1. Static Process Scheduling
Yi Sun

2. Overview
Before execution, processes need to be scheduled and allocated with resources
Objective
Enhance overall system performance metric
Process completion time and processor utilization
In distributed systems: location and performance transparency
In distributed systems
Local scheduling (on each node) + global scheduling
Communication overhead
Effect of underlying architecture
Dynamic behavior of the system

3. Process Interaction Models
Precedence process model: Directed Acyclic Graph (DAG)
Represent precedence relationships between processes
Minimize total completion time of task (computation + communication)
Communication process model
Represent the need for communication between processes
Optimize the total cost of communication and computation
Disjoint process model
Processes can run independently and completed in finite time
Maximize utilization of processors and minimize turnaround time of processes

4. Process Models Partition 4 processes onto two nodes
Communication overhead

5. System Performance Model
Attempt to minimize the total completion time of (makespan) of a set of interacting processes

6. System Performance Model (Cont.)
Related parameters
OSPT: optimal sequential processing time; the best time that can be achieved on a single processor using the best sequential algorithm
CPT: concurrent processing time; the actual time achieved on a n-processor system with the concurrent algorithm and a specific scheduling method being considered
OCPTideal: optimal concurrent processing time on an ideal system; the best time that can achieved with the concurrent algorithm being considered on an ideal n-processor system(no inter-communication overhead) and scheduled by an optimal scheduling policy
Si: the ideal speedup by using a multiple processor system over the best sequential time
Sd: the degradation of the system due to actual implementation compared to an ideal system

7. System Performance Model (Cont.)
Pi: the computation time of the concurrent algorithm on node i P4 P1 P3 P1
(RP  1) P2 P4 P2
OCPTideal P3 P4
OCPTideal

8. System Performance Model (Cont.)
(The smaller, the better)
(The larger, the better)

9. System Performance Model (Cont.)
RP: Relative processing (algorithm)
How much loss of speedup is due to the substitution of the best sequential algorithm by an algorithm better adapted for concurrent implementation but which may have a greater total processing need
Loss of parallelism due to algorithm conversion
Increase in total computation requirement Sd
Degradation of parallelism due to algorithm implementation
RC: Relative concurrency (algorithm?)
How far from optimal the usage of the n-processor is
RC=1  best use of the processors
Theoretic loss of parallelism
: loss of parallelism when implemented on a real machine (system architecture + scheduling)

10. Efficiency Loss 
Impact factors: scheduling, system, and communication

11. Efficiency Loss  (Cont.)

12. Workload Distribution
Performance can be further improved by workload distribution
Loading sharing: static workload distribution
Dispatch process to the idle processors statically upon arrival
Corresponding to processor pool model
Load balancing: dynamic workload distribution
Migrate processes dynamically from heavily loaded processors to lightly loaded processors
Corresponding to migration workstation model
Model by queuing theory: X/Y/c
Proc. arrival time distribution:X; Service time distribution:Y; # of servers: c
: arrival rate; : service rate; : migration rate
: depends on channel bandwidth, migration protocol, context and state information of the process being transferred.

13. Processor-Pool and Workstation Queueing Models
Static Load Sharing
Dynamic Load Balancing
M for Markovian distribution

14. Comparison of Performance for Workload Sharing
(Communication overhead)
(Negligible Communication overhead)

15. Static Process Scheduling
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

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

17. Precedence Process Model
Precedence Process Model – NP-complete
A program is represented by a DAG (Figure 5.5 (a))
Node: task with a known execution time
Edge: weight showing message units to be transferred
Communication system model: Figure 5.5 (b)
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

18. Makespan Calculation for LS, ELS, and ETF

19. 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
e = process execution cost (cost to run process j on processor i)
C = communication cost (C==0 if i==j)
Again!!! NP-Complete

20. Stone’s two-processor model to achieve minimum total execution and communication cost
Example: Figure 5.7 (Don’t consider execution cost)
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: Figure 5.8 (Consider execution cost)
Maximum flow and minimum cut in a commodity-flow network
Find the maximum flow from source to destination

21. Computation Cost and Communication Graphs

22. Minimum-Cost Cut
Only the cuts that separate A and B are feasible

23. Discussion – Static Process Scheduling
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 realistic

24. Reference
Distributed Operating Systems & Algorithms, by Randy Chow and Theodore Johnson, 1997