This document provides an outline and overview of parallel computing platforms and trends in microprocessor architectures. It discusses limitations in memory system performance and dichotomy of parallel platforms. Implicit parallelism through techniques like pipelining and superscalar execution aim to improve processor performance by executing multiple instructions concurrently. However, dependencies and other factors limit efficiency. Alternative approaches like VLIW aim to simplify hardware by moving scheduling to compile time. Memory latency and bandwidth are also significant bottlenecks, as data access times are orders of magnitude slower than processor speeds. Overall parallelism seeks to address performance limitations in processors, memory, and communication.

1. Chapter 2Chapter 2
Parallel Computing PlatformsParallel Computing Platforms
Dr. Muhammad Hanif Durad
Department of Computer and Information Sciences
Pakistan Institute Engineering and Applied Sciences
hanif@pieas.edu.pk
Some slides have bee adapted with thanks DANA PETCU'S at
http://web.info.uvt.ro/~petcu/index.html

2. Dr. Hanif Durad 2
Lecture Outline (1/2)
 Implicit Parallelism: Trends in Microprocessor
Architectures
 Limitations of Memory System Performance
 Dichotomy of Parallel Computing Platforms
 Communication Model of Parallel Platforms

3. Dr. Hanif Durad 3
Lecture Outline (2/2)
 Communication Costs in Parallel Machines
 Messaging Cost Models and Routing
Mechanisms
 Mapping Techniques
 Case Studies

4. Dr. Hanif Durad 4
Scope of Parallelism (1/2)
 Conventional architectures coarsely comprise of a
processor, memory system, and the datapath.
 Each of these components present significant
performance bottlenecks.
 Parallelism addresses each of these components in
significant ways.

5. Dr. Hanif Durad 5
Scope of Parallelism (2/2)
 Different applications utilize different aspects of
parallelism - e.g., data itensive applications utilize high
aggregate throughput, server applications utilize high
aggregate network bandwidth, and scientific applications
typically utilize high processing and memory system
performance.
 It is important to understand each of these performance
bottlenecks.

6. Dr. Hanif Durad 6
2.1 Implicit Parallelism: Trends in
Microprocessor Architectures (1/2)
 Microprocessor clock speeds have posted impressive
gains over the past two decades (two to three orders of
magnitude).
 Higher levels of device integration have made
available a large number of transistors.
 The question of how best to utilize these resources is
an important one.

7. Dr. Hanif Durad 7
2.1 Implicit Parallelism: Trends in
Microprocessor Architectures (2/2)
 Current processors use these resources in multiple
functional units and execute multiple instructions in the
same cycle.
 The precise manner in which these instructions are
selected and executed provides impressive diversity in
architectures.

8. Dr. Hanif Durad 8
2.1.1 Pipelining and Superscalar
Execution (1/4)
 Pipelining overlaps various stages of instruction
execution to achieve performance.
 At a high level of abstraction, an instruction can
be executed while the next one is being decoded
and the next one is being fetched.
 This is akin to an assembly line for manufacture
of cars.

9. Dr. Hanif Durad 9
Pipelining and Superscalar
Execution (2/4)
 Pipelining, however, has several limitations.
 The speed of a pipeline is eventually limited by
the slowest stage.
 For this reason, conventional processors rely
on very deep pipelines (20 stage pipelines in
state-of-the-art Pentium processors).

10. Dr. Hanif Durad 10
Pipelining and Superscalar
Execution (3/4)
 However, in typical program traces, every 5-6th instruction
is a conditional jump! This requires very accurate branch
prediction.
 The penalty of a misprediction grows with the depth of the
pipeline, since a larger number of instructions will have to
be flushed.
 One simple way of alleviating these bottlenecks is to use
multiple pipelines.
 The question then becomes one of selecting these
instructions

11. Dr. Hanif Durad 11
Superscalar Execution: An Example
(2.1)
(a) Three different code fragments for a list of
four numbers

12. Dr. Hanif Durad 12
Superscalar Execution: An Example
Execution Schedule for code fragment (i) above

13. Dr. Hanif Durad 13
Superscalar Execution: An
Example
 In the above example, there is some wastage of
resources due to data dependencies.
 The example also illustrates that different
instruction mixes with identical semantics can
take significantly different execution time.
load R1, @1000 and add R1, @1004
etc.

14. Dr. Hanif Durad 14
Pipelining Execution
Instruction i IF ID EX WB
IF ID EX WB
IF ID EX WB
IF ID EX WB
IF ID EX WB
Instruction i+1
Instruction i+2
Instruction i+3
Instruction i+4
Instruction # 1 2 3 4 5 6 7 8
Cycles
IF: Instruction fetch ID : Instruction decode
EX : Execution WB : Write back

15. Dr. Hanif Durad 15
Super-Scalar Execution
Instruction type
31 2 4 5 6 7
Cycles
Integer IF ID EX WB
Floating point IF ID EX WB
Integer
Floating point
Integer
Floating point
Integer
Floating point
IF ID EX WB
IF ID EX WB
IF ID EX WB
IF ID EX WB
IF ID EX WB
IF ID EX WB
2-issue super-scalar machine

16. Dr. Hanif Durad 16
Superscalar Execution
 Scheduling of instructions is determined by a
number of factors: (1/2)
 True Data Dependency: The result of one operation is
an input to the next. (?)
 Resource Dependency: Two operations require the
same resource. (?)
 Branch or Procedural Dependency: Scheduling
instructions across conditional branch statements
cannot be done deterministically a-priori.

17. Dr. Hanif Durad 17
Superscalar Execution
 Scheduling of instructions is determined by a
number of factors: (2/2)
 The scheduler, a piece of hardware looks at a large
number of instructions in an instruction queue and
selects appropriate number of instructions to execute
concurrently based on these factors.
 The complexity of this hardware is an important
constraint on superscalar processors.

18. Dr. Hanif Durad 18
Legend for next slide taken from
CA course
 Fetch Instruction (FI)
 Decode Instruction (DI)
 Calculate operands (i.e. EAs) (CO)
 Fetch Operands (FO)
 Execute Instructions (EI)
 Write Operands (WO)
 Overlap these operations

19. Dr. Hanif Durad 19
Timing Diagram for
Instruction Pipeline Operation

20. Dr. Hanif Durad 20
The Effect of a Conditional Branch on Instruction
Pipeline Operation No inst completed
in these 4 cycles
Know about conditional jump
Must be flushed

21. Dr. Hanif Durad 21
Superscalar Execution:
Issue Mechanisms
 In the simpler model, instructions can be issued
only in the order in which they are encountered.
That is, if the second instruction cannot be
issued because it has a data dependency with
the first, only one instruction is issued in the
cycle. This is called in-order issue.

22. Dr. Hanif Durad 22
Superscalar Execution:
Issue Mechanisms
 In a more aggressive model, instructions can be
issued out-of-order. In this case, if the second
instruction has data dependencies with the first, but
the third instruction does not, the first and third
instructions can be co-scheduled. This is also
called dynamic instruction issue.
 Performance of in-order issue is generally limited.

23. Dr. Hanif Durad 23
Superscalar Execution:
Efficiency Considerations
 Not all functional units can be kept busy at all
times.
 If during a cycle, no functional units are utilized,
this is referred to as vertical waste.
 If during a cycle, only some of the functional
units are utilized, this is referred to as horizontal
waste.

24. Dr. Hanif Durad 24
Superscalar Execution: An Example
Hardware utilization trace for schedule in (b).

25. Dr. Hanif Durad 25
Superscalar Execution:
Efficiency Considerations
 Due to limited parallelism in typical instruction
traces, dependencies, or the inability of the
scheduler to extract parallelism, the performance
of superscalar processors is eventually limited.
 Conventional microprocessors typically support
four-way superscalar execution.

26. Dr. Hanif Durad 26
2.1.2 Very Long Instruction
Word (VLIW) Processors
 The hardware cost and complexity of the
superscalar scheduler is a major consideration in
processor design.
 To address this issues, VLIW processors rely on
compile time analysis to identify and bundle
together instructions that can be executed
concurrently.

27. Dr. Hanif Durad 27
Very Long Instruction Word
(VLIW) Processors
 These instructions are packed and dispatched
together, and thus the name very long
instruction word.
 This concept was used with some commercial
success in the Multiflow Trace machine (circa
1984).
 Variants of this concept are employed in the
Intel IA64 processors.

28. Dr. Hanif Durad 28
VLIW Processors: Considerations
 Issue hardware is simpler.
 Compiler has a bigger context from which to
select co-scheduled instructions.
 Compilers, however, do not have runtime
information such as cache misses. Scheduling is,
therefore, inherently conservative.
 Branch and memory prediction is more difficult.

29. Dr. Hanif Durad 29
VLIW Processors: Considerations
 Very sensitive to the compilers' ability to detect
data and resource dependencies and read and
write hazards, and to schedule instructions for
maximum parallelism.
 A number of techniques such as loop unrolling,
speculative execution, branch prediction are
critical.
 Typical VLIW processors are limited to 4-way
to 8-way parallelism.

30. Dr. Hanif Durad 30

31. Dr. Hanif Durad 31
2.2 Limitations of
Memory System Performance
 Memory system, and not processor speed, is often the
bottleneck for many applications.
 Memory system performance is largely captured by two
parameters, latency and bandwidth.
 Latency is the time from the issue of a memory request
to the time the data is available at the processor.
 Bandwidth is the rate at which data can be pumped to
the processor by the memory system.

32. Dr. Hanif Durad 32
Memory System Performance:
Bandwidth and Latency
 It is very important to understand the difference between latency
and bandwidth.
 Consider the example of a fire-hose. If the water comes out of the
hose two seconds after the hydrant is turned on, the latency of the
system is two seconds.
 Once the water starts flowing, if the hydrant delivers water at the
rate of 5 gallons/second, the bandwidth of the system is 5
gallons/second.
 If you want immediate response from the hydrant, it is important
to reduce latency.
 If you want to fight big fires, you want high bandwidth.

33. Dr. Hanif Durad 33
Memory Latency: An Example
(2.2)
 Consider a processor operating at 1 GHz (1 ns clock)
connected to a DRAM with a latency of 100 ns (no
caches). Assume that the processor has two multiply-add
units and is capable of executing four instructions in each
cycle of 1 ns. The following observations follow:
 The peak processor rating is 4 GFLOPS.
 Since the memory latency is equal to 100 cycles and
block size is one word, every time a memory request is
made, the processor must wait 100 cycles before it can
process the data.

34. Dr. Hanif Durad 34

35. Dr. Hanif Durad 35
Memory Latency: An Example
 On the above architecture, consider the problem of
computing a dot-product of two vectors.
 A dot-product computation performs one multiply-add
on a single pair of vector elements, i.e., each floating
point operation requires one data fetch.
 It follows that the peak speed of this computation is
limited to one floating point operation every 100 ns, or
a speed of 10 MFLOPS, a very small fraction of the
peak processor rating! Solution ?

36. Dr. Hanif Durad 36
2.2.1 Improving Effective Memory
Latency Using Caches
 Caches are small and fast memory elements between the
processor and DRAM.
 This memory acts as a low-latency high-bandwidth storage.
 If a piece of data is repeatedly used, the effective latency of this
memory system can be reduced by the cache.
 The fraction of data references satisfied by the cache is called the
cache hit ratio of the computation on the system.
 Cache hit ratio achieved by a code on a memory system often
determines its performance.

37. Traditional (ISA) (with cache)

38. Dr. Hanif Durad 38
Impact of Caches: Example (2.3)
Consider the architecture from the previous
example. In this case, we introduce a cache of
size 32 KB with a latency of 1 ns or one cycle.
We use this setup to multiply two matrices A and
B of dimensions 32 × 32. We have carefully
chosen these numbers so that the cache is large
enough to store matrices A and B, as well as the
result matrix C.

39. Dr. Hanif Durad 39
Impact of Caches: Example (continued)
 The following observations can be made about the problem:
 Fetching the two matrices into the cache corresponds to fetching
2K words, which takes approximately 200 µs.
 Multiplying two n × n matrices takes 2n3
operations. For our
problem, this corresponds to 64K operations, which can be
performed in 16K cycles (or 16 µs) at four instructions per cycle.
 The total time for the computation is therefore approximately the
sum of time for load/store operations and the time for the
computation itself, i.e., 200 + 16 µs.
 This corresponds to a peak computation rate of 64K/216 or 303
MFLOPS.

40. Dr. Hanif Durad 40
Impact of Caches
 Repeated references to the same data item
correspond to temporal locality.
 In our example, we had O(n2
) data accesses and
O(n3
) computation. This asymptotic difference
makes the above example particularly desirable
for caches.
• Data reuse is critical for cache performance.

41. Dr. Hanif Durad 41
2.2.2 Impact of Memory Bandwidth
 Memory bandwidth is determined by the
bandwidth of the memory bus as well as the
memory units.
 Memory bandwidth can be improved by
increasing the size of memory blocks.
 The underlying system takes l time units (where l
is the latency of the system) to deliver b units of
data (where b is the block size).

42. Dr. Hanif Durad 42
 Consider the same setup as before, except in this case, the block
size is 4 words instead of 1 word i.e., the processor can fetch a
four-word cache line every 100 cycles. We repeat the dot-product
computation in this scenario:
 Assuming that the vectors are laid out linearly in memory,
eight FLOPs (four multiply-adds) can be performed in 200
cycles.
 This is because a single memory access fetches four
consecutive words in the vector.
 Therefore, two accesses can fetch four elements of each of the
vectors. This corresponds to a FLOP every 25 ns, for a peak
speed of 40 MFLOPS. (Exact? )
Impact of Memory Bandwidth: Example
(2.4)

43. Dr. Hanif Durad 43
)(1 )c c mt h t h t t
−
+ += − (

44. Dr. Hanif Durad 44
Impact of Memory Bandwidth
 It is important to note that increasing block size does not
change latency of the system.
 Physically, the scenario illustrated here can be viewed as a
wide data bus (4 words or 128 bits) connected to multiple
memory banks.
 In practice, such wide buses are expensive to construct.
 In a more practical system, consecutive words are sent on
the memory bus on subsequent bus cycles after the first
word is retrieved. (What change ?)

45. Dr. Hanif Durad 45
Impact of Memory Bandwidth
 The above examples clearly illustrate how increased
bandwidth results in higher peak computation rates.
 The data layouts were assumed to be such that consecutive
data words in memory were used by successive
instructions (spatial locality of reference).
 If we take a data-layout centric view, computations must
be reordered to enhance spatial locality of reference.

46. Example 2.5 Impact of Strided Access
Consider the following code fragment:
for (i = 0; i < 1000; i++)
b[i] = 0.0;
for (j = 0; j < 1000; j++)
b[i] += A[j][i];
The code fragment sums columns of the matrix A
into a vector b.
Dr. Hanif Durad 46

47. Dr. Hanif Durad 47
Multiplying a matrix with a vector:
(a) multiplying column-by-column, keeping a running sum;
Small & fits cache

48. Dr. Hanif Durad 48
Impact of Memory Bandwidth: Example
 The vector b is small and easily fits into the cache
 The matrix A is accessed in a column order.
 The strided access results in very poor performance.

49. Dr. Hanif Durad 49
Example 2.6 Eliminating Strided Access
We can fix the above code as follows:
for (i = 0; i < 1000; i++)
b[i] = 0.0;
for (j = 0; j < 1000; j++)
for (i = 0; i < 1000; i++)
b[i] += A[j][i];
In this case, the matrix is traversed in a row-order and performance
can be expected to be significantly better.

50. Dr. Hanif Durad 50
Multiplying a matrix with a vector:
(b) computing each element of the result as a dot product of a row of the
matrix with the vector.
The concept is called tiling or loop tiling

51. Dr. Hanif Durad 51
Memory System Performance: Summary
 The series of examples presented in this section illustrate the
following concepts:
 Exploiting spatial and temporal locality in applications is critical
for amortizing memory latency and increasing effective memory
bandwidth.
 The ratio of the number of operations to number of memory
accesses is a good indicator of anticipated tolerance to memory
bandwidth.
 Memory layouts and organizing computation appropriately can
make a significant impact on the spatial and temporal locality.

52. Dr. Hanif Durad 52
2.2.3 Alternate Approaches for Hiding
Memory Latency
• Consider the problem of browsing the web on a very
slow network connection. We deal with the problem in
one of three possible ways:
– we anticipate which pages we are going to browse ahead of
time and issue requests for them in advance;
– we open multiple browsers and access different pages in
each browser, thus while we are waiting for one page to
load, we could be reading others; or
– we access a whole bunch of pages in one go - amortizing
the latency across various accesses.
• The first approach is called prefetching, the second
multithreading, and the third one corresponds to
spatial locality (already discussed) in accessing
memory words.

53. 2.2.3.1 Multithreading for Latency Hiding
A thread is a single stream of control in the flow of a
program.
We illustrate threads with a simple example:
for (i = 0; i < n; i++)
c[i] = dot_product(get_row(a, i), b);
Each dot-product is independent of the other, and
therefore represents a concurrent unit of execution.
We can safely rewrite the above code segment as:
for (i = 0; i < n; i++)
c[i] = create_thread(dot_product,get_row(a, i),
b);
Example 2.7 Threaded execution of matrix multiplication

54. Dr. Hanif Durad 54
Multithreading for Latency Hiding:
Example
 In the code, the first instance of this function accesses a pair of
vector elements and waits for them.
 In the meantime, the second instance of this function can access two
other vector elements in the next cycle, and so on.
 After l units of time, where l is the latency of the memory system,
the first function instance gets the requested data from memory and
can perform the required computation.
 In the next cycle, the data items for the next function instance
arrive, and so on. In this way, in every clock cycle, we can perform
a computation.

55. Dr. Hanif Durad 55
Multithreading for Latency Hiding
 The execution schedule in the previous example is
predicated upon two assumptions: the memory system is
capable of servicing multiple outstanding requests, and the
processor is capable of switching threads at every cycle.
 It also requires the program to have an explicit specification
of concurrency in the form of threads.
 Machines such as the HEP and Tera rely on multithreaded
processors that can switch the context of execution in every
cycle. Consequently, they are able to hide latency
effectively.

56. 56
2.2.3.2 Prefetching for Latency
Hiding
 Misses on loads cause programs to stall.
 Why not advance the loads so that by the time
the data is actually needed, it is already there!
 The only drawback is that you might need more
space to store advanced loads.
 However, if the advanced loads are overwritten,
we are no worse than before!
 Hiding latency by prefetching Example 2.8

57. 2.2.4 Tradeoffs of Multithreading and Prefetching
• Multithreading and prefetching are critically impacted
by the memory bandwidth. Consider the following
example (2.9):
– Consider a computation running on a machine with a 1 GHz
clock, 4-word cache line, single cycle access to the cache,
and 100 ns latency to DRAM. The computation has a cache
hit ratio at 1 KB of 25% and at 32 KB of 90%.
– Consider two cases: first, a single threaded execution in
which the entire cache is available to the serial context, and
second, a multithreaded execution with 32 threads where
each thread has a cache residency of 1 KB.
– If the computation makes one data request in every cycle of
1 ns, you may notice that the first scenario requires 400MB/s
of memory bandwidth and the second, 3GB/s.

58. Tradeoffs of Multithreading and Prefetching
• Bandwidth requirements of a multithreaded system
may increase very significantly because of the
smaller cache residency of each thread.
• Multithreaded systems become bandwidth bound
instead of latency bound.
• Multithreading and prefetching only address the
latency problem and may often exacerbate the
bandwidth problem.
• Multithreading and prefetching also require
significantly more hardware resources in the form of
storage.

59. Dr. Hanif Durad 59
Explicitly Parallel Platforms

60. Dr. Hanif Durad 60
2.3 Dichotomy of Parallel
Computing Platforms
 An explicitly parallel program must specify
concurrency and interaction between concurrent
subtasks.
 The former is sometimes also referred to as the
control structure and the latter as the
communication model.

61. Example 2.10 Parallelism from single
instruction on multiple processors
 Consider the following code segment that
adds two vectors:
 for (i = 0; i < 1000; i++)
 c[i] = a[i] + b[i];
 various iterations of the loop are independent
of each other; can all be executed
independently on all the processors with
appropriate data
 we could execute this loop much fasterDr. Hanif Durad 61

62. Dr. Hanif Durad 62
2.3.1 Control Structure of Parallel
Programs
 Parallelism can be expressed at various levels of
granularity - from instruction level to processes.
 Between these extremes exist a range of models,
along with corresponding architectural support.
 Best explained by Flynn’s Taxonomy of Computer
Architecture

63. Dr. Hanif Durad 63
Flynn’s Taxonomy of Computer
Architecture
 Processing units in parallel computers either
operate under the centralized control of a
single control unit or work independently.
 Single Instruction Single Data (SISD)
 Single Instruction Multiple Data (SIMD)
 Multiple Instruction Multiple Data (MIMD)
 Multiple Instruction Single Data (MISD)

64. Computer Architecture Classifications
Tanenbaum, SCO, P-104

65. Dr. Hanif Durad 65
Potential of the four classes

66. Dr. Hanif Durad 66
2.3.1.1 SISD Architecture
 A single-processor computer (uniprocessor)
in which a single stream of instructions is
generated from the program.
Hesham, P-5

67. Dr. Hanif Durad 67
2.3.1.2 SIMD Architecture
 Each instruction is executed on a different set of
data by different processors. (Used for vector
and array processing)

68. SIMD Architecture
Dr. Hanif Durad 68

69. Dr. Hanif Durad 69
2.3.1.3 MIMD Architecture
 If each processor has its own control control
unit, each processor can execute different
instructions on different data items. This model
is called multiple instruction stream, multiple
data stream (MIMD).

70. Dr. Hanif Durad 70
SIMD and MIMD Architectures
A typical SIMD architecture (a) and a typical MIMD architecture (b).

71. Dr. Hanif Durad 71
SIMD Processors
 Some of the earliest parallel computers such as
the Illiac IV, MPP, DAP, CM-2, and MasPar MP-
1 belonged to this class of machines.
 Variants of this concept have found use in co-
processing units such as the MMX units in Intel
processors and DSP chips such as the Sharc.

72. Dr. Hanif Durad 72
SIMD Processors
 SIMD relies on the regular structure of
computations (such as those in image processing).
 It is often necessary to selectively turn off
operations on certain data items. For this reason,
most SIMD programming paradigms allow for an
``activity mask'', which determines if a processor
should participate in a computation or not.

73. Dr. Hanif Durad 73
Example 2.11 Execution of conditional
statements on a SIMD architecture
If (B==0)
C=A;
Else
C=A/B;
Executing a conditional statement on an SIMD computer with four
processors: (a) the conditional statement;.
(a)

74. Dr. Hanif Durad 74
Conditional Execution in SIMD Processors
(b) the execution of the statement in two steps.

75. Dr. Hanif Durad 75
MIMD Processors
 In contrast to SIMD processors, MIMD
processors can execute different programs on
different processors.
 A variant of this, called single program multiple
data streams (SPMD) executes the same
program on different processors.

76. Dr. Hanif Durad 76
MIMD Processors
 It is easy to see that SPMD and MIMD are
closely related in terms of programming
flexibility and underlying architectural support.
 Examples of such platforms include current
generation Sun Ultra Servers, SGI Origin
Servers, multiprocessor PCs, workstation
clusters, and the IBM SP.

77. Dr. Hanif Durad 77
SIMD-MIMD Comparison
 SIMD computers require less hardware than MIMD
computers (single control unit).
 However, since SIMD processors ae specially designed,
they tend to be expensive and have long design cycles.
 Not all applications are naturally suited to SIMD
processors.
 In contrast, platforms supporting the SPMD paradigm can
be built from inexpensive off-the-shelf components with
relatively little effort in a short amount of time.

78. Dr. Hanif Durad 78
2.3.1.3 Multiple Instruction Single Data
(MISD)• Multiple PEs operate on different Instructions but use same data
• Never been commercially implemented
• More of an intellectual exercise than a practical configuration
• Some people say systolic arrays
Data
Input
Stream
Data
Output
Stream
Processor
A
Processor
B
Processor
C
Instruction
Stream A
Instruction
Stream B
Instruction Stream C
With thanks to Rajkumar Buyya
File: ParallelCompOverview.ppt

79. Dr. Hanif Durad 79
2.3.2 Communication Model
of Parallel Platforms
 There are two primary forms of data exchange
between parallel tasks - accessing a shared data
space and exchanging messages.
 Platforms that provide a shared data space are
called shared-address-space machines or
multiprocessors.
 Platforms that support messaging are also called
message passing platforms or multicomputers.

80. Computer Architecture Classifications
Tanenbaum, SCO, P-104
(SMP)(SMP)
threads (POSIX, NT) and directives (OpenMP) MPI and PVM

81. Dr. Hanif Durad 81
2.3.2 .1 Shared-Address-Space
Platforms
 Part (or all) of the memory is accessible to all processors.
 Processors interact by modifying data objects stored in this
shared-address-space.
 If the time taken by a processor to access any memory
word in the system global or local is identical, the platform
is classified as a uniform memory access (UMA), else, a
non-uniform memory access (NUMA) machine.

82. Dr. Hanif Durad 82
NUMA and UMA Shared-Address-
Space Platforms
Typical shared-address-space architectures: (a) Uniform-memory access
shared-address-space computer; (b) Uniform-memory-access shared-
address-space computer with caches and memories; (c) Non-uniform-
memory-access shared-address-space computer with local memory only.

83. NUMA and UMA
 The distinction between NUMA and UMA platforms
is important from the point of view of algorithm
design.
 NUMA machines require locality from underlying
algorithms for performance.
 Programming these platforms is easier since reads
and writes are implicitly visible to other processors.
 However, read-write data to shared data must be
coordinated (this will be discussed in greater detail
when we talk about threads programming) Caches
in such machines require coordinated access to
multiple copies. This leads to the cache coherence
problem.

84. Dr. Hanif Durad 84
NUMA and UMA
Shared-Address-Space Platforms
 Caches in such machines require coordinated
access to multiple copies. This leads to the cache
coherence problem.
 A weaker model of these machines provides an
address map, but not coordinated access. These
models are called non cache coherent shared
address space machines.

85. Shared-Address-Space Platforms
 Shared-address-space programming paradigms
such as threads (POSIX, NT) and directives
(OpenMP) therefore support synchronization
using locks and related mechanisms.
Dr. Hanif Durad 85

86. Dr. Hanif Durad 86
Shared-Address-Space vs. Shared
Memory Machines
 It is important to note the difference between the
terms shared address space and shared memory.
 We refer to the former as a programming
abstraction and to the latter as a physical machine
attribute.
 It is possible to provide a shared address space
using a physically distributed memory.

87. Dr. Hanif Durad 87
2.3.2 .2 Message-Passing
Platforms
 These platforms comprise of a set of processors and their
own (exclusive) memory.
 Instances of such a view come naturally from clustered
workstations and non-shared-address-space
multicomputers.
 These platforms are programmed using (variants of) send
and receive primitives.
 Libraries such as MPI and PVM provide such primitives.

88. Dr. Hanif Durad 88
Message Passing vs. Shared
Address Space Platforms
 Message passing requires little hardware
support, other than a network.
 Shared address space platforms can easily
emulate message passing. The reverse is more
difficult to do (in an efficient manner).

89. Dr. Hanif Durad 89
Wilkinson, P-15 Wilkinson, P-27

90. Dr. Hanif Durad 90
2.4 Physical Organization
of Parallel Platforms
 We begin this discussion with an ideal parallel
machine called Parallel Random Access
Machine, or PRAM.

91. Dr. Hanif Durad 91
2.4.1 Architecture of an
Ideal Parallel Computer
 A natural extension of the Random Access
Machine (RAM) serial architecture is the
Parallel Random Access Machine, or PRAM.
 PRAMs consist of p processors and a global
memory of unbounded size that is uniformly
accessible to all processors.
 Processors share a common clock but may
execute different instructions in each cycle.

92. Dr. Hanif Durad 92
Architecture of an
Ideal Parallel Computer
 Depending on how simultaneous memory accesses
are handled, PRAMs can be divided into four
subclasses.
 Exclusive-read, exclusive-write (EREW) PRAM.
 Concurrent-read, exclusive-write (CREW) PRAM.
 Exclusive-read, concurrent-write (ERCW) PRAM.
 Concurrent-read, concurrent-write (CRCW) PRAM.

93. Dr. Hanif Durad 93
Architecture of an
Ideal Parallel Computer
 What does concurrent write mean, anyway?
 Common: write only if all values are identical.
 Arbitrary: write the data from a randomly selected
processor.
 Priority: follow a predetermined priority order.
 Sum: Write the sum of all data items. (?)

94. Dr. Hanif Durad 94
2.4.1.1 Architectural Complexity
of an Ideal Parallel Computer
 Processors and memories are connected via
switches.
 Since these switches must operate in O(1) time
at the level of words, for a system of p
processors and m words, the switch complexity
is O(mp).
 Clearly, for meaningful values of p and m, a
true PRAM is not realizable.

95. Dr. Hanif Durad 95
2.4.2 Interconnection Networks
for Parallel Computers
 Interconnection networks carry data between
processors and to memory.
 Interconnects are made of switches and links
(wires, fiber).
 Interconnects are classified as static or dynamic.

96. Dr. Hanif Durad 96
Interconnection Networks
for Parallel Computers
 Static networks consist of point-to-point
communication links among processing nodes
and are also referred to as direct networks.
 Dynamic networks are built using switches and
communication links. Dynamic networks are
also referred to as indirect networks.

97. Dr. Hanif Durad 97
Static and Dynamic Interconnection Networks
Classification of interconnection networks: (a) a static network; and (b)
a dynamic network.

98. Dr. Hanif Durad 98
Interconnection Networks
 Switches map a fixed number of inputs to
outputs.
 The total number of ports on a switch is the
degree of the switch.
 The cost of a switch grows as the square of the
degree of the switch, the peripheral hardware
linearly as the degree, and the packaging costs
linearly as the number of pins.

99. Dr. Hanif Durad 99
Interconnection Networks:
Network Interfaces
 Processors talk to the network via a network
interface.
 The network interface may hang off the I/O bus
or the memory bus.
 In a physical sense, this distinguishes a cluster
from a tightly coupled multicomputer.
 The relative speeds of the I/O and memory buses
impact the performance of the network.

100. Dr. Hanif Durad 100
2.4.3 Network Topologies
 A variety of network topologies have been
proposed and implemented.
 These topologies tradeoff performance for cost.
 Commercial machines often implement hybrids
of multiple topologies for reasons of packaging,
cost, and available components.

101. Dr. Hanif Durad 101
2.4.3.1 Network Topologies:
Buses
 Some of the simplest and earliest parallel machines
used buses.
 All processors access a common bus for
exchanging data.
 The distance between any two nodes is O(1) in a
bus. The bus also provides a convenient broadcast
media.

102. Dr. Hanif Durad 102
Network Topologies: Buses
 However, the bandwidth of the shared bus is a
major bottleneck.
 Typical bus based machines are limited to dozens
of nodes.
 Sun Enterprise servers and Intel Pentium based
shared-bus multiprocessors are examples of such
architectures.

103. Network Topologies: Buses
Bus-based interconnects (a) with no local caches; (b) with local
memory/caches.

104. Dr. Hanif Durad 104
Network Topologies: Buses
 Since much of the data accessed by processors
is local to the processor, a local memory can
improve the performance of bus-based
machines.

105. Dr. Hanif Durad 105
2.4.3.2 Network Topologies:
Crossbars
 A crossbar network uses an p×m grid of
switches to connect p inputs to m outputs in a
non-blocking manner

106. Dr. Hanif Durad 106
Figure 8.17 Crossbar switch with three inputs and four outputs
FOROUZAN, P-228

107. Dr. Hanif Durad 107
Network Topologies: Crossbars
A completely non-blocking crossbar network connecting p
processors to b memory banks.

108. Dr. Hanif Durad 108
Network Topologies: Crossbars
 The cost of a crossbar of p processors grows as
O(p2
).
 This is generally difficult to scale for large
values of p.
 Examples of machines that employ crossbars
include the Sun Ultra HPC 10000 and the
Fujitsu VPP500.

109. Dr. Hanif Durad 109
2.4.3.3 Network Topologies:
Multistage Networks
 Crossbars have excellent performance
scalability but poor cost scalability.
 Buses have excellent cost scalability, but poor
performance scalability.
 An intermediate class of networks called
multistage interconnection networks (MINs)
strike a compromise between these extremes

110. Dr. Hanif Durad 110
Network Topologies: Multistage
Networks
The schematic of a typical multistage interconnection network.

111. Dr. Hanif Durad 111
Network Topologies: Multistage
Omega Network
 One of the most commonly used multistage
interconnects is the Omega network.
 This network consists of log p stages, where p
is the number of inputs/outputs.
 At each stage, input i is connected to output j
if:

112. Dr. Hanif Durad 112
Network Topologies: Multistage
Omega Network
Each stage of the Omega network implements a perfect
shuffle as follows:
A perfect shuffle interconnection for eight inputs and outputs.

113. Dr. Hanif Durad 113
Network Topologies: Multistage
Omega Network
 The perfect shuffle patterns are connected using
2×2 switches.
 The switches operate in two modes – crossover or
passthrough.
Two switching configurations of the 2 × 2 switch:
(a) Pass-through; (b) Cross-over.

114. Dr. Hanif Durad 114
 A complete Omega network with the perfect
shuffle interconnects and switches can now be
illustrated:
Network Topologies: Multistage
Omega Network

115. Network Topologies: Multistage Omega
Network
•A complete omega network connecting eight inputs and eight
outputs.
•An omega network has p/2 × log p switching nodes, and the cost of
such a network grows as (p log p). Here p=8
p/2 × log p=4x3=12
p log p=8x3=24

116. Dr. Hanif Durad 116
Network Topologies:Multistage
Omega Network – Routing
 Let s be the binary representation of the source and d be
that of the destination processor.
 The data traverses the link to the first switching node. If
the most significant bits of s and d are the same, then the
data is routed in pass-through mode by the switch else, it
switches to crossover.
 This process is repeated for each of the log p switching
stages.
 Note that this is not a non-blocking switch.

117. Dr. Hanif Durad 117
Network Topologies: Multistage
Omega Network – Routing
An example of blocking in omega network: one of the messages
(010 to 111 or 110 to 100) is blocked at link AB.

118. Dr. Hanif Durad 118
Figure 8.18 Multistage switch
FOROUZAN, P-228

119. Dr. Hanif Durad 119
In a three-stage switch, the total
number of cross-points is
2kN + k(N/n)2
which is much smaller than the number
of cross-points in a single-stage switch
(N2
).
FOROUZAN, P-229

120. Dr. Hanif Durad 120
Design a three-stage, 200 × 200 switch (N = 200) with
k = 4 and n = 20.
Solution
In the first stage we have N/n or 10 crossbars, each of size
20 × 4. In the second stage, we have 4 crossbars, each of
size 10 × 10. In the third stage, we have 10 crossbars,
each of size 4 × 20. The total number of crosspoints is
2kN + k(N/n)2
, or 2000 crosspoints. This is 5 percent of
the number of crosspoints in a single-stage switch (200 ×
200 = 40,000).
Example 8.3
FOROUZAN, P-229

121. Dr. Hanif Durad 121
2.4.3.4 Completely Connected
Network
 Each processor is connected to every other processor.
 The number of links in the network scales as O(p2
).
 While the performance scales very well, the hardware
complexity is not realizable for large values of p.
 In this sense, these networks are static counterparts of
crossbars.
 # of interconnections=?

122. Dr. Hanif Durad 122
Completely Connected Networks
Example of an 8-node completely connected network.
(a) A completely-connected network of eight nodes;

123. Dr. Hanif Durad 123
2.4.3.5 Star Connected Network
 Every node is connected only to a common node
at the center.
 Distance between any pair of nodes is O(1).
However, the central node becomes a bottleneck
 In this sense, star connected networks are static
counterparts of buses.

124. Dr. Hanif Durad 124
Star Connected Networks
Example of an 8-node star connected network.
(b) a star connected network of nine nodes.

125. Dr. Hanif Durad 125
2.4.3.6 Linear Arrays, Meshes,
and k-d Meshes
 Due to the large number of links in completely connected
networks, sparser networks are typically used to build parallel
computers
 A family of such networks spans the space of linear arrays and
hypercubes

126. Dr. Hanif Durad 126
2.4.3.6.1 Linear Arrays
 In a linear array, each node has two neighbors, one to its left and
one to its right. If the nodes at either end are connected, we refer
to it as a 1-D torus or a ring.

127. Dr. Hanif Durad 127
Linear Arrays
Linear arrays: (a) with no wraparound links (linear Array); (b)
with wraparound link (1-D ring or torus)

128. Dr. Hanif Durad 128
2.4.3.6.2 Meshes, and k-d
Meshes
 A generalization to 2 dimensions has nodes with 4 neighbors, to
the north, south, east, and west.
 A further generalization to d dimensions has nodes with 2d
neighbors.

129. Dr. Hanif Durad 129
Two- and Three Dimensional
Meshes
Two and three dimensional meshes: (a) 2-D mesh with no
wraparound; (b) 2-D mesh with wraparound link (2-D torus); and
(c) a 3-D mesh with no wraparound.

130. Dr. Hanif Durad 130
2.4.3.6.3 Hypercubes

131. Properties of Hypercubes
 A special case of a d-dimensional mesh is a
hypercube. Here, d = log p, where p is the total
number of nodes
 The distance between any two nodes is at most log p
 Each node has log p neighbors.
 The distance between two nodes is given by the
number of bit positions at which the two nodes
differ (XOR)

132. Dr. Hanif Durad 132
Hypercubes and their
Construction

133. Dr. Hanif Durad 133
2.4.3.6.4 Tree-Based Networks
Complete binary tree networks: (a) a static tree network; and (b) a
dynamic tree network.

134. Dr. Hanif Durad 134
Tree Properties
 The distance between any two nodes is no more than
2logp
 Links higher up the tree potentially carry more traffic
than those at the lower levels.
 For this reason, a variant called a fat-tree, fattens the
links as we go up the tree.
 Trees can be laid out in 2D with no wire crossings.
This is an attractive property of trees.

135. Dr. Hanif Durad 135
Fat Trees
A fat tree network of 16 processing nodes.

136. Dr. Hanif Durad 136
2.4.4 Evaluating Static
Interconnection Networks
 Various criteria used to characterize the cost and
performance of static interconnection include
 Diameter
 Bisection Width
 Cost

137. Dr. Hanif Durad 137
2.4.4.1 Diameter
 Diameter: The distance between the farthest two nodes in
the network.
 The diameter of
 linear array is p − 1,
 mesh is 2( − 1),
 tree and hypercube is log p,
 completely connected network is O(1).

138. Dr. Hanif Durad 138
2.4.4.2 Bisection Width
 Bisection Width: The minimum number of wires you
must cut to divide the network into two equal parts.
 The bisection width
 linear array and tree is 1
 a mesh is
 hypercube is p/2
 completely connected network is p2
/4.

139. Dr. Hanif Durad 139
2.4.4.2 Cost
 The number of links or switches (whichever is
asymptotically higher) is a meaningful measure of the
cost.
 However, a number of other factors, such as the ability to
layout the network, the length of wires, etc., also factor in
to the cost.

140. 140
Evaluating Static Interconnection
Networks
Network Diameter
Bisection
Width
Arc
Connecti-
vity
Cost
(No. of links)
Completely-connected
Star
Complete binary tree
Linear array
2-D mesh, no wraparound
2-D wraparound mesh
Hypercube
Wraparound k-ary d-cube
Not Discussed

141. Dr. Hanif Durad 141
2.4.5 Evaluating Dynamic
Interconnection Networks
Network Diameter
Bisection
Width
Arc
Connectivity
Cost
(No. of
links)
Crossbar
Omega Network
Dynamic Tree
Self Study
*This measure appears off..
Our 3 stage, 8 in/out
network has 32 links or
p*(log(p) + 1) links

142. 2.4.6 Cache Coherence
in Multiprocessor Systems
 One or two levels of cache typically
associated with each processor – this is
essential for performance
 Problem
 Multiple copies of same data in different caches
 Can result in an inconsistent view of memory

143. Write Policy Review
 Write back policy
 Write goes only to cache
 Main memory updated only when cache block is
replaced
 Can lead to inconsistency
 Write through policy
 All writes made to cache and main memory
 Inconsistencies can occur unless all caches monitor
memory traffic

144. Dr. Hanif Durad 144
Basic Cache Coherency Methods
 Cache-memory coherence using two policies:
Hesham, Chapter 04, P-8/61

145. Software Solutions
 Compiler and operating system deal with problem
 Overhead transferred to compile time
 Design complexity transferred from hardware to
software
 Software tends to make conservative decisions
leading to inefficient cache utilization
 Analyze code to determine safe periods for
caching shared variables WSCOA7e, P-650

146. Hardware Solution
 Cache coherence protocols
 Dynamic recognition of potential problems
 Run time
 More efficient use of cache
 Transparent to programmer
 Snoopy protocols
 Directory protocols

147. Dr. Hanif Durad 147
Snoopy Protocols-
Cache Coherence in Multiprocessor
Systems
Cache coherence in multiprocessor systems: (a) Invalidate protocol;
When the value of a variable is changes, all its copies must
either be invalidated or updated.

148. Dr. Hanif Durad 148
Cache Coherence in
Multiprocessor Systems
Cache coherence in multiprocessor systems: (b) Update protocol for shared
variables.

149. Dr. Hanif Durad 149
Cache Coherence:
Update and Invalidate Protocols
• If a processor just reads a value once and does not need it
again, an update protocol may generate significant
overhead
• If two processors make interleaved test and updates to a
variable, an update protocol is better.
• Both protocols suffer from false sharing overheads (two
words that are not shared, however, they lie on the same
cache line).
• Most current machines use invalidate protocols

150. Dr. Hanif Durad 150
Cache Coherency
– The goal of cache coherence is to ensure that every cache sees
the same value for a referenced location, which means making
sure that any shared operand that is changed is updated
throughout the system.
– This brings us to the issue of false sharing, which reduces
cache performance when two operands that are not shared
between processes share the same cache line. The situation is
shown below. The problem is that each process will invalidate
the other’s cache line when writing data without a real need,
unless the compiler prevents this.
Murdocca,CAO, Chapter 07, P-38/53

151. Dr. Hanif Durad 151
Cache Coherency
Murdocca, CAO, Chapter 07, P-38/53

152. Dr. Hanif Durad 152
2.4.6.1 Maintaining Coherence
Using Invalidate Protocols
• Each copy of a data item is associated with a state.
• One example of such a set of states is shared, invalid, or dirty.
• In shared state, the line in the shared by many processors
• In dirty/modified state, only one copy exists and therefore, no
invalidates need to be generated.
• In invalid state, the data copy is invalid, therefore, a read
generates a data request (and associated state changes).

153. Cache line has 4 states
 Each line of a cache has associated with it two bits –
four states
 Modified – line in this cache is modified and only
valid in this cache
 Exclusive – line in this cache is same as that in
memory (unmodified) and not present in any other
cache
 Shared – line in this cache is same as that in memory
(unmodified) and may also be present in another cache
 Invalid – line in this cache contains bad data
MESI-Protocol
Used in Intel
MSI-Protocol MOESI-Protocol
Used in AMDHB PC & Stat. , P-51

154. Dr. Hanif Durad 154
Maintaining Coherence
Using Invalidate Protocols
State diagram of a simple three-state coherence protocol.
MSI-Protocol

155. Dr. Hanif Durad 155
Maintaining Coherence Using
Invalidate Protocols
Example of
parallel
program
execution
with the
simple
three-state
coherence
protocol.
D=Modified /Dirty
S=Shared
I=Invalid

156. Write Invalidate (a.k.a. MESI)
 Multiple readers, one writer
 When a write is required, command is issued and
all other caches of the line are invalidated
 Writing processor then has exclusive (cheap)
access until line required by another processor
 A state is associated with every line
 Modified
 Exclusive
 Shared
 Invalid

157. Write Update (a.k.a. write
broadcast)
 Multiple readers and writers
 Updated word is distributed to all other
processors

158. Snoopy Protocols –
Implementations
 Performance of these two implementations
depends on number of caches and pattern of
read/writes
 Some systems use adaptive protocols to use
both methods
 Write invalidate most common – Used in
Pentium 4 and PowerPC systems

159. MESI Protocol
 Each line of a cache has associated with it two bits –
four states
 Modified – line in this cache is modified and only valid
in this cache
 Exclusive – line in this cache is same as that in memory
(unmodified) and not present in any other cache
 Shared – line in this cache is same as that in memory
(unmodified) and may also be present in another cache
 Invalid – line in this cache contains bad data
 Write throughs from an L1 cache to an L2 cache makes
it visible to the MESI protocol

160. MESI Protocol (continued)

161. MESI – State Transition Diagram

162. Dr. Hanif Durad 162
Snoopy Cache Systems
•How are invalidates sent to the right processors?
•In snoopy caches, there is a broadcast media that listens to all
invalidates and read requests and performs appropriate coherence
operations locally.
A simple snoopy bus based cache coherence system.

163. Performance of Snoopy Caches
 Once copies of data are tagged dirty, all subsequent
operations can be performed locally on the cache
without generating external traffic.
 If a data item is read by a number of processors, it
transitions to the shared state in the cache and all
subsequent read operations become local.
 If processors read and update data at the same time, they
generate coherence requests on the bus - which is
ultimately bandwidth limited.
Dr. Hanif Durad 163

164. 2.4.6.2 Directory Based Systems
 In snoopy caches, each coherence operation is
sent to all processors. This is an inherent
limitation.
 Why not send coherence requests to only those
processors that need to be notified?
 This is done using a directory, which maintains a
presence vector for each data item (cache line)
along with its global state
Dr. Hanif Durad 164

165. Directory Protocols – Central
control
 Central memory controller maintains
directory of:
 where blocks are held
 in which caches they are held
 what state the data is in
 Appropriate transfers are performed by
controller

166. Directory Protocols – Write
Process
 Requests to write to a line are made to controller
 Using directory, controller tells all other processors
with copy of same data to invalidate
 Write is granted to requesting processor and that
processor has exclusive rights to that data
 Request to read from another processor forces
controller to issue command to processor with
exclusive rights to update (write back) main
memory.

167. Directory Protocols (continued)
 Problems
 Creates central bottleneck
 Communication overhead
 Effective in large scale systems with
complex interconnection schemes

168. Dr. Hanif Durad 168
Directory Based Systems
Architecture of typical directory based systems: (a) a centralized
directory; and (b) a distributed directory.

169. Performance of
Directory Based Schemes
 The need for a broadcast media is replaced by the
directory.
 The additional bits to store the directory may add
significant overhead.
 The underlying network must be able to carry all
the coherence requests.
 The directory is a point of contention, therefore,
distributed directory schemes must be used.
Dr. Hanif Durad 169

170. 2.5 Communication Costs
in Parallel Machines (1/2)
 Major overheads in the execution of parallel
programs: from communication of information
between processing elements.
 The cost of communication is dependent on a
variety of features including:
 programming model semantics,
 network topology,
 data handling and routing, and
 associated software protocols. 170

171. Communication Costs
in Parallel Machines (2/2)
 Time taken to communicate a message between
two nodes in a network = time to prepare a
message for transmission + time taken by the
message to traverse the network to its destination.
Dr. Hanif Durad 171

172. 2.5.1 Message Passing Costs in
Parallel Computers (1/3)
 Startup time (ts): The startup time is the time required to
handle a message at the sending and receiving nodes.
 Includes
 the time to prepare the message (adding header, trailer & error
correction information),
 the time to execute the routing algorithm, and
 the time to establish an interface between the local node and the
router.
 This delay is incurred only once for a single message
transfer. Dr. Hanif Durad 172

173. Message Passing Costs in
Parallel Computers (2/3)
 Per-hop time (th):
 After a message leaves a node, it takes a finite amount
of time to reach the next node in its path.
 The time taken by the header of a message to travel
between two directly connected nodes in the network
 It is also known as node latency
 Is directly related to the latency within the routing
switch for determining which output buffer or channel
the message should be forwarded to.
Dr. Hanif Durad 173

174. 2.5.1 Message Passing Costs in
Parallel Computers (3/3)
 Per-word transfer time (tw):
 If the channel bandwidth is r words per second, then
each word takes time tw= 1/r to traverse the link.
 This time includes network as well as buffering
overheads..
Dr. Hanif Durad 174

175. Terminalogy
 transmission time

time taken to emit all bits into medium
 propagation time

time for a bit to traverse the link
Dr. Hanif Durad 175
Latency=
propagation time+ transmission time+ queing time+ processing delay
FOROUZAN DCN , P-90

176. Overheads of message passing
Dr. Hanif Durad 176

177. 2.5.1.1 Store-and-Forward
Routing
 When a message is traversing a path with multiple links,
each intermediate node on the path forwards the message
to the next node after it has received and stored the entire
message.
 Suppose that a message of size m is being transmitted
through such a network. Assume that it traverses l links.
 At each link, the message incurs a cost th for the header
and twmfor the rest of the message to traverse the link.
Dr. Hanif Durad 177

178. Store-and-Forward Routing
 Since there are l such links, the total time is (th +
twm)l.
 Therefore, for store-and-forward routing, the total
communication cost for a message of size m
words to traverse l communication links is
Dr. Hanif Durad 178

179. Store-and-Forward Routing
 In current parallel computers, the per-hop time th is quite
small.
 For most parallel algorithms, it is less than twm even for
small values of m and thus can be ignored.
 For parallel platforms using store-and-forward routing,
the time given by the above equation can be simplified to
Dr. Hanif Durad 179

180. Dr. Hanif Durad 180
Store-and-Forward Routing
The environment of the network layer protocols.
Tanenbaum, Chapter 05, Fig 5-1

181. Dr. Hanif Durad 181
Store-and-Forward Routing
Passing a message from node P0 to P3 (a) through a store-and-
forward communication network;

182. 2.5.1.2 Packet Routing (1/8)
 Store-and-forward: message is sent from one
node to the next only after the entire message
has been received
 Consider the scenario in which the original
message is broken into two equal sized parts
before it is sent.
 An intermediate node waits for only half of the
original message to arrive before passing it on.
Dr. Hanif Durad 182

183. Packet Routing (2/8)
 A step further: breaks the message into four
parts.
 In addition to better utilization of
communication resources, this principle offers
other advantages:
 lower overhead from packet loss (errors),
 possibility of packets taking different paths, and
 better error correction capability.
Dr. Hanif Durad 183

184. Packet Routing (3/8)
 This technique is the basis for long-haul
communication networks such as the Internet,
where error rates, number of hops, and variation
in network state can be higher.
 The overhead here is that each packet must carry
routing, error correction, and sequencing
information.
Dr. Hanif Durad 184

185. Dr. Hanif Durad 185
Packet Routing (4/8)
Passing a message from node P0 to P3 (b) and (c) extending the concept to
cut-through routing. The shaded regions represent the time that the message
is in transit. The startup time associated with this message transfer is
assumed to be zero.

186. Dr. Hanif Durad 186
Packet Routing (5/8)
Passing a message from node P0 to P3 (b) and (c) extending the concept to
cut-through routing. The shaded regions represent the time that the message
is in transit. The startup time associated with this message transfer is
assumed to be zero.

187. Packet Routing (6/8)
 Consider the transfer of an m word message through the
network.
 Assume:
 routing tables are static over the time of message transfer - all
packets traverse the same path
 The time taken for programming the network interfaces &
computing the routing info, is independent of the message
length and is aggregated into the startup time ts
 Size of a packet: r + s, r = original message, s = additional
information carried in the packet
187

188. Packet Routing (7/8)
 Time for packetizing the message is proportional to
the length of the message: mtw1.
 The network is capable of communicating one word
every tw2 seconds,
 Incurs a delay of th on each hop, and
 The first packet traverses l hops,
 Then the packet takes time thl + tw2(r + s) to reach
the destination.
Dr. Hanif Durad 188

189. Packet Routing (8/8)
 Since there are m/r - 1 additional packets, the total
communication time is given by:
 Packet routing suited to networks with highly dynamic
states & higher error rates,
 such as local- and wide-area networks.
 Individual packets may take different routes &retransmissions
can be localized to lost packets.

190. General Observation (1/2)
 In interconnection networks for parallel computers,
additional restrictions can be imposed on message
transfers to further reduce the overheads associated
with packet switching
 By forcing all packets to take the same path, we can
eliminate the overhead of transmitting routing
information with each packet.
 By forcing in-sequence delivery, sequencing
information can be eliminated.
Dr. Hanif Durad 190

191. General Observation (2/2)
 By associating error information at message level
rather than packet level, the overhead associated
with error detection and correction can be reduced.
 Finally, since error rates in interconnection
networks for parallel machines are extremely low,
lean error detection mechanisms can be used instead
of expensive error correction schemes.
 Routing scheme resulting from these optimizations:
cut-through routing.

192. Dr. Hanif Durad 192
2.5.1.3 Cut-Through Routing
(1/2)
 A message is broken into fixed size units called
flow control digits or flits.
 Flits do not contain the overheads of packets, they
can be much smaller than packets.
 A tracer is first sent from the source to the
destination node to establish a connection.
 Once a connection has been established, all flits
follow the same path in a dovetailed fashion.

193. Dr. Hanif Durad 193
Cut-Through Routing (2/2)
 An intermediate node does not wait for the entire
message to arrive before forwarding it
 As soon as a flit is received at an intermediate node,
the flit is passed on to the next node.
 No necessary a buffer at each intermediate node to
store the entire message.
 cut-through routing uses less memory at intermediate
nodes, and is faster.

194. Cost of cut-through routing (1/3)
 Assume:
 the message traverses l links, and
 th is the per-hop time ⇒ the header of the message
takes time lth to reach the destination.
 the message is m words long => the entire message
arrives in time twm after the arrival of the header of the
message.
 The total communication time for cut-through
routing is

195. Cost of cut-through routing (2/3)
 If the communication is between nearest neighbors (that
is, l = 1), or if the message size is small, then the
communication time is similar for store-and- forward
 Most current parallel computers & many LANs support
cut-through routing.
 The size of a flit is determined by a variety of network
parameters.
 The control circuitry must operate at the flit rate.
 Select a very small flit size, for a given link bandwidth, the
required flit rate becomes large.
Dr. Hanif Durad 195

196. Cost of cut-through routing (3/3)
 As flit sizes become large, internal buffer sizes increase (and
the latency of message transfer)
 Flit sizes in recent cut-through interconnection networks range
from four bits to 32 bytes.
 In many parallel programming paradigms that rely
predominantly on short messages (such as cache lines),
the latency of messages is critical.
 Routers are using multilane cut-through routing.
 In multilane cut-through routing, a single physical channel is
split into a no. of virtual channel
Dr. Hanif Durad 196

197. Deadlocks in cut-through routing
(1/3)
 While traversing the network, if a message needs to use a
link that is currently in use, then the message is blocked.
 This may lead to deadlock.
 Fig. illustrates a deadlock in a cut through routing
network
 The destinations of messages 0, 1, 2, and 3 are A, B, C, and D,
respectively.
 A flit from message 0 occupies the link CB (and the associated
buffers).
Dr. Hanif Durad 197

198. Dr. Hanif Durad 198
Deadlocks in cut-through routing
An example of deadlock in a cut-through routing network
(2/3)

199. Deadlocks in cut-through routing
(3/3)
 Since link BA is occupied by a flit from message 3, the flit
from message 0 is blocked.
 Similarly, the flit from message 3 is blocked since link AD is
in use.
 No messages can progress in the network and the network is
deadlocked.
 Can be avoided by using appropriate routing
techniques & message buffers.
199

200. Reducing the Cost (1/4)
 The equation of cost of communicating a message
between two nodes l hops away using cut-through
routing implies that in order to optimize the cost of
message transfers:
1. Communicate in bulk:
 instead of sending small messages and paying a startup cost ts for
each, aggregate small messages into a single large message and
amortize the startup latency across a larger message.
 Because on typical platforms such as clusters and message-
passing machines, the value of tsis much larger than those of th or
tw.

201. Reducing the Cost (2/4)
2. Minimize the volume of data.
 To minimize the overhead paid in terms of per-word transfer time
tw, it is desirable to reduce the volume of data communicated as
much as possible.
3. Minimize distance of data transfer.
 Minimize the number of hops l that a message must traverse.
 First two objectives s are relatively easy to achieve,
third is difficult (unnecessary burden algorithm
designer)
Dr. Hanif Durad 201

202. Reducing the Cost (3/4)
 In mess-pass lib. (e.g. MPI), the programmer has little
control on the mapping of processes onto physical
processors.
 In such paradigms, while tasks might have well defined
topologies and may communicate only among neighbors in the
task topology, the mapping of processes to nodes might destroy
this structure
 Many architectures rely on randomized (two-step)
routing,
 A message is first sent to a random node from source and from
this intermediate node to the destination.

203. Reducing the Cost (4/4)
 This alleviates hot-spots & contention on the network.
 Minimizing number of hops in a randomized routing network
yields no benefits.
 The per-hop time (th) is typically dominated either by the
startup latency (ts)for small messages or by perword
component (twm) for large messages.
 Since the max no. hops (l) in most networks is relatively
small, the per-hop time can be ignored
Dr. Hanif Durad 203

204. 2.5.1.4 Simplified Cost Model
(1/3)
 Cost of transferring a message between two nodes on a
network is given by:
 It takes the same amount of time to communicate between
any pair of nodes ⇒ it corresponds to a completely
connected network.
 Instead of designing algs for each specific arch (a mesh,
hypercube, or tree), we design algs with this cost model in
mind & port it to any target parallel comp.
Dr. Hanif Durad 204

205. Simplified Cost Model (2/3)
 Loss of accuracy (or fidelity) of prediction when
the alg is ported from our simplified model (for a
completely connected network) to an actual
machine arch.
 If our initial assumption that the th term is typically
dominated by the ts or tw terms is valid, then the loss in
accuracy should be minimal.
Dr. Hanif Durad 205

206. Simplified Cost Model (3/3)
 Valid only for uncongested networks.
 Architectures have varying thresholds for when they
get congested;
 a linear array has a much lower threshold for
congestion than a hypercube.
 Valid only as long as the communication pattern
does not congest the network.
 Different communication patterns congest a given
network to different extents.
206

207. Example 2.15 Effect of congestion
on communication cost (1/5)
 Consider a mesh in which each node is only
communicating with its nearest neighbor.
 Since no links in the network are used for more than
one communication, the time for this operation is ts +
twm, where m is the number of words communicated.
 This time is consistent with our simplified model.
Dr. Hanif Durad 207
p p×

208. Effect of congestion on
communication cost (2/5)
 Consider an alternate scenario in which each node
is communicating with a randomly selected node.
 This randomness implies that there are p/2
communications (or p/4 bi-directional
communications) occurring across any equi-
partition of the machine (since the node being
communicated with could be in either half with
equal probability).
Dr. Hanif Durad 208

209. Effect of congestion on
communication cost (3/5)
 From our discussion of bisection width, we know
that a 2-D mesh has a bisection width of .
 From these two, we can infer that some links
would now have to carry at least
messages, assuming bi-directional communication
channels.
 These messages must be serialized over the link.
 If each message is of size m, the time for this
operation is at least
p
/4
/ 4
p
p
p=
)( s wt t m p+ × / 4

210. Effect of congestion on
communication cost (4/5)
 This time is not in conformity with our simplified
model
 For a given architecture some communication patterns
can be non-congesting & others congesting
 This makes the task of modeling communication costs
dependent not just on the architecture, but also on the
communication pattern.
 To address this, we introduce the notion of effective
bandwidth.

211. Effective Bandwidth
 also known as throughput
 is the fraction of aggregate bandwidth delivered
by the network to an application
Dr. Hanif Durad 211

212. Effect of congestion on
communication cost (5/5)
 For communication patterns that do not congest the
network, is identical to the link bandwidth
 For communication operations that congest the network,
is the link bandwidth scaled down by the degree of
congestion on the most congested link.
 Difficult to estimate: it is a function of process to node mapping,
routing algorithms, & communication schedule.
 Therefore, we use a lower bound on the message
communication time: The associated link bandwidth is scaled
down by a factor p/b, b is the bisection width of the network.

213. 2.5.2 Cost Models for Shared
Address Space Machines (1/3)
 Difficulty reasons:
 Memory layout is typically determined by the system.
 Finite cache sizes can result in cache thrashing
 Overheads associated with invalidate and update operations
are difficult to quantify
 Spatial locality is difficult to model
 Prefetching can play a role in reducing the overhead
associated with data access.
 False sharing and contention are difficult to model.
 Contention in shared accesses is often a major contributing
overhead in shared address space machines.

214. Cost Models for Shared Address
Space Machines (2/3)
 Building these into a single cost model results in a
model that is
 too cumbersome to design programs for and
 too specific to individual machines to be generally
applicable.
 A simplified model presented above accounts
primarily for remote data access but does not
model a variety of other overheads (see the
textbook) 214

215. Cost Models for Shared Address
Space Machines (3/3)
 Accurate cost model for shared memory communication is difficult
 Same equation
 can applied keeping in mind
 difference that the value of the constant ts relative to tw is likely to be much
smaller on a shared-memory machine than on a distributed memory machine
(tw is likely to be near zero for a UMA machine).

216. 2.6 Routing Mechanisms for
Interconnection Networks (1/4)
 Critical to the performance of parallel computers
 A routing mechanism
 Determine the path a message takes through the network to get
from source to destination
 It takes as input a message's source and destination nodes
 It may also use information about the state of the network
 It returns one or more paths through the network from the source
to the destination

217. Routing Mechanisms for
Interconnection Networks (2/4)
 Classification based on route selection:
 A minimal routing mechanism

always selects one of the shortest paths between the source
and the destination.

each link brings a message closer to its destination,

can lead to congestion in parts of the network.
 A non-minimal routing scheme

may route the message along a longer path to avoid network
congestion.

218. Routing Mechanisms for
Interconnection Networks (3/4)
 Classification on the basis on information regarding the
state of the network
 A deterministic routing scheme

determines a unique path for a message, based on its source
and destination.

It does not use any information regarding the state of the
network.

may result in uneven use of the communication resources in a
network.

219. Routing Mechanisms for
Interconnection Networks (4/4)
 An adaptive routing scheme
 uses information regarding the current state of the netw to
determine the path of the mes
 detects congestion in the network and routes messages around it

220. Dimension-Ordered Routing
(DOR)
 Commonly used deterministic minimal routing
technique
 Assigns successive channels for traversal by a message
based on a numbering scheme determined by the
dimension of the channel.
 For a two-dimensional mesh is called XY-routing
 For a hypercube is called E-cube routing
Dr. Hanif Durad 220

221. DOR XY-Routing (1/2)
 Consider a two-dimensional mesh without wraparound
connections.
 A message is sent first along the X dimension until it
reaches the column of the destination node and then
along the Y dimension until it reaches its destination.
 Let PSy,Sx represent the position of the source node and PDy,Dx
represent that of the destination node.
 Any minimal routing scheme should return a path of
length |Sx - Dx| + |Sy - Dy|.
Dr. Hanif Durad 221

222. DOR XY-Routing (2/2)
 Assume that Dx Sx and Dy Sy.
 The message is passed through intermediate nodes PSy,Sx+1,
PSy,Sx+2, ..., PSy,Dx along the X dimension and
 Then through nodes PSy+1,Dx, PSy+2,Dx, ..., PDy,Dx along the Y
dimension to reach the destination
 Note that the length of this path is indeed
 Sx - Dx| + |Sy - Dy|.
Dr. Hanif Durad 222
≥ ≥

223. E-cube Routing (1/4)
 Consider a d-dimensional hypercube of p nodes.
 Let Ps and Pd be the labels of the source and destination
nodes
 We know that the binary representations of these labels
are d bits long.
 The minimum distance between these nodes is given by
the number of ones in Ps Pd , where represents the
bitwise exclusive-OR operation.
Dr. Hanif Durad 223
⊗ ⊗

224. E-cube Routing (2/4)
 Node Ps computes Ps Pd and sends the message along
dimension k, where k is the position of the least
significant nonzero bit in Ps Pd .
 At each intermediate step, node Pi , which receives the
message, computes Pi Pd and forwards the message
along the dimension corresponding to the least
significant nonzero bit.
 This process continues until the message reaches its
destination.
Dr. Hanif Durad 224
⊗
⊗
⊗

225. E-cube routing- Example (3/4)
 Let Ps = 010 and Pd = 111 represent the source and
destination nodes for a message.
 Node Ps computes 010 111 = 101.
 In the first step, Psforwards the message along the
dimension corresponding to the least significant bit to
node 011.
 Node 011 sends the message along the dimension
corresponding to the most significant bit (011 111 = 100)
 The message reaches node 111, which is the destination of
the message.
⊗
⊗

226. Dr. Hanif Durad 226
E-cube routing- Example (4/4)
Routing a message from node Ps (010) to node Pd (111) in a three-
dimensional hypercube using E-cube routing.

227. 2.7 Impact of Process-Processor
Mapping (1/4)
 programmer often does not have control over
how logical processes are mapped to physical
nodes in a network
 For this reason, even communication patterns
that are not inherently congesting may congest
the network.
 We illustrate this with the following example:
Dr. Hanif Durad 227

228. Impact of Process-Processor Mapping
(2/4)
 Problem:
 A programmer often does not have control over
how logical processes are mapped to physical
nodes in a network.
 even communication patterns that are not inherently
congesting may congest the network
Dr. Hanif Durad 228

229. Impact of Process-Processor Mapping
(3/4)
Dr. Hanif Durad 229
Processes and their
interactions
Processors
G (E,V)G′(E′,V′)

230. Impact of process mapping (4/4)
An intuitive mapping of
processes to nodes
 a single link in the underlying
architecture only carries data
corresponding to a single
communication channel
between processes.
a random mapping of processes
to nodes
 each link in the machine carries
up to six channels of data between
processes.
considerably larger communication
times if the required data rates on
communication channels between
processes is high
Congestion=1
Congestion=6 ?
Map a=1, b=6

231. Dr. Hanif Durad 231
2.7.1 Mapping Techniques for
Graphs
 Often, we need to embed a known communication
pattern into a given interconnection topology.
 We may have an algorithm designed for one network,
which we are porting to another topology.
For these reasons, it is useful to understand mapping
between graphs.

232. Mapping Techniques for Graphs
 Given two graphs, G(V, E), G'(V', E'), mapping graph G
into graph G' maps
 each vertex in the set V onto a vertex (or a set of
vertices) in set V' and
 each edge in the set E onto an edge (or a set of edges) in
E'.
 Three parameters are important:
 Congestion of the mapping:
 Dilation of the mapping:
 Expansion of the mapping:

233. 2.7.1 Mapping Techniques for
Graphs
 Congestion of the mapping:
 The maximum number of edges in E mapped onto any edge in E'
 it is possible that more than one edge in E is mapped onto a
single edge in E'.
 Dilatation of the mapping:
 The maximum number of edges in E' that any edge in E is
mapped onto

An edge in E may be mapped onto multiple contiguous edges in E'.

This is significant because traffic on the corresponding communication
link must traverse more than one link, possibly contributing to congestion
on the network.
233

234. Mapping Techniques for Graphs
 Expansion of the mapping:
 It is the ratio of the number of nodes in the set V' to
that in set V
 The sets V and V' may contain different numbers of
vertices. In this case, a node in V corresponds to more
than one node in V'.
 In the context of process-processor mapping, the
expansion of the mapping must be identical to the ratio
of virtual & physical processors.
Dr. Hanif Durad 234

235. Embedding a logical topology
into a physical topology
Example: embedding a 7 node binary tree into 3x3 mesh
Embedding = node mapping + edge mapping
Behrooz,P-263
G (E,V) G′(E′,V′)

236. Embedding a logical topology
into a physical topology
Example: embedding a 7 node binary tree into 2x4 mesh
Embedding = node mapping + edge mapping
Behrooz,P-263
G (E,V)
G′(E′,V′)

237. Embedding a logical topology
into a physical topology
Example: embedding a 7 node binary tree into 2x2 mesh
Embedding = node mapping + edge mapping
Behrooz,P-263
G (E,V)
G′(E′,V′)
Dilation =?

238. Properties of embeddings
2D-mesh Sizes 3x3 2x4 2x2
Congestion: maximum number of logical edges
(joining processes) mapped onto one physical
edge (joining processors) (sort of edge ratio)
1 2 2
Dilation: length of the longest path to which a
logical edge (joining processes) is mapped
1 2 1
Load Factor: maximum number of logical
nodes (processes) mapped onto one physical
node (processor) (sort node ratio)
1 1 2
Expansion: ratio of the number of nodes in the
two topologies (over all node ratio)
9/7 8/7 4/7
?

239. 2.7.1.1 Embedding a Linear Array
into a Hypercube (1/5)
Dr. Hanif Durad 239
Meshcube.pdf, P-1

240. Dr. Hanif Durad 240
Embedding a Linear Array
into a Hypercube (2/5)
 A linear array (or a ring) composed of 2d
nodes (0 :2d
− 1)
can be embedded into a d-dimensional hypercube by
mapping node i of the linear array onto node G(i, d) of the
hypercube
 The function G(i, x) is defined as follows:
0

241. Dr. Hanif Durad 241
Embedding a Linear Array
into a Hypercube (3/5)
 G : the binary reflected Gray code (RGC).
 The entry G(i, d) denotes the ith entry in the sequence of
Gray codes of d bits.
 Gray codes of d + 1 bits are derived from Gray codes of
d bits by reflecting the table & prefixing the reflected
entries with a 1 & the original entries with a 0.
 Adjoining entries (G(i, d) and G(i + 1, d)) differ from
each other at only one bit position.

242. Dr. Hanif Durad 242
Embedding a Linear Array
into a Hypercube (4/5)
 Node i in the linear array is mapped to node G(i, d), and
node i + 1 is mapped to G(i + 1, d) ⇒ is a direct link in
the hypercube that corresponds to each direct link in the
linear array.
 Mapping specified by the function G has a dilation of
one and a congestion of one.

243. Dr. Hanif Durad 243
Embedding a Linear Array into a Hypercube: Example
(a) A three-bit reflected Gray code ring; and (b) its embedding into a three-
dimensional hypercube.
Dilation 1
Congestion 1
(5/5)

244. Dr. Hanif Durad 244
2.7.1.2 Embedding a Mesh
into a Hypercube (1/4)
 A 2r
× 2s
wraparound mesh can be mapped to a
2r+s
-node hypercube by mapping node (i, j) of
the mesh onto node G(i, r) || G(j, s) of the
hypercube (where || denotes concatenation of
the two Gray codes).
Note :Mistake in book

245. Dr. Hanif Durad 245
Embedding a Mesh into a Hypercube
(a) A 4 × 4 mesh illustrating the mapping of mesh nodes to the nodes
in a four-dimensional hypercube;
(2/4)

246. Embedding a Mesh into a Hypercube
(a) A 4 × 4 mesh illustrating the mapping of mesh nodes to the nodes
in a four-dimensional hypercube;
A 4-Dimensional hypercube
4 × 4 mesh
A better presentation
workout mapping yourself (?)
Dilation 1
Congestion 1
communication.pdf, P-7
(3/4)

247. Dr. Hanif Durad 247
Embedding a Mesh into a Hypercube
(b) a 2 × 4 mesh embedded into a three-dimensional hypercube.
Once again, the congestion, dilation, and expansion of the mapping is 1
(4/4)

248. Dr. Hanif Durad 248
2.7.1.3 Embedding a Mesh into a
Linear Array (1/5)
 An intuitive mapping of a linear array into a
mesh is illustrated in Figure (a):
 the solid lines correspond to links in the linear array
and
 normal lines to links in the mesh.
 congestion-one, dilation-one mapping of a linear
array to a mesh is possible

249. Dr. Hanif Durad 249
Embedding a Mesh into a Linear Array:
Example
(a) Embedding a 16 node linear array into a 2-D mesh; Solid lines correspond
to links in the linear array and normal lines to links in the mesh.
Dilation 1
Congestion 1
(2/5)

250. Dr. Hanif Durad 250
Embedding a Mesh into a Linear
Array (3/5)
 Consider now the inverse of this mapping,
 given a mesh, map vertices of the mesh to those in a linear
array using the inverse of the same mapping function-Fig. (b)
 solid lines correspond to edges in the linear array and normal
lines to edges in the mesh.
 the congestion of the mapping in this case is five – i.e., no
solid line carries more than five normal
 In general: the congestion of this (inverse) mapping is +1
for a general p-node mapping (one for each of the edges to
the next row, and one additional edge).

251. Dr. Hanif Durad 251
Embedding a Mesh into a Linear Array:
Example
(b) the inverse of the mapping. Solid lines correspond to links in the linear array
and normal lines to links in the mesh.
(4/5)

252. Embedding a Mesh into a Linear
Array (5/5)
 We can do better?
 Congestion of any mapping is lower bounded by

see textbook – why
 In general:
 the lower bound on congestion of a mapping of network
S with x links into network Q with y links is x/y.
 In the case of the mapping from a mesh to a linear array,
this would be 2p/p, or 2.

see textbook – why not?

253. Dr. Hanif Durad 253
2.7.1.4 Embedding a Hypercube
into a 2-D Mesh (1/3)
 p-node hypercube into a p-node 2-D mesh, p is an even power of
two
 visualize the hypercube as subcubes, each with nodes.
 let d = log p be the dim of the hypercube .
 take the d/2 least significant bits and use them to define individual
subcubes of nodes.
 For example, in the case of a 4D hypercube, we use the lower two
bits to define the subcubes as (0000, 0001, 0011, 0010), (0100,
0101, 0111, 0110), (1100, 1101, 1111, 1110), and (1000, 1001,
1011, 1010).

254. Dr. Hanif Durad 254
Embedding a Hypercube into a 2-
D Mesh (2/3)
 The (row) mapping from a hypercube to a mesh can now be
defined as follows:
 Each node subcube is mapped to a node row of the mesh.
 We do this by simply inverting the linear-array to hypercube mapping.
 The congestion: /2
 Fig: p = 16 and p = 32
 Column mapping:
 We map the hypercube nodes into the mesh in such a way that nodes with
identical d/2 least significant bits in the hypercube are mapped to the same
column.
 The congestion: /2

255. Dr. Hanif Durad 255
Embedding a Hypercube into a 2-D Mesh:
Example
Embedding a hypercube into a 2-D mesh.
Congestion /2
(3/3)

256. 2.7.2 Cost-Performance
Tradeoffs (1/3)
 Remark: it is possible to map denser networks into sparser
networks with associated congestion overheads.
 a sparser network whose link bandwidth is increased to
compensate for the congestion can perform as well as the denser
network (modulo dilation effects).
 Example: a mesh whose links are faster by a factor of /2 will
yield comparable performance to a hypercube ⇒ call it fat-mesh

A fat-mesh has the same bisection-bandwidth as a hypercube;

However it has a higher diameter.

Using appropriate message routing techniques, the effect of node distance
can be minimized.

257. Cost-Performance Tradeoffs
(2/3)
 Analyzing the performance of a mesh & a
hypercube network with identical costs:
 Cost of a network is proportional to the number of
wires,

A -node wraparound mesh with (log p)/4 wires per
channel costs as much as a p-node hypercube with one wire
per channel
 Average communication times of these two networks.

See textbook

258. Cost-Performance Tradeoffs
(3/3)
 For p > 16 and sufficiently large message sizes, a mesh
outperforms a hypercube of the same cost.
 For large enough messages, a mesh is always better than a
hypercube of the same cost, provided the network is lightly
loaded.
 Even when the network is heavily loaded, the performance of a
mesh is similar to that of a hypercube of the same cost.

259. Dr. Hanif Durad 259
Case Studies: The IBM Blue-Gene Architecture
The hierarchical architecture of Blue Gene.

260. Dr. Hanif Durad 260
Case Studies:The Cray T3E Architecture
Interconnection network of the Cray T3E: (a) node architecture;
(b) network topology

261. Dr. Hanif Durad 261
Case Studies: The SGI Origin 3000 Architecture
Architecture of the SGI Origin 3000 family of servers.

262. Dr. Hanif Durad 262
Case Studies: The Sun HPC Server
Architecture
Architecture of the Sun Enterprise family of servers.

263. Self Study
1. Chapter 4- Advanced computer architecture and
parallel processing by Hesham and Mostafa
(provided in soft form on data server folder)
2. Chapter 2 - Handbook of Parallel Computing
and Statistic (provided in soft form on data
server folder)
Dr. Hanif Durad 263