Global Virtual Time Wallclock time T (GVT t ) during the execution of - PDF document

Global Virtual Time Wallclock time T (GVT t ) during the execution of a Time Warp simulation is defined as the minimum time stamp among all unprocessed and partially Advanced Simulation processed messages and anti-messages in the system at wall-clock T. PDES: Time Warp Mechanism Distributed Snapshots and Fossil Collection 2 Maria Hybinette, UGA Maria Hybinette, UGA Outline Review: Samadi � s Algorithm ● Consistent Cuts ● Transient message problem: » Cut points » Solution: Message acknowledgements » Cut messages ● Simultaneous message problem: » Cut values » Solution: Mark acknowledgements sent after reporting local minimum ● Mattern � s GVT Algorithm » Caveat: Just message acks are not enough (marked » Colors message acks are needed). » Vector counters ● Overhead: » Pipelined algorithm » Message acknowledgments: ● Fossil Collection – Message acknowledgment for ● Thursday: We will do an additional example ● each message and using Mattern’s Algorithms to determine GVT. ● anti-message. 3 4 Maria Hybinette, UGA Maria Hybinette, UGA Consistent Cuts Mattern’s Algorithm Cut point: Cut: ● Asynchronous Cut message: » Executes in background concurrent with time warp Consistent cut: execution (does not require the simulation to � freeze � (i.e., block the LPs). cut ● Avoids message acknowledgements LP 4 message ● Approach: Based on techniques for creating LP 3 Past distributed snapshots (consistent cut) LP 2 » We will see what it means to be a consistent cut Future LP 1 wallclock time » Can some asynchronous algorithms compute GVT(t)? » What about synchronous algorithms? Cut value: 5 Maria Hybinette, UGA

Consistent Cuts Consistent Cuts Cut point: an instant dividing computation into past and future Cut point: an instant dividing computation into past and future Cut: Cut: set of cut points, one per processor Cut message: Cut message: Consistent cut: Consistent cut: cut cut LP 4 LP 4 message message LP 3 LP 3 Past Past LP 2 LP 2 Future Future LP 1 LP 1 wallclock time wallclock time Cut value: Cut value: Consistent Cuts Consistent Cuts Cut point: an instant dividing computation into past and future Cut point: an instant dividing computation into past and future Cut: set of cut points, one per processor Cut: set of cut points, one per processor Cut message: a message that was sent in the past, and received in the future Cut message: a message that was sent in the past, and received in the future Consistent cut: Consistent cut: a cut where all messages crossing the cut are cut messages cut cut LP 4 LP 4 message message LP 3 LP 3 Past Past LP 2 LP 2 Future Future LP 1 LP 1 wallclock time wallclock time Cut value: Cut value: Consistent Cuts Cuts: Divides Past and Future Cut point: an instant dividing computation into past and future cut LP 4 message Cut: set of cut points, one per processor LP 3 Past Cut message: a message that was sent in the past, and received in the future LP 2 Consistent cut: a cut where all messages crossing the cut are cut messages Future LP 1 wallclock time cut LP 4 message ● Consistent Cuts: Includes local state at its cut-point & all its LP 3 transient messages. Past ● Observation: Time stamp of a message sent after a cut point at LP 2 wallclock time T must be at least as large as the minimum of: Future » the smallest time stamp of any unprocessed event in the processor at LP 1 time T » the smallest time stamp of any message received by the processor wallclock time after time T. Cut value: minimum among (1) local minimum of each LP at its cut point and ● GVT must be smaller than or equal to both of these quantities (2) time stamp of cut messages

Observation 1 Observation 2 Asynchronous execution Execution, each LP blocks at cut point LP 4 cut T 1 > Y T 1 T 3 message LP 4 T 2 Z LP 4 T 2 > min( Y, U ) Z LP 3 Y T 3 > min( Y, U, S ) idle Past LP 3 S Y LP 3 Y Y S > X, so LP 2 X T 3 > min( Y, U, X ) U LP 2 X LP 2 X Future LP 1 (Cut value ≤ X, Y, U) U U V V LP 1 LP 1 W W idle wallclock time Wallclock time Any message crossing cut from future to past must have a T Cut value GVT(T) time stamp > the cut value, so they can be ignored when = min( W, X, Y, Z ,U ,V ) = min ts ∀ unprocessed message @ T computing the cut value = min( W, X, Y, Z , U, V ) Message generated by an LP after its cut point must have time ● Cut value equal to GVT(T) using synchronous GVT algorithm stamp greater than the minimum of (freeze LPs: no new computations nor message sends/receives). » The LP � s local minimum at its cut point » Events generated after cut have time stamp > cut value » The time stamp of messages received after the cut point ● Cut value can be used as a GVT value Mattern � s GVT Algorithm Algorithm Overview Challenge: accounting for cut messages LP 4 LP 4 LP 3 cut point LP 3 cut point LP 2 LP 2 LP 1 Wallclock time C1 C2 LP 1 Wallclock time C1 C2 Approach : ● The first cut: ● Construct two cuts C1, C2, approximate cut value along C2 » Changes color of each process (green to red) » Organize processes in ring, pass token around ring » Determine number of green messages sent to each process ● Ensure no message that crosses C1 also cross C2 ● The second cut: » Color LPs, change LP color at each cut point » Color (green/red) each message to that of LP sending message » Each process makes sure all green messages sent to it (message tag) have been received before laying down a cut point » Maintain send/receive message counters » Compute global minimum (GVT value) ● GVT = min( local min along C2, time stamp of red messages ) Example: Vector Counters How does an LP know it has received all its green messages? LP 4 LP 4 LP 3 LP 3 cut point cut point LP 2 LP 2 LP 1 LP 1 Wallclock time Wallclock time C1 C2 C1 C2 ● LP i maintains vector V i [1:N] , where N = #LPs Vector counters for green messages (at C2) i = j received: » V i [i] = number of green messages received by LP i V 1 V 2 V 3 V 4 » V i [r] = number of green messages sent by LP i to LP r V 1 [4] = 0 ● C2: LP i cannot pass token until » V i [i] = ∑ V s [i] (summed over all s ≠ i ) ● C1: Token includes vector to accumulate send counters

Example: Vector Counters Example: Vector Counters LP 4 LP 4 LP 3 LP 3 cut point cut point LP 2 LP 2 LP 1 LP 1 Wallclock time Wallclock time C1 C2 C1 C2 Vector counters for green messages (at C2) i = j received: Vector counters for green messages (at C2) i = j received: V 1 V 2 V 3 V 4 V 1 V 2 V 3 V 4 V 1 [4] = 0 V 1 [4] = 0 V 1 [3] = 0 V 1 [3] = 0 V 1 [2] = 1 . Example: Vector Counters Example: Vector Counters LP 4 LP 4 LP 3 LP 3 cut point cut point LP 2 LP 2 LP 1 LP 1 Wallclock time Wallclock time C1 C2 C1 C2 Vector counters for green messages (at C2) i = j received: Vector counters for green messages (at C2) i = j received: V 1 V 2 V 3 V 4 V 1 V 2 V 3 V 4 V 1 [4] = 0 V 1 [4] = 0 V 2 [4] = 0 V 1 [3] = 0 V 1 [3] = 0 V 2 [3] = 0 V 1 [2] = 1 V 1 [2] = 1 V 2 [2] = -3 V 1 [1] = -2 V 1 [1] = -2 V 2 [1] = 1 Example: Vector Counters Example: Vector Counters LP 4 LP 4 LP 3 LP 3 cut point cut point LP 2 LP 2 LP 1 LP 1 Wallclock time Wallclock time C1 C2 C1 C2 Vector counters for green messages (at C2) i = j received: Vector counters for green messages (at C2) i = j received: V 1 V 2 V 3 V 4 V 1 V 2 V 3 V 4 V 1 [4] = 0 V 2 [4] = 0 V 3 [4] = 1 V 1 [4] = 0 V 2 [4] = 0 V 3 [4] = 1 V 4 [4] = -1 V 1 [3] = 0 V 2 [3] = 0 V 3 [3] = 0 V 1 [3] = 0 V 2 [3] = 0 V 3 [3] = 0 V 4 [3] = 0 V 1 [2] = 1 V 2 [2] = -3 V 3 [2] = 0 V 1 [2] = 1 V 2 [2] = -3 V 3 [2] = 0 V 4 [2] = 2 V 1 [1] = -2 V 2 [1] = 1 V 3 [1] = 0 V 1 [1] = -2 V 2 [1] = 1 V 3 [1] = 0 V 4 [1] = 1