Exercise 1.16 Another pitfall, relating to the execution of programs in multiprocessors systems, is expecting improvement in perfor mance by improving only the execution time of part of the routines. The following table shows the execution time of fi ve routines of a program running on different numbers of processors.

# Processors Routine A

(ms)

Routine B

(ms)

Routine C

(ms)

Routine D

(ms)

Routine E

(ms)

a. 2 20 80 10 70 5

b. 16 4 14 2 12 2 1.16.1 [10] <1.8> Find the total execution time and by how much it is reduced if the time of routines A, C, and E is improved by 15%.

1.16.2 [10] <1.8> By how much is the total time reduced if routine B is improved by 10%?

1.16.3 [10] <1.8> By how much is the total time reduced if routine D is improved by 10%?

Execution time in a multiprocessor system can be split into computing time for the routines plus routing time spent sending data from one processor to another.

Consider the execution time and routing time given in the following table. In this case, the routing time is an important component of the total time.

# Processors Routine A

(ms)

Routine B

(ms)
Routine C (ms)
Routine D (ms)
Routine E (ms)
Routing (ms)
2 20 78 9 65 4 11 4 12 44 4 34 2 13 8 1 23 3 19 3 17 16 4 13 1 10 2 22 32 2 5 1 5 1 23 64 1 3 0.5 1 1 26 1.16.4 [10] <1.8> For each doubling of the number of processors, determine the ratio of new to old computing time and the ratio of new to old routing time.
1.16.5 [5] <1.8> Using the geometric means of the ratios, extrapolate to fi nd the computing time and routing time in a 128-processor system.
1.16.6 [10] <1.8> Find the computing time and routing time for a system with one processor.