Pradeep Konduri

Static Process Scheduling:  Proceedance process model  Communication system model  Application  Dicussion  References

Static process scheduling: deterministic scheduling policy Scheduling a set of partially ordered tasks on a non-preemptive multi-processor system of identical processors to minimize the overall finishing time (makespan) Optimize makespan  NP-complete Need approximate or heuristic algorithms… Attempt to balance and overlap computation and communication Mapping processes to processors is determined before the execution Once a process starts, it stays at the processor until completion Need prior knowledge about process behavior (execution time, precedence relationships, communication patterns) Scheduling decision is centralized and non-adaptive

Communication overhead for one message Execution time Communication overhead for A(P1) and E(P3) = 4 * 2 = 8 No. of messages to communicate

Proceedance Process model: Static multiprocessor scheduling Represented by DAG Minimize overall makespan Nodes : Task with known execution time Edges : Weight showing message units to be transferred Weights Hides the details of hardware architecture NP-Complete

Communication system model: Scheduling strategies List Scheduling (LS): no processor remains idle if there are some tasks available that it could process (no communication overhead) Extended List Scheduling (ELS): LS first + communication overhead Earliest Task First (ETF) scheduling: the earliest schedulable task is scheduled first Critical path: longest execution path Lower bound of the makespan Try to map all tasks in a critical path onto a single processor

Communication process model: Maximize resource utilization and minimize inter-process communication Undirected graph G=(V,E) V: Processes E: weight = amount of interaction between processes Cost equation Cost(G,P) = E e j (p i ) + E c i,j (p i,p j ) e = process execution cost (cost to run process j on processor i) C = communication cost (C==0 if i==j) NP-Complete

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

Only the cuts that separate A and B are feasible

There are many applications that are developed and being developed using these models. Some of them are: System-level design methods for MPSoC [1] Functional Validation of System Level Static Scheduling [2] Battery-aware static scheduling for distributed real-time embedded systems [3] Static scheduling algorithms for allocating directed task graphs to multiprocessors [4]

Once a process is assigned to a processor, it remain there until its execution has been completed Need prior knowledge of execution time and communication behavior Not effective Not realistic We need a dynamic scheduling algorithm

[1] Chengmo Yang, Alex Orailoglu; System-level design methods for MPSoC: Predictable execution adaptivity through embedding dynamic reconfigurability into static MPSoC schedules; Proceedings of the 5th IEEE/ACM international conference on Hardware/software codesign and system synthesis CODES+ISSS '07; September 2007 [2] Samar Abdi, Daniel Gajski; Functional Validation of System Level Static Scheduling; Proceedings of the conference on Design, Automation and Test in Europe - Volume 1 DATE '05; March 2005 [3] Jiong Luo, Niraj K. Jha; Battery-aware static scheduling for distributed real-time embedded systems; Proceedings of the 38th conference on Design automation DAC '01; June 2001 [4] Yu-Kwong Kwok, Ishfaq Ahmad; Static scheduling algorithms for allocating directed task graphs to multiprocessors; ACM Computing Surveys; December 1999

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