The effective bandwidth **b _{eff}** measures
the accumulated bandwidth
of the communication network of a parallel and/or distributed
computing system. Several message sizes, communication patterns and
methods are used. The algorithm uses an average to take
into account that in real applications short and long messages
result in different bandwidth values.

b =
_{eff} | logavg | ( | logavg_{cartesian pattern}
| (sum_{L} (max_{mthd} (max_{rep} ( b(cartes.pat.,L,mthd,rep)
| )))/21 ), |

logavg_{random pattern}
| (sum_{L} (max_{mthd} (max_{rep} ( b(random pat.,L,mthd,rep)
| )))/21 ) | |||

) |

with

- b(pat,L,mthd,rep) = L * (total number of messages of a pattern "pat") * looplength / (maximum time on each process for executing the communication pattern looplength times)
- Each measurement is repeated 3 times (rep=1..3).
The maximum bandwidth of all repetitions is used
(see max
_{mthd}in the formula above). - Each pattern is programmed with three methods.
The maximum bandwidth of all methods is used
(max
_{mthd}). - The measurement is done for different sizes of a message:
The message length L has the following 21 values:

L = 1B, 2B, 4B, ... 2kB, 4kB, 4kB*(a**1), 4kB*(a**2), ... 4kB*(a**8)

with and 4kB*(a**8) = L_max and L_max = (memory per processor) / 128

and looplength = min( 300, L_Max / L ).

The average of the bandwidth of all messages sizes is computed (sum_{L}(...)/21). - A set of cartesian and random pattern is used (see details section below).
- The average for all cartesian and the average of all random
pattern is computed on the logarithmic scale

(logavg_{cartesian pattern}and logavg_{random pattern}). - Finally the effective bandwidth is the logarithmic average
of these two values

(logavg(logavg_{cartesian pattern}, logavg_{random pattern}).

- Each node sends sends in each measurement messages to
one or more nodes.
Three cyclic cartesian topologies and the following communication
patterns are used:
- 1-dimensional x-direction
- 2-dimensional x-direction
- 2-dimensional y-direction
- 2-dimensional x-direction and y-direction
- 3-dimensional x-direction
- 3-dimensional y-direction
- 3-dimensional z-direction
- 3-dimensional x-direction and y-direction and z-direction

- For the random patterns the same ring-communication as in the 1-dimensional topology is used, but the processes get random ranks.
- The average is computed in two steps to guarantee that the cartesian and random patterns are weighted the same.

First approach from Karl Solchenbach, Hans-Joachim Plum and Gero Ritzenhoefer [1,2] was based on the bi-section bandwidth.

Due to several problems a redesign was done by the b_eff group. This redesign tries not to violate the rules defined by Rolf Hempel in [3] and by William Gropp and Ewing Lusk in [4].

Each run of the benchmark on a paricular system results in an output file. the last line of this output file reports e.g.

b_eff = *9709.549* MB/s = *37.928* * *256* PEs
with *128* MB/PE
on *sn6715 hwwt3e 2.0.4.71 unicosmk CRAY T3E*

This line reports

- the effective bandwidth
**b**of the whole system,_{eff} - the effective bandwidth of each processor (or node),
- the number of processors (or nodes),
- the memory of each processor (or node),
- the output of
`uname -a`.

- [1]
- Karl Solchenbach: Benchmarking the Balance of Parallel Computers. SPEC Workshop on Benchmarking Parallel and High-Performance Computing Systems (copy of the slides), Wuppertal, Germany, Sept. 13, 1999.
- [2]
- Karl Solchenbach, Hans-Joachim Plum and Gero Ritzenhoefer: Pallas Effective Bandwidth Benchmark - source code and sample results ( EFF_BW.tar.gz, 43 KB)
- [3]
- Rolf Hempel: Basic message passing benchmarks, methodology and pitfalls. SPEC Workshop on Benchmarking Parallel and High-Performance Computing Systems (copy of the slides), Wuppertal, Germany, Sept. 13, 1999.
- [4]
- William Gropp and Ewing Lusk: Reproducible Measurement of MPI Performance Characteristics. In J. Dongarra et al. (eds.), Recent Advances in Parallel Virtual Machine and Message Passing Interface, proceedings of the 6th European PVM/MPI Users' Group Meeting, EuroPVM/MPI'99, Barcelona, Spain, Sept. 26-29, 1999, LNCS 1697, pp 11-18.

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