Load Balancing

1. Load Balancing A load is balanced if no processes are idle • How? • Partition the computation into units of work (tasks or jobs) • Assign tasks to different processors • Load Balancing Categories • Static (load assigned before application runs) • Dynamic (load assigned as applications run) • Centralized (Tasks assigned by the master or root process) • De-centralized (Tasks reassigned among slaves) • Semi-dynamic (application periodically suspended and load balanced) • Load Balancing Algorithms are: • Adaptive if they adapt to different system load levels • Thresholds control how they adapt • Stable if load balancing traffic is independent of load levels • Symmetric if both senders and receivers initiate action • Effective if load balancing overhead is minimal

2. Improving the Load Balance By realigning processing work, we improve speed-up

3. Round Robin Tasks given to processes in sequential order. If there are more tasks than processors, the allocation wraps around to the first Randomized Tasks are assigned randomly to processors Partitioning – Tasks represented by a graph Recursive Bisection Simulated Annealing Genetic Algorithms Multi-level Contraction and Refinement Advantage Simple to implement Minimal run time overhead Disadvantages Predicting execution times is often not knowable before execution Affect of communication dynamics is often not considered The number of iterations is often indeterminate Static Load Balancing Done prior to executing the parallel application

4. Dynamic Load Balancing Done as a parallel application executes • Centralized • A single process hands out tasks • Processes ask for more work when their processing completes • Double buffering can be effective • Decentralized • Processes detect that their work load is low • Processes can sense an overload condition • This occurs when new tasks are spawned during execution • Questions • Which neighbors are part of the rebalancing? • How should thresholds be set? • What are the communications needed to balance? • How often should balancing occur?

5. Centralized Load Balancing Work Pool, Processer Farm, or Replicated Worker Algorithm Master Processor While ( task=Remove()) != null) Receive(pi, request_msg) Send(pi, task) While(more processes) Receive(pi, request_msg) Send(pi, termination_msg) Slave Processor task = Receive(pmaster, message) While (task!=terminate) Process task Send(pmaster, request_msg) task = Receive(pmaster, message) Master Slaves In this case, the slaves don’t spawn new tasks

6. Centralized Termination How do we terminate when slave processes spawn new tasks? Necessary Requirements • The task queue is empty • Every process has requested another task Master Processor WHILE (true) Receive(pi, msg) IF msg contains a new task Add the new task to the task queue ELSE Add pi to wait queue and waitCount++ IF waitCount>0 and task queue not empty Remove pi & task respectively from wait & task queue Send(task, pi) and waitCount—- IF waitCount==P THEN send termination messages & exit

7. Decentralized Load Balancing (Worker processes interact among themselves) • There is no Master Processor • Each Processor maintains a work queue • Processors interact with neighbors to request and distribute tasks

8. Balancing Algorithm Application Decentralized Mechanisms Balancing is among a subset of the total running processes • Receiver Initiated • Process requests tasks when it is about to go idle • Effective when the load is heavy • Unstable when the load is light (A request frequency threshold is necessary) • Sender Initiated • Process with a heavy load distributes the excess • Effective when the load is heavy • Can cause thrashing when loads are heavy (synchronizing system load with neighbors is necessary) Task Queue

9. Process Selection • Global or Local? • Global involves all of the processors of the network • May require expensive global synchronization • May be difficult if the load dynamic is rapidly changing • Local involves only neighbor processes • Overall load may not be balanced • Easier to manage and less overhead than the global approach • Neighbor selection algorithms • Random: randomly choose another process • Easy to implement and studies show reasonable results • Round Robin: Select among neighbors using modular arithmetic • Easy to implement. Results similar to random selection • Adaptive Contracting: Issue bids to neighbors; best bid wins • Handshake between neighbors needed • Possible to synchronize loads

10. Choosing Thresholds • How do we estimate system load? • Synchronization averages task queue length or processes • Average number of tasks or projected execution time • When is the load low? • When a process is about to go idle • Goal: prevent idleness, not achieve perfect balance • A low threshold constant is sufficient • When is the load high? • When some processes have many tasks and others are idle • Goal: prevent thrashing • Synchronization among processors is necessary • An exponentially growing threshold works well • What is the job request frequency? • Goal: minimize load balancing overhead

11. L 1 2 1 1 2 2 2 2 Gradient Algorithm Maintains a global pressure grid • Node Data Structures • For each neighbor • Distance, in hops, to the nearest lightly-loaded process • A load status flag indicating if the current processor is lightly-loaded, or normal • Routing • Spawned jobs go to the nearest lightly-loaded process • Local Synchronization • Node status changes are multicast to its neighbors

12. Symmetric Broadcast Networks (SBN) Stage 3 5 Global Synchronization Stage 2 1 • Characteristics • A unique SBN starts at each node • Each SBN is lg P deep • Simple operations algebraically compute successors • Easily adapts to the hypercube • Algorithm • Starts with a lightly loaded process • Phase 1: SBN Broadcast • Phase 2: Gather task queue lengths • Load is balanced during the load and gather phases Stage 1 3 7 Stage 0 4 2 0 6 Successor 1 = (p+2s-1)%P; 1≤s≤3Successor 2 = (p-2s-1); 1≤s<3Note: If successor 2<0 successor2 +=P

13. pi pi+1 requests task Request task if queue not full Receive task from request Deliver task to pi+1 Dequeue and process task Line BalancingAlgorithm • Master processor adds to the pipeline • Slave processors • Request and receives tasks if queue not full • Pass tasks on if task request is posted • Non blocking receives are necessary to implement this algorithm Uses a pipeline approach Note: This algorithm easily extends to a tree topology

14. Semi-dynamic • Pseudo code Run algorithm Time to check balance? Suspend application IF load is balanced, resume application Re-partition the load Distribute data structures among processors Resume execution • Partitioning • Model application execution by a partitioning graph • Partitioning is an NP-Complete problem • Goals: Balance processing and minimize communication • Partitioning Heuristics • Recursive Bisection, Simulated Annealing, Multi-level, MinEx • Data Redistribution • Goal: Minimize the data movement cost

15. P9R6 P6R6 c4 c6 P2R1 c3 P1 c5 P2 c2 P4R1 P4R4 c3 c1 P7R5 P5R3 c1 P8R3 c8 c7 P2R1 Partitioning Graph P1 Load = (9+4+7+2) + (4+3+1+7) = 37 P2 Load = (6+2+4+8+5) + (4+3+1+7) = 40 Question: When can we move a task to improve load balance?

16. Distributed Termination • Insufficient condition for distributed termination • Empty task queues at every process • Sufficient condition for distributed termination requires • All local termination conditions satisfied • No messages in transit that could restart an inactive process • Termination algorithms • Acknowledgment • Ring • Tree • Fixed energy distribution

17. Acknowledge first task First task Inactive Active Acknowledgement Termination Pi • Process Receives task • Immediately acknowledge if source is not parent • Acknowledge parent as process goes idle • Process goes idle after it • completes processing local tasks • Sends all acknowledgments • Receives all acknowledgments • Note • A process always becomes inactive before its parent • The application can terminate when the master goes idle Pj Definition: Parent is the process sending initial task to a process

18. Single Pass Ring Termination • Pseudo code P0 sends a token to P1 when it goes idle Pi receives token IF Pi is idle it passes token to Pi+1 ELSE Pi sends token to Pi+1 when it goes idle P0receives token Broadcast final termination message • Assumptions • Processes cannot reactivate after going idle • Processes cannot pass new tasks to an idle process Token P0 P1 P2 Pn

19. Dual Pass Ring Termination Handles task sent to a process that already passed the token on Key Point: Token and processors are colored either White or Black Pseudo code WHEN P0 goes idle, it sends a white token to p1 WHEN Pi sends a task to Pj where j<i Pi becomes a black process WHEN Pi>0 receives token and goes idle IF Pi is a black process Pi colors the token black, Pi becomes White ELSE Pi sends token to P(i+1)%n unchanged in color IF P0 receives token and is idle IF token is White, application terminates ELSE po sends a White token to P1

20. AND Terminated Leaf Nodes Tree Termination • When a Leaf process terminates, it sends a token to it’s parent process • Internal nodes send tokens to it’s parent when all of its children processes terminate • When the root node receives the token, the application can terminate • Either one-pass or two pass algorithms can apply

21. Fixed Energy Termination Energy defined by an integer or long value • P0 starts with full energy • When Pi receives a task, it also receives an energy allocation • When Pi spawns tasks, it assigns them to processors with additional energy allocations within its allocation • When a process completes it returns its energy allotment • The application terminates when the master becomes idle • Implementation • Problem: Integer division eventually becomes zero • Solution: • Use two level energy allocation <generation, energy> • The generation increases each time energy value goes to zero

22. Example: Shortest Path Problem Definitions Graph: Collection of nodes (vertices) and edges Directed Graph: Edge can be traversed in only one direction Weighted Graph: Edges have weights that define cost Shortest Path Problem: Find the path from one node to another in a weighted graph that has the smallest accumulated weights Applications • Shortest distance between points on a map • Quickest travel route • Least expensive flight path • Network routing • Efficient manufacturing design

23. F 17 9 E D 51 24 13 14 8 10 B C A A Climbing a Mountain B C D • Weights: expended effort • Directed graph • Effort in one direction ≠ effort in another direction • Ex: Downhill versus uphill E F Adjacency List Graphic Representation Adjacency Matrix

24. di wi,j i j dj Moore’s Algorithm Less efficient than Dijkstra but more easily parallelized • Assume • w[i][j] =weight of edge (i,j) • Dist[v] = distance to vertex v • Pred[v] = predecessor to vertex v • Pseudo code Insert the source vertex into a queue For each vertex, v, dist[v]=∞ infinity, dist[0] = 0 WHILE (v = dequeue() exists) FOR (j=; j<n; j++) newdist = dist[i] + w[i][j] IF (newdist < dist[j]) dist[j] = newdist pred[j] = I append(j) dj=min(dj,di+wi,j)

25. Graph Analysis Stages Vertex Queue Dist[j]

26. Centralized Work Pool Solution • The Master maintains • The work pool queue of unchecked vertices • The distance array • Every slave holds • The graph weights which is static • The Slaves • Request a vertex • Compute new minimums • Send updated distance values and vertex to master • The Master • Appends received vertices to its work queue • Sends new vertex and the updated distance array.

27. Distributed Work Pool Solution • Data held in each processor • The graph weights • The distances to vertices stored locally • The processor assignments • When a process receiving a distance: • If its local value is reduced • Updates its local value of dist[v] • Send distances to adjacent vertices to appropriate processors • Notes • Inefficient with one vertex per processor • Poor computation to communication ratio • Many processors can be inactive • One of the termination algorithms is necessary