared memory scenario, I think it’s true. But this is not always true.

6. Causal order vs Total order in the broadcast scenario
[Lamport, Comm. ACM 1978]
[Lamport, Distrib. Comput. 1986]
Causal order
If the broadcast of message m1 "happens before" or "causally precedes" the broadcast of message m2, then no correct process delivers m2 before it delivers m1.
m1 “Chase charges 10%!”
m2 “That is outrageous!”

7. Causal order vs Total order in the broadcast scenario✓
Causal order
Chase:
“Charge 10%”
Outrageous!
$100
$90
Chase:
“Charge 10%”
Outrageous!
$100
$90
$100

8. Causal order vs Total order in the broadcast scenario✘
Causal order
Chase:
“Charge 10%”
Outrageous!
$100
$100
$90
Chase:
“Charge 10%”
Outrageous!
$100
$90
$90
$100

9. Causal order vs Total order in the broadcast scenario✓ ✘
Causal order Total order
Chase:
“Charge 10%”
Client 1:
“Deposit $100”
Outrageous!
$100
$90
$190
Client 1:
“Deposit $100”
Chase:
“Charge 10%”
Outrageous!
$100
$200
$180
$100

10. Causal order vs Total order in the broadcast scenario✘ ✓
Causal order Total order
Chase:
“Charge 10%”
Outrageous!
$100
$100
$90
Chase:
“Charge 10%”
Outrageous!
$100
$100
$90
$100

11. Causal order vs Total order in the broadcast scenario✓ ✓
Causal order Total order
Chase:
“Charge 10%”
Client 1:
“Deposit $100”
Outrageous!
$100
$90
$190
Chase:
“Charge 10%”
Client 1:
“Deposit $100”
Outrageous!
$100
$90
$190
$100