Martha Garcia

 Goals of Static Process Scheduling  Types of Static Process Scheduling  Future Research  References

GOALS :  Given a set or partially ordered tasks, define a mapping of processes to processors before the execution of the processes.  Cost model:CPU cost and communication cost, both should be specified in prior  Minimize the overall finish time on a non- preemptive(can not be interrupted) multiprocessor system (of identical processors) -Except for some very restricted cases, scheduling to optimize the makespand are NP-Complete -Heuristic solutions are usually proposed.

Two Types :  Precedence Process Model  Communication Process Model

 Precedence Process Model : - Program is represented by a DAG(Directed Acyclic Graph). Direct edges represent the precedence relationship. - The longest execution path in the DAG often used to compare the performance of a heuristic algorithm. I J K L [Chow and Johnson 1997]

 Precedence constraints among tasks in a program are explicitly specified.  Scheduling goal: minimize the makespan time No. of messages to communicate Execution time Communication overhead for A(P1) and E(P3)= 4 * 2 = 8 Communication overhead for one message [Chow and Johnson 1997]

Algorithms:  List Scheduling (LS): Communication overhead is not considered. Using a simple greedy heuristic: No processor remains idle if there are some tasks available that it could process.  Extended List Scheduling (ELS): the actual scheduling results of LS with communication consideration.  Earliest Task First scheduling (ETF): the earliest schedulable task (with communication delay considered) is scheduled first. [Chow and Johnson 1997]

Makespan Calculation for LS, ELS, and ETF [Chow and Johnson 1997]

Communication Process Model  There are no precedence constrains among processes  modeled by a undirected graph G, node represent processes and weight on the edge is the amount of communication messages between two connected processes.  Process execution cost might be specified some times to handle more general cases.  Scheduling goal: maximize the resource utilization [Chow and Johnson 1997]

 the problem is to find an optimal assignment of m process to P processors with respect to the target function:  P: a set of processors. ej(pi): computation cost of execution process pi in processor Pj.  ci,j(pi,pj): communication overhead between processes pi and pj.  Assume a uniform communicating speed between processors. [Chow and Johnson 1997]

 This is referred as Module Allocation problem. It is NP-complete except for a few cases:  For P=2, Stone suggested an polynomial time solution using Ford-Fulkerson’s maximum flow algorithm.  Known results: The mapping problem for an arbitrary number of processors is NP- complete. [Chow and Johnson 1997]

 Stone’s two-processor model to achieve minimum total execution and communication cost Example: Partition the graph by drawing a line cutting through some edges Result in two disjoint graphs, one for each process Set of removed edges  cut set Cost of cut set  sum of weights of the edges Total inter-process communication cost between processors Of course, the cost of cut sets is 0 if all processes are assigned to the same node Computation constraints (no more k, distribute evenly…) Example: Maximum flow and minimum cut in a commodity-flow network Find the maximum flow from source to destination [Chow and Johnson 1997]

Maximum Flow Algorithm in Solving the Scheduling Problem [Chow and Johnson 1997]

Minimum-Cost Cut Only the cuts that separate A and B are feasible [Chow and Johnson 1997]

Future Research :  Use AI techniques for Static Scheduling : Genetic Algorithm

References :  Design Optimization of Time – and Cost – Constrained Fault – Tolerant Distributed Embedded Systems.- Viacheslav Izosimov, Paul Pop. Petru Eles, Zebo Peng  A Static Task Scheduling Framework for Independent Tasks Accelerated using a Shared Graphics Processing Unit.- Teng Li, Vikram K.Narayana, Tarek El-Ghazawi, IEEE 2011  MAPPLE chip: a processing element for a static scheduling centric multiprocessor.- Kenta Yasufuku, Riku Ogawa, Keisure Iwai, Hideharu Amanu, IEEE 2003

 Thank you!!