Scheduling Status

1
Scheduling Status

• Yury Markovskiy
• 07-30-01

2
Outline

• Array Activity
• Makespan vs. Activity model (no overhead)
• Results
• Adding overhead
• Building a new complete model tradeoff between
  runtime and overhead

3
Array Activity(1)
1
0.5
1
1
A
B

• Example
• Each node has inherent (FSM-dependent) IO rates
• Units for rates are tokens/fire
• If nodes A and B are co-resident, expected
  activity
• FA 1 fire/cycle
• FB 0.5 fire/cycle

4
Array Activity(2)
1
0.5
1
1
0.1
1
A
B
C

• Continuing the example
• Node C was added with low input rate
• If nodes A and B are co-resident, expected
  activity
• FA 0.2 fire/cycle (former 1)
• FB 0.1 fire/cycle (former 0.5)
• FC 1 fire/cycle

5
Array Activity(3)

• Need mathematical model to relate
• Makespan (or throughput)
• Activity
• Start with Drain Time D
• Number of cycles to fill up the Buffer
• Depends on how active graph is

Buffer
Graph
Buffer
Buffer
6
Array Activity(4)

• Scheduler breaks the graph into schedulable
  timeslices

• Variables
• R schedule repetition factor
• Q scaling factor (will be discussed later)
• Di drain time for timeslice i

Graph
7
Makesp. vs Activity no overhead

• Makespan and Activity are inversely related
• Activity

8
Results(1)

• No overhead
• Evaluate quality of partitioning by
• Topological traversal
• Mincut multi-way (based on Wong)
• Exhaustive search

9
Results(2)
10
Results(3)
Ave error from optimal Topological 12, Mincut
11
11
Results(4)
12
Results(5)
Ave error from optimal Topological 3, Mincut
8.7
13
Results(6)
14
Results(7)
Ave error from optimal Topological 16, Mincut 6
15
Results(8)

• Neither Topological nor Mincut partioner
  consistently exhibit superior behavior
• Need more work?
• Play more with edge capacities
• Both algorithms are within 20 in Makespan from
  the optimal

16
Adding Overhead(1)

• Previous models did not include the configuration
  overhead

• Develop a complete model

17
Adding Overhead(2)
Y 0.5
X 1
1
0.5
1
1
A
B

• Given buffers X and Y, their relative sizes are
  easily computed
• Q is the scaling factor that is applied to all
  buffers.
• X will be of size Q1, and Y Q 0.5
• Q constraints how much work can be done in a
  timeslice before the buffer empties/fills up.

18
Complete Model
recon
recon
recon
ts1
ts2
ts3

• ConfigCost(i,Q) consists of two components
• Fixed costs associated with number of pages and
  segments resident in timeslice i.
• Variable cost associated with the size of
  buffers that must be xfer from/to primary mem.

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Complete Model(2)

• Q vs ConfigCost
• Large Q since CMB resources are limited, fixed
  costs go up (in addition to variable costs)
• Small Q fixed costs are negligible, all content
  is cached (little work is done per timeslice)

CMB
Large Q
Small Q
20
Complete Model(3)

• ConfigCosts vs Activity
• The ratio ConfigCosts/Runtime must be kept as
  small as possible
• Activity is inversely proportional to
  ConfigCosts/Runtime ratio.
• Examples of both extremes

r
r
r
High Activity
ts1
ts2
ts3
recon
recon
recon
Low Activity
ts1
ts2
ts3
21
Conclusion/Status

• Demonstrated a detailed model relating Makespan,
  Throughput, Activity with no overhead.
• Shown the effectiveness of two partitioning
  methods against the optimal.
• Simplified memory allocation model is complete.
• Developing a complete and accurate model
• Relate ConfigCosts, scaling param Q.
• Use this model to drive buffer allocation