Balance Point

1
Balance Point

• The basis for the argument against putting all
  your (speedup) eggs in one basket Amdahls Law
• Note the balance point in the denominator where
  both parts are equal.
• Increasing N (number of processors) beyond this
  point can at best halve the denominator, and
  double the speedup.

2
Parallel Speedup Summary

• Level 1 Pipeline

3
Level 2 Superscalar Multiple Pipelines
S number of stages n number of instructions M
number of pipelines s frequency of pipeline
stalls f probability that an instruction causes
a pipeline flush P Degree of
Multi-pipelining (number of concurrent pipes
working) Pr fraction of total work that runs on
P pipelines
Unified Speedup Model
4
Level 3 Algorithm Parallelism
N number of processors in the
architecture Alpha fraction of the process that
can be distributed across multiple
processors PA Probability of Acceptance of
requests (by the interconnection network)
Unified Speedup Model
5
Level 3b Scaled Algorithm Parallelism
N number of processors in the
architecture Alpha fraction of the process that
can be distributed across multiple
processors PA Probability of Acceptance of
requests (by the interconnection
network) kP Scaling factor on parallel work kS
Scaling factor on serial work
Unified Speedup Model
6
Level 4 Multi-Process or Clustered Speedup
N number of processors in the architecture C
number of processors in a cluster Alpha
fraction of the process that can be
distributed across multiple processors PA
Probability of Acceptance of requests (by
the inter-cluster I.N.) kP Scaling factor on
parallel work kS Scaling factor on serial work
Unified Speedup Model
7
Level 4b Scaled Multi-Process or Clustered
Speedup
N number of processors in the architecture C
number of processors in a cluster Alpha
fraction of the process that can be
distributed across multiple processors PA
Probability of Acceptance of requests (by
the inter-cluster I.N.) kP Scaling factor on
parallel work kS Scaling factor on serial
work k2 Workload scaling factor
Unified Speedup Model
8
Level 5 N-tiered Client-Server Distributed
Parallel System
M1 number of Tier1 machines (clients) m2
number of Tier2 machines (server2) ?1 workload
balance, of workload on Tier1 (client) ?2 of
workload on Tier2 (server2) Sup1 Speedup of
Tier1 machine (Levels 1 4)
Unified Speedup Model
9
Level 5b Scaled N-tiered Client-Server
Distributed Parallel System
Mi number of Tieri machines ?i of workload
on Tieri Supi Speedup of Tieri machine
(Parallel Levels 1 4) kC/S Client/Server
scaling factor Ali Average Latency at
Tieri PAi(kC/S ) Probability of Acceptance at
Tieri (A function of kC/S)
Unified Speedup Model