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lynch

Implement algorithms from Nancy Lynch's Distributed Algorithms book, in Erlang.

runtime

The runtime library defines a framework for testing algorithms. It is in its very early stages, and currently only supports synchronous ring topologies.

1> application:start(runtime).
ok
2> runtime:run(lcr, 3).
ok
3> runtime:crank(verbose).
Round: 0
Proc #1 (291147458) will send 291147458 (status unknown)
Proc #2 (388349957) will send 388349957 (status unknown)
Proc #3 (486716090) will send 486716090 (status unknown)

ok
4> runtime:crank(verbose).
Round: 1
Proc #1 (291147458) will send 486716090 (status unknown)
Proc #2 (388349957) will send null (status unknown)
Proc #3 (486716090) will send null (status unknown)

ok
5> runtime:crank(verbose).
Round: 2
Proc #1 (291147458) will send 486716090 (status unknown)
Proc #2 (388349957) will send 486716090 (status unknown)
Proc #3 (486716090) will send null (status unknown)

I'm the leader: 3/486716090
ok
6> runtime:crank(verbose).
Algorithm has reached a stopping point
Stopped: stop
ok

The runtime application defines crank/{0,1} functions which "turn the crank" on the processes, moving the round (as defined in Lynch's synchronous algorithms) forward each time. crank(verbose) will print a status dump before executing the round.

runtime:autocrank() can be used instead of repeatedly turning the crank. It will optionally take a boolean verbose argument to mirror crank/{0,1}.

The process module defines a process behavior for the algorithm to leverage.

Application flow

  1. When application:start(runtime) is invoked a supervisor and runtime process will launch.
  2. runtime:run(Algorithm, <n>) will spawn n processes with the specified algorithm module.
  3. runtime:crank/{0,1} or runtime:autocrank/0 will start the synchronous network spinning.
  4. runtime will call process:start_round/2 for each algorithm process at each turn of the crank.
  5. Each algorithm process will call Algorithm:step/2, which will return stop, continue, or messages; in the last case, a list of messages with routing information will be stored in the process state for later retrieval and delivery
  6. If any process returns stop via start_round, the runtime will end the algorithm.
  7. If the algorithm is not yet complete, runtime will call process:retrieve_messages for each algorithm process for a list of messages to deliver.
  8. Between retrieve_messages calls each batch of returned messages is sent via process:message and Algorithm:handle_message to the appropriate destination; if any of those messages results in a stop response, the runtime will end the algorithm after that batch has been fully delivered.

Results

runtime:info/0 will return the runtime state, which includes

  • Number of rounds executed so far
  • Number of messages sent
  • Number of processes
  • Whether the running algorithm (if any) has reached a point of completion

info/0 is invoked as the last act of autocrank/{0,1}.

Complexity analysis

Algorithm modules can optionally define complexity/2 to return time and communications complexity estimates.

For example, the LCR algorithm defines it as such:

complexity(time, N) ->
    2 * N;
complexity(msgs, N) ->
    N*N.

If the module defines these, runtime:complexity() can be invoked after a run. In the example below, LCR estimated 2000 rounds, with only 1000 executed, and 1,000,000 messages, with only 7238 sent. One might question either my LCR implementation or Lynch's complexity analysis.

9> runtime:complexity().
"Time: 2000 > 1000 / Msgs: 1000000 > 7238"

This is still quite raw; currently runtime:complexity/0 will crash if the algorithm module doesn't define complexity/2, or if the algorithm hasn't been executed yet.