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CPSC 668 Distributed Algorithms and Systems

This set focuses on tools and abstractions for simplifying the design of distributed algorithms through problem specifications and implementations (simulations). Learn how to specify problems and model communication systems effectively.

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CPSC 668 Distributed Algorithms and Systems

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  1. CPSC 668Distributed Algorithms and Systems Fall 2009 Prof. Jennifer Welch Set 14: Simulations

  2. Motivation • Next section of the course focuses on tools and abstractions for simplifying the design of distributed algorithms. • To approach this rigorously, we need to treat specifications and implementations (a.k.a. "simulations") more generally. Set 14: Simulations

  3. Problem Specifications So Far • Approach so far has been problem-specific: • put conditions on processor states as they relate to each other and to initial states • for example: consensus, leader election, etc. • Not so convenient when we want to study simulations from one system model to another, with respect to arbitrary problems Set 14: Simulations

  4. New Way to Specify Problems A problem specification consists of • an interface • set of inputs and • set of outputs • and a set of allowable sequences of inputs and outputs This is how users of a solution to the problem communicate with the solution. Set 14: Simulations

  5. A New Way to Specify Problems P outputs inputs Set 14: Simulations

  6. Mutual Exclusion Example • inputs: • T0, …, Tn-1 • Ti indicates pi wants to try to enter the critical section • E0,…, En-1 • Eiindicates pi wants to exit the critical section • outputs: • C0,…,Cn-1 • Ci indicates pi may now enter the critical section • Ri,…,Rn-1 • Ri indicates pi may now enter the remainder section Set 14: Simulations

  7. Mutual Exclusion Example p1 T1 C1 E1 R1 T2 Mutual Exclusion T0 C2 C0 p2 E2 p0 E0 R2 R0 Set 14: Simulations

  8. Mutual Exclusion Example (cont'd) • a sequence  of inputs and outputs is allowable iff, for each i, • |i cycles through Ti, Ci, Ei, Ri • each proc cycles through trying, critical, exit, and remainder sections in that order • whenever Cioccurs, most recent preceding input or output for any j ≠ i is not Cj • only one process is in the critical section at a time Set 14: Simulations

  9. Mutual Exclusion Example (cont'd) • T1T2 C1T3 E1C3 R1E3 R3 • allowable • T1T2 C1T3C3 E1 R1E3 R3 • not allowable Set 14: Simulations

  10. Communication Systems So Far • So far, we have explicitly modeled the communication system • inbuf and outbuf state components and deliver events for message passing, • explicit shared variables as part of configurations for shared memory • Not so convenient when we want to study how to provide one kind of communication in software, given another kind. Set 14: Simulations

  11. Different Kinds of Communication Systems • Message passing vs. shared memory • different interfaces (sends/receives vs. invocations/responses) • Within message passing: • different levels of reliability, ordering • different guarantees on content (when malicious failures are possible) • Within shared memory: • different shared variable semantics Set 14: Simulations

  12. What Kinds of Simulations? • How to provide broadcast (with different reliability and ordering guarantees) on top of point-to-point message passing • How to provide shared objects on top of message passing • How to provide one kind of shared objects on top of another kind • How to provide stronger synchrony on top of an asynchronous system • How to provide better-behaved faulty processors on top of worse-behaved ones Set 14: Simulations

  13. New Way to Model Communication Systems • Interpose a communication system between the processors • A particular type of communication system is specified using the approach just described • focus on the desired behavior of the communication system, as observed at its interface, instead of the details of how that behavior is provided Set 14: Simulations

  14. Asynchronous Point-to-Point Message Passing Example Interface is: • inputs: sendi(M) • models pisending set of msgs M • each msg indicates sender and recipient (must be consistent with assumed topology) • outputs: recvi(M) • models pi receiving set of msgs M • each msg in M must have pi as its recipient Set 14: Simulations

  15. Asynch MP Example (cont'd) • For a sequence of inputs and outputs (sends and receives) to be allowable, there must exist a mapping  from the msgs in recv events to msgs in send events s.t. • each msg in a recv event is mapped to a msg in a preceding send event •  is well-defined: every msg received was previously sent (no corruption or spurious msgs) •  is one-to-one: no duplicates •  is onto: every msg sent is received Set 14: Simulations

  16. Asynchronous Broadcast Example • Inputs: bc-sendi(m) • an input to the broadcast service • pi wants to use the broadcast service to send m to all the procs • Outputs:bc-recvi(m,j) • an output of the broadcast service • broadcast service is delivering msg m, sent by pj, to pi Set 14: Simulations

  17. Asynch Bcast Example (cont'd) • A sequence of inputs and outputs (bc-sends and bc-recvs) is allowable iff there exists a mapping  from each bc-recvi(m,j) event to an earlier bc-sendj(m) event s.t. •  is well-defined: every msg bc-recv'ed was previously bc-sent •  restricted to bc-recvi events, for each i, is one-to-one: no msg is bc-recv'ed more than once at any single proc. •  restricted to bc-recvi events, for each i, is onto: every msg bc-sent is received at every proc. Set 14: Simulations

  18. Processes • Running on each processor will be a piece of code (process) to simulate the desired communication system. • No longer accurate to identify "the algorithm" with the processor, because there may be several algorithms (processes) running on the same processor. For example: • one process (algorithm) that uses the broadcast service • another process (algorithm) that implements the broadcast service on top of a point-to-point MP system Set 14: Simulations

  19. modeled as a problem spec (interface & allowable sequences) layer 1 layer 2 layer 3 communicate via appropriate primitives: shared events modeled as a problem spec (interface & allowable sequences) Modeling Process Stack at a Node environment modeled as state machines communication system Set 14: Simulations

  20. Intra-Node Communication Pattern • Activity is initiated by a node input (input coming in from environment on top or communication system at bottom) • Triggers some activity at the top (or bottom) layer, which in turn can trigger some activity at the layer above or below • Chain reaction can continue for some time but must eventually die out • All activity at one node, in response to a single node input, is assumed to execute atomically (w.r.t. other nodes) Set 14: Simulations

  21. Definition of Execution Sequence C0 e1 C1 e2 C2 … of alternating configurations and events s.t. • C0 is an initial configuration • event ei is enabled in Ci-1(there is a transition from the state(s) of the relevant process(es) in Ci-1 labeled ei) • state components of processes change according to the transition functions for ei • can chop the execution into pieces so that • each piece starts with a node input • all events in each piece occur at the same node • the next node input does not occur until no events (other than node inputs) are enabled Set 14: Simulations

  22. Definition of Admissible Execution • We only require an algorithm to be correct if • each process is given enough opportunities to take steps (called fairness) • the communication system behaves "properly" and • the environment behaves "properly" • Executions satisfying these conditions are admissible. Set 14: Simulations

  23. Proper Behavior of Communication System • The restriction of the execution to the events of the interface at the "bottom of the stack" is an allowable sequence for the problem specification corresponding to the underlying communication system • Example: message passing, every message sent is eventually received Set 14: Simulations

  24. Proper Behavior of Environment • The environment (user) interacts "properly" with the top layer of the stack (through the interface events) as long as the top layer is also behaving properly. • Mutex example: the user only requests to leave the critical section if it is currently in the critical section. Set 14: Simulations

  25. Simulations System C1simulates system C2 if there is a set of processes, one per node, called Sim s.t. • top interface of Sim is the interface of C2 • bottom interface of Sim is the interface of C1 • For every admissible execution  of Sim, the restriction of  to the interface of C2 is allowable for C2 (according to its problem spec). Set 14: Simulations

  26. Simulations C2 inputs C2 outputs C2 inputs C2 outputs C2 Sim … Sim0 Simn-1 C1 inputs C1 outputs C1 inputs C1 outputs C1 If user of C2 behaves properly and if C1 behaves properly, then Sim ensures that user of C2 thinks it is really using C2 (and not C1 plus a simulation layer) Set 14: Simulations

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