Termination detection

1. Termination detection During the progress of a distributed computation, processes may periodically turn active or passive. A distributed computation termination when: (a) every process is passive, (b) all channels are empty, and (c) the global state satisfies the desired postcondition

2. Visualizing diffusing computation initiator active passive Notice how one process engages another process. Eventually all processes turn white, and no message is in transit -this signals termination. How to develop a signaling mechanism to detect termination?

3. An initiator initiates termination detection by sending signals (messages) down the edges via which it engages other nodes. At a “suitable time,” the recipient sends an ack back. When the initiator receives ack from every node that it engaged, it detects termination. Node j engages node k. Dijkstra-Scholten algorithm The basic scheme j k signal j k j k ack

4. Deficit (e) = # of signals on edge e - # of ack on edge e For any node, C = total deficit along incoming edges and D = total deficit along outgoing edges edges For the initiator, by definition, C = 0 Dijkstra-Scholten algorithm used the following two Invariants to develop their algorithm: Invariant 1. (C ≥ 0)  (D ≥ 0) Invariant 2. (C > 0)  (D = 0) Dijkstra-Scholten algorithm 0 1 2 3 4 5

5. The invariants must hold when an interim node sends an ack. So, acks will be sent when (C-1 ≥ 0)  (C-1 > 0 D=0) {follows from INV1 and INV2} = (C > 1)  (C ≥1  D=0) = (C > 1) (C =1  D=0) Dijkstra-Scholten algorithm 0 1 2 3 4 5

6. program detect {for an internal node i} initially C=0, D=0, parent = i do m = signal  (C=0)  C:=1; state:= active; parent := sender {this node can send out messages to engage other nodes, or turn passive} m = ack  D:= D-1 (C=1 D=0)  state = passive  send ack to parent; C:= 0; parent := i m = signal  (C=1) send ackto the sender; od Dijkstra-Scholten algorithm 0 1 2 3 4 5 Note that the engaged nodes induce a spanning tree

7. Distributed deadlock Assume each process owns a few resources, and review how resources are allocated. Why deadlocks occur? - Exclusive (i.e not shared) resources - Non-preemptive scheduling - Circular waiting by all or a subset of processes

8. Distributed deadlock Three aspects of deadlock • deadlockdetection • deadlock prevention • deadlock recovery

9. Distributed deadlock • May occur due to bad designs/bad strategy [Sometimes prevention is more expensive than detection and recovery. So designs may not care about deadlocks, particularly if it is rare.] • Caused by failures or perturbations in the system

10. Represents who waits for whom. No single process can see the WFG. Review how the WFG is formed. Wait-for Graph (WFG)

11. Resource deadlock [R1 AND R2 AND R3 …] also known as AND deadlock Communication deadlock [R1 OR R2 OR R3 …] also known as OR deadlock Another classification

12. Notations w(j) = true  (j is waiting) depend [j,i] = true j  succn(i) (n>0) P(i,s,k) is a probe (i=initiator, s= sender, r=receiver) Detection of resource deadlock 2 1 3 4 P(4,4,3) initiator

13. {Program for process k} do P(i,s,k) received  w[k]  (k ≠ i) ¬ depend[k, i]  send P(i,k,j) to each successor j; depend[k, i]:= true P(i,s, k) received w[k]  (k = i) process k is deadlocked od Detection of resource deadlock

14. To detect deadlock, the initiator must be in a cycle Message complexity = O(|E|) (edge-chasing algorithm) Observations E=set of edges Should the links be FIFO?

15. Communication deadlock This has a resource deadlock but no communication deadlock

16. A process ignores a probe, if it is not waiting for any process. Otherwise, first probe mark the sender as parent; forwards the probe to successors Not the first probe Send ack to that sender ack received from every successor send ack to the parent Communication deadlock is detected if the initiator receives ack. Detection of communication deadlock Has many similarities with Dijkstra-Scholten’s termination detection algorithm